t81_558_class04_training.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# T81-558: Applications of Deep Neural Networks\n",
    "**Class 4: Training a Neural Network**\n",
    "* Instructor: [Jeff Heaton](https://sites.wustl.edu/jeffheaton/), School of Engineering and Applied Science, [Washington University in St. Louis](https://engineering.wustl.edu/Programs/Pages/default.aspx)\n",
    "* For more information visit the [class website](https://sites.wustl.edu/jeffheaton/t81-558/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module Video Material\n",
    "\n",
    "Main video lecture:\n",
    "\n",
    "* [Part 4.1: Early Stopping and Feature Vector Encoding](https://www.youtube.com/watch?v=ATuyK_HWZgc&index=12&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN)\n",
    "* [Part 4.2: Evaluating Classification and Regression Networks](https://www.youtube.com/watch?v=hXkZqGi5mB4&index=13&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN)\n",
    "* [Part 4.3: Cross-Validation for Neural Networks](https://www.youtube.com/watch?v=SIyMm5DFwQ8&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN)\n",
    "* [Part 4.4: Manual Error Calculation](https://www.youtube.com/watch?v=iMyGyZYE9Lc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Helpful Functions\n",
    "\n",
    "You will see these at the top of every module.  These are simply a set of reusable functions that we will make use of.  Each of them will be explained as the semester progresses.  They are explained in greater detail as the course progresses.  Class 4 contains a complete overview of these functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import base64\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import requests\n",
    "from sklearn import preprocessing\n",
    "\n",
    "\n",
    "# Encode text values to dummy variables(i.e. [1,0,0],[0,1,0],[0,0,1] for red,green,blue)\n",
    "def encode_text_dummy(df, name):\n",
    "    dummies = pd.get_dummies(df[name])\n",
    "    for x in dummies.columns:\n",
    "        dummy_name = f\"{name}-{x}\"\n",
    "        df[dummy_name] = dummies[x]\n",
    "    df.drop(name, axis=1, inplace=True)\n",
    "\n",
    "\n",
    "# Encode text values to a single dummy variable.  The new columns (which do not replace the old) will have a 1\n",
    "# at every location where the original column (name) matches each of the target_values.  One column is added for\n",
    "# each target value.\n",
    "def encode_text_single_dummy(df, name, target_values):\n",
    "    for tv in target_values:\n",
    "        l = list(df[name].astype(str))\n",
    "        l = [1 if str(x) == str(tv) else 0 for x in l]\n",
    "        name2 = f\"{name}-{tv}\"\n",
    "        df[name2] = l\n",
    "\n",
    "\n",
    "# Encode text values to indexes(i.e. [1],[2],[3] for red,green,blue).\n",
    "def encode_text_index(df, name):\n",
    "    le = preprocessing.LabelEncoder()\n",
    "    df[name] = le.fit_transform(df[name])\n",
    "    return le.classes_\n",
    "\n",
    "\n",
    "# Encode a numeric column as zscores\n",
    "def encode_numeric_zscore(df, name, mean=None, sd=None):\n",
    "    if mean is None:\n",
    "        mean = df[name].mean()\n",
    "\n",
    "    if sd is None:\n",
    "        sd = df[name].std()\n",
    "\n",
    "    df[name] = (df[name] - mean) / sd\n",
    "\n",
    "\n",
    "# Convert all missing values in the specified column to the median\n",
    "def missing_median(df, name):\n",
    "    med = df[name].median()\n",
    "    df[name] = df[name].fillna(med)\n",
    "\n",
    "\n",
    "# Convert all missing values in the specified column to the default\n",
    "def missing_default(df, name, default_value):\n",
    "    df[name] = df[name].fillna(default_value)\n",
    "\n",
    "\n",
    "# Convert a Pandas dataframe to the x,y inputs that TensorFlow needs\n",
    "def to_xy(df, target):\n",
    "    result = []\n",
    "    for x in df.columns:\n",
    "        if x != target:\n",
    "            result.append(x)\n",
    "    # find out the type of the target column.  Is it really this hard? :(\n",
    "    target_type = df[target].dtypes\n",
    "    target_type = target_type[0] if hasattr(\n",
    "        target_type, '__iter__') else target_type\n",
    "    # Encode to int for classification, float otherwise. TensorFlow likes 32 bits.\n",
    "    if target_type in (np.int64, np.int32):\n",
    "        # Classification\n",
    "        dummies = pd.get_dummies(df[target])\n",
    "        return df[result].values.astype(np.float32), dummies.values.astype(np.float32)\n",
    "    # Regression\n",
    "    return df[result].values.astype(np.float32), df[[target]].values.astype(np.float32)\n",
    "\n",
    "# Nicely formatted time string\n",
    "def hms_string(sec_elapsed):\n",
    "    h = int(sec_elapsed / (60 * 60))\n",
    "    m = int((sec_elapsed % (60 * 60)) / 60)\n",
    "    s = sec_elapsed % 60\n",
    "    return f\"{h}:{m:>02}:{s:>05.2f}\"\n",
    "\n",
    "\n",
    "# Regression chart.\n",
    "def chart_regression(pred, y, sort=True):\n",
    "    t = pd.DataFrame({'pred': pred, 'y': y.flatten()})\n",
    "    if sort:\n",
    "        t.sort_values(by=['y'], inplace=True)\n",
    "    plt.plot(t['y'].tolist(), label='expected')\n",
    "    plt.plot(t['pred'].tolist(), label='prediction')\n",
    "    plt.ylabel('output')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "# Remove all rows where the specified column is +/- sd standard deviations\n",
    "def remove_outliers(df, name, sd):\n",
    "    drop_rows = df.index[(np.abs(df[name] - df[name].mean())\n",
    "                          >= (sd * df[name].std()))]\n",
    "    df.drop(drop_rows, axis=0, inplace=True)\n",
    "\n",
    "\n",
    "# Encode a column to a range between normalized_low and normalized_high.\n",
    "def encode_numeric_range(df, name, normalized_low=-1, normalized_high=1,\n",
    "                         data_low=None, data_high=None):\n",
    "    if data_low is None:\n",
    "        data_low = min(df[name])\n",
    "        data_high = max(df[name])\n",
    "\n",
    "    df[name] = ((df[name] - data_low) / (data_high - data_low)) \\\n",
    "        * (normalized_high - normalized_low) + normalized_low\n",
    "\n",
    "\n",
    "# This function submits an assignment.  You can submit an assignment as much as you like, only the final\n",
    "# submission counts.  The paramaters are as follows:\n",
    "# data - Pandas dataframe output.\n",
    "# key - Your student key that was emailed to you.\n",
    "# no - The assignment class number, should be 1 through 1.\n",
    "# source_file - The full path to your Python or IPYNB file.  This must have \"_class1\" as part of its name.  \n",
    "# .             The number must match your assignment number.  For example \"_class2\" for class assignment #2.\n",
    "def submit(data,key,no,source_file=None):\n",
    "    if source_file is None and '__file__' not in globals(): raise Exception('Must specify a filename when a Jupyter notebook.')\n",
    "    if source_file is None: source_file = __file__\n",
    "    suffix = '_class{}'.format(no)\n",
    "    if suffix not in source_file: raise Exception('{} must be part of the filename.'.format(suffix))\n",
    "    with open(source_file, \"rb\") as image_file:\n",
    "        encoded_python = base64.b64encode(image_file.read()).decode('ascii')\n",
    "    ext = os.path.splitext(source_file)[-1].lower()\n",
    "    if ext not in ['.ipynb','.py']: raise Exception(\"Source file is {} must be .py or .ipynb\".format(ext))\n",
    "    r = requests.post(\"https://api.heatonresearch.com/assignment-submit\",\n",
    "        headers={'x-api-key':key}, json={'csv':base64.b64encode(data.to_csv(index=False).encode('ascii')).decode(\"ascii\"),\n",
    "        'assignment': no, 'ext':ext, 'py':encoded_python})\n",
    "    if r.status_code == 200:\n",
    "        print(\"Success: {}\".format(r.text))\n",
    "    else: print(\"Failure: {}\".format(r.text))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building the Feature Vector\n",
    "\n",
    "Neural networks require their input to be a fixed number of columns.  This is very similar to spreadsheet data.  This input must be completely numeric.  \n",
    "\n",
    "It is important to represent the data in a way that the neural network can train from it.  In class 6, we will see even more ways to preprocess data.  For now, we will look at several of the most basic ways to transform data for a neural network.\n",
    "\n",
    "Before we look at specific ways to preprocess data, it is important to consider four basic types of data, as defined by [Stanley Smith Stevens](https://en.wikipedia.org/wiki/Stanley_Smith_Stevens).  These are commonly referred to as the [levels of measure](https://en.wikipedia.org/wiki/Level_of_measurement):\n",
    "\n",
    "* Character Data (strings)\n",
    "    * **Nominal** - Individual discrete items, no order. For example: color, zip code, shape.\n",
    "    * **Ordinal** - Individual discrete items that can be ordered.  For example: grade level, job title, Starbucks(tm) coffee size (tall, vente, grande) \n",
    "* Numeric Data\n",
    "    * **Interval** - Numeric values, no defined start.  For example, temperature.  You would never say \"yesterday was twice as hot as today\".\n",
    "    * **Ratio** - Numeric values, clearly defined start.  For example, speed.  You would say that \"The first car is going twice as fast as the second.\"\n",
    "\n",
    "The following code contains several useful functions to encode the feature vector for various types of data.  Encoding data:\n",
    "\n",
    "* **encode_text_dummy** - Encode text fields, such as the iris species as a single field for each class.  Three classes would become \"0,0,1\" \"0,1,0\" and \"1,0,0\". Encode non-target predictors this way. Good for nominal.\n",
    "* **encode_text_index** - Encode text fields, such as the iris species as a single numeric field as \"0\" \"1\" and \"2\".  Encode the target field for a classification this way.  Good for nominal.\n",
    "* **encode_numeric_zscore** - Encode numeric values as a z-score.  Neural networks deal well with \"centered\" fields, zscore is usually a good starting point for interval/ratio.\n",
    "\n",
    "*Ordinal values can be encoded as dummy or index.  Later we will see a more advanced means of encoding*\n",
    "\n",
    "Dealing with missing data:\n",
    "\n",
    "* **missing_median** - Fill all missing values with the median value.\n",
    "\n",
    "Creating the final feature vector:\n",
    "\n",
    "* **to_xy** - Once all fields are numeric, this function can provide the x and y matrixes that are used to fit the neural network.\n",
    "\n",
    "Other utility functions:\n",
    "\n",
    "* **hms_string** - Print out an elapsed time string.\n",
    "* **chart_regression** - Display a chart to show how well a regression performs.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dealing with Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length before MPG outliers dropped: 398\n",
      "Length after MPG outliers dropped: 388\n",
      "      mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
      "0    18.0          8         307.0       130.0    3504          12.0    70   \n",
      "1    15.0          8         350.0       165.0    3693          11.5    70   \n",
      "2    18.0          8         318.0       150.0    3436          11.0    70   \n",
      "3    16.0          8         304.0       150.0    3433          12.0    70   \n",
      "4    17.0          8         302.0       140.0    3449          10.5    70   \n",
      "5    15.0          8         429.0       198.0    4341          10.0    70   \n",
      "6    14.0          8         454.0       220.0    4354           9.0    70   \n",
      "7    14.0          8         440.0       215.0    4312           8.5    70   \n",
      "8    14.0          8         455.0       225.0    4425          10.0    70   \n",
      "9    15.0          8         390.0       190.0    3850           8.5    70   \n",
      "10   15.0          8         383.0       170.0    3563          10.0    70   \n",
      "11   14.0          8         340.0       160.0    3609           8.0    70   \n",
      "12   15.0          8         400.0       150.0    3761           9.5    70   \n",
      "13   14.0          8         455.0       225.0    3086          10.0    70   \n",
      "14   24.0          4         113.0        95.0    2372          15.0    70   \n",
      "15   22.0          6         198.0        95.0    2833          15.5    70   \n",
      "16   18.0          6         199.0        97.0    2774          15.5    70   \n",
      "17   21.0          6         200.0        85.0    2587          16.0    70   \n",
      "18   27.0          4          97.0        88.0    2130          14.5    70   \n",
      "19   26.0          4          97.0        46.0    1835          20.5    70   \n",
      "20   25.0          4         110.0        87.0    2672          17.5    70   \n",
      "21   24.0          4         107.0        90.0    2430          14.5    70   \n",
      "22   25.0          4         104.0        95.0    2375          17.5    70   \n",
      "23   26.0          4         121.0       113.0    2234          12.5    70   \n",
      "24   21.0          6         199.0        90.0    2648          15.0    70   \n",
      "25   10.0          8         360.0       215.0    4615          14.0    70   \n",
      "26   10.0          8         307.0       200.0    4376          15.0    70   \n",
      "27   11.0          8         318.0       210.0    4382          13.5    70   \n",
      "28    9.0          8         304.0       193.0    4732          18.5    70   \n",
      "29   27.0          4          97.0        88.0    2130          14.5    71   \n",
      "..    ...        ...           ...         ...     ...           ...   ...   \n",
      "367  28.0          4         112.0        88.0    2605          19.6    82   \n",
      "368  27.0          4         112.0        88.0    2640          18.6    82   \n",
      "369  34.0          4         112.0        88.0    2395          18.0    82   \n",
      "370  31.0          4         112.0        85.0    2575          16.2    82   \n",
      "371  29.0          4         135.0        84.0    2525          16.0    82   \n",
      "372  27.0          4         151.0        90.0    2735          18.0    82   \n",
      "373  24.0          4         140.0        92.0    2865          16.4    82   \n",
      "374  23.0          4         151.0        93.5    3035          20.5    82   \n",
      "375  36.0          4         105.0        74.0    1980          15.3    82   \n",
      "376  37.0          4          91.0        68.0    2025          18.2    82   \n",
      "377  31.0          4          91.0        68.0    1970          17.6    82   \n",
      "378  38.0          4         105.0        63.0    2125          14.7    82   \n",
      "379  36.0          4          98.0        70.0    2125          17.3    82   \n",
      "380  36.0          4         120.0        88.0    2160          14.5    82   \n",
      "381  36.0          4         107.0        75.0    2205          14.5    82   \n",
      "382  34.0          4         108.0        70.0    2245          16.9    82   \n",
      "383  38.0          4          91.0        67.0    1965          15.0    82   \n",
      "384  32.0          4          91.0        67.0    1965          15.7    82   \n",
      "385  38.0          4          91.0        67.0    1995          16.2    82   \n",
      "386  25.0          6         181.0       110.0    2945          16.4    82   \n",
      "387  38.0          6         262.0        85.0    3015          17.0    82   \n",
      "388  26.0          4         156.0        92.0    2585          14.5    82   \n",
      "389  22.0          6         232.0       112.0    2835          14.7    82   \n",
      "390  32.0          4         144.0        96.0    2665          13.9    82   \n",
      "391  36.0          4         135.0        84.0    2370          13.0    82   \n",
      "392  27.0          4         151.0        90.0    2950          17.3    82   \n",
      "393  27.0          4         140.0        86.0    2790          15.6    82   \n",
      "395  32.0          4         135.0        84.0    2295          11.6    82   \n",
      "396  28.0          4         120.0        79.0    2625          18.6    82   \n",
      "397  31.0          4         119.0        82.0    2720          19.4    82   \n",
      "\n",
      "     origin  \n",
      "0         1  \n",
      "1         1  \n",
      "2         1  \n",
      "3         1  \n",
      "4         1  \n",
      "5         1  \n",
      "6         1  \n",
      "7         1  \n",
      "8         1  \n",
      "9         1  \n",
      "10        1  \n",
      "11        1  \n",
      "12        1  \n",
      "13        1  \n",
      "14        3  \n",
      "15        1  \n",
      "16        1  \n",
      "17        1  \n",
      "18        3  \n",
      "19        2  \n",
      "20        2  \n",
      "21        2  \n",
      "22        2  \n",
      "23        2  \n",
      "24        1  \n",
      "25        1  \n",
      "26        1  \n",
      "27        1  \n",
      "28        1  \n",
      "29        3  \n",
      "..      ...  \n",
      "367       1  \n",
      "368       1  \n",
      "369       1  \n",
      "370       1  \n",
      "371       1  \n",
      "372       1  \n",
      "373       1  \n",
      "374       1  \n",
      "375       2  \n",
      "376       3  \n",
      "377       3  \n",
      "378       1  \n",
      "379       1  \n",
      "380       3  \n",
      "381       3  \n",
      "382       3  \n",
      "383       3  \n",
      "384       3  \n",
      "385       3  \n",
      "386       1  \n",
      "387       1  \n",
      "388       1  \n",
      "389       1  \n",
      "390       3  \n",
      "391       1  \n",
      "392       1  \n",
      "393       1  \n",
      "395       1  \n",
      "396       1  \n",
      "397       1  \n",
      "\n",
      "[388 rows x 8 columns]\n"
     ]
    }
   ],
   "source": [
    "import tensorflow.contrib.learn as skflow\n",
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "# create feature vector\n",
    "missing_median(df, 'horsepower')\n",
    "df.drop('name',1,inplace=True)\n",
    "#encode_numeric_binary(df,'mpg',20)\n",
    "#df['origin'] = df['origin'].astype(str)\n",
    "#encode_text_tfidf(df, 'origin')\n",
    "\n",
    "# Drop outliers in horsepower\n",
    "print(\"Length before MPG outliers dropped: {}\".format(len(df)))\n",
    "remove_outliers(df,'mpg',2)\n",
    "print(\"Length after MPG outliers dropped: {}\".format(len(df)))\n",
    "\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Google API Keys\n",
    "---------------\n",
    "\n",
    "Sometimes you will use external API's to obtain data.  The following examples show how to use the Google API keys to encode addresses for use with neural networks.  To use these, you will need your own Google API key.  The key I have below is not a real key, you need to put your own in there.  Google will ask for a credit card, but unless you use a very large number of lookups, there will be no actual cost.  YOU ARE NOT required to get an Google API key for this class, this only shows you how.  If you would like to get a Google API key, visit this site and obtain one for **geocode**.\n",
    "\n",
    "[Google API Keys](https://developers.google.com/maps/documentation/embed/get-api-key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "GOOGLE_KEY = 'AIzaSyshdufhsdiuhfuhdfuhduhiuxbUrg'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other Examples: Dealing with Addresses\n",
    "\n",
    "Addresses can be difficult to encode into a neural network.  There are many different approaches, and you must consider how you can transform the address into something more meaningful.  Map coordinates can be a good approach.  [Latitude and longitude](https://en.wikipedia.org/wiki/Geographic_coordinate_system) can be a useful encoding.  Thanks to the power of the Internet, it is relatively easy to transform an address into its latitude and longitude values.  The following code determines the coordinates of [Washington University](https://wustl.edu/):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'lat': 38.6482003, 'lng': -90.3050494}\n"
     ]
    }
   ],
   "source": [
    "import requests\n",
    "\n",
    "address = \"1 Brookings Dr, St. Louis, MO 63130\"\n",
    "\n",
    "response = requests.get('https://maps.googleapis.com/maps/api/geocode/json?key={}&address={}'.format(GOOGLE_KEY,address))\n",
    "\n",
    "resp_json_payload = response.json()\n",
    "\n",
    "if 'error_message' in resp_json_payload:\n",
    "    print(resp_json_payload['error_message'])\n",
    "else:\n",
    "    print(resp_json_payload['results'][0]['geometry']['location'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If latitude and longitude are simply fed into the neural network as two features, they might not be overly helpful.  These two values would allow your neural network to cluster locations on a map.  Sometimes cluster locations on a map can be useful.  Consider the percentage of the population that smokes in the USA by state:\n",
    "\n",
    "![Smokers by State](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_6_smokers.png \"Smokers by State\")\n",
    "\n",
    "The above map shows that certian behaviors, like smoking, can be clustered by global region. \n",
    "\n",
    "However, often you will want to transform the coordinates into distances.  It is reasonably easy to estimate the distance between any two points on Earth by using the [great circle distance](https://en.wikipedia.org/wiki/Great-circle_distance) between any two points on a sphere:\n",
    "\n",
    "The following code implements this formula:\n",
    "\n",
    "$\\Delta\\sigma=\\arccos\\bigl(\\sin\\phi_1\\cdot\\sin\\phi_2+\\cos\\phi_1\\cdot\\cos\\phi_2\\cdot\\cos(\\Delta\\lambda)\\bigr)$\n",
    "\n",
    "$d = r \\, \\Delta\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distance, St. Louis, MO to Ft. Lauderdale, FL: 1685.3102481229685 km\n"
     ]
    }
   ],
   "source": [
    "from math import sin, cos, sqrt, atan2, radians\n",
    "\n",
    "# Distance function\n",
    "def distance_lat_lng(lat1,lng1,lat2,lng2):\n",
    "    # approximate radius of earth in km\n",
    "    R = 6373.0\n",
    "\n",
    "    # degrees to radians (lat/lon are in degrees)\n",
    "    lat1 = radians(lat1)\n",
    "    lng1 = radians(lng1)\n",
    "    lat2 = radians(lat2)\n",
    "    lng2 = radians(lng2)\n",
    "\n",
    "    dlng = lng2 - lng1\n",
    "    dlat = lat2 - lat1\n",
    "\n",
    "    a = sin(dlat / 2)**2 + cos(lat1) * cos(lat2) * sin(dlng / 2)**2\n",
    "    c = 2 * atan2(sqrt(a), sqrt(1 - a))\n",
    "\n",
    "    return R * c\n",
    "\n",
    "# Find lat lon for address\n",
    "def lookup_lat_lng(address):\n",
    "    response = requests.get('https://maps.googleapis.com/maps/api/geocode/json?key={}&address={}'.format(GOOGLE_KEY,address))\n",
    "    json = response.json()\n",
    "    if len(json['results']) == 0:\n",
    "        print(\"Can't find: {}\".format(address))\n",
    "        return 0,0\n",
    "    map = json['results'][0]['geometry']['location']\n",
    "    return map['lat'],map['lng']\n",
    "\n",
    "\n",
    "# Distance between two locations\n",
    "\n",
    "import requests\n",
    "\n",
    "address1 = \"1 Brookings Dr, St. Louis, MO 63130\" \n",
    "address2 = \"3301 College Ave, Fort Lauderdale, FL 33314\"\n",
    "\n",
    "lat1, lng1 = lookup_lat_lng(address1)\n",
    "lat2, lng2 = lookup_lat_lng(address2)\n",
    "\n",
    "print(\"Distance, St. Louis, MO to Ft. Lauderdale, FL: {} km\".format(\n",
    "        distance_lat_lng(lat1,lng1,lat2,lng2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distances can be useful to encode addresses as.  You must consider what distance might be useful for your dataset.  Consider:\n",
    "\n",
    "* Distance to major metropolitan area\n",
    "* Distance to competitor\n",
    "* Distance to distribution center\n",
    "* Distance to retail outlet\n",
    "\n",
    "The following code calculates the distance between 10 universities and washu:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "School 'Princeton', distance to wustl is: 1354.4905812310371\n",
      "School 'Harvard', distance to wustl is: 1670.6505836338872\n",
      "School 'University of Chicago', distance to wustl is: 418.0829173700165\n",
      "School 'Yale', distance to wustl is: 1508.224917173613\n",
      "School 'Columbia University', distance to wustl is: 1418.1537657313474\n",
      "School 'Stanford', distance to wustl is: 2780.805742296612\n",
      "School 'MIT', distance to wustl is: 1672.451136482304\n",
      "School 'Duke University', distance to wustl is: 1046.8063308945887\n",
      "School 'University of Pennsylvania', distance to wustl is: 1307.2030819428105\n",
      "School 'Johns Hopkins', distance to wustl is: 1184.3910679675719\n"
     ]
    }
   ],
   "source": [
    "# Encoding other universities by their distance to Washington University\n",
    "\n",
    "schools = [\n",
    "    [\"Princeton University, Princeton, NJ 08544\", 'Princeton'],\n",
    "    [\"Massachusetts Hall, Cambridge, MA 02138\", 'Harvard'],\n",
    "    [\"5801 S Ellis Ave, Chicago, IL 60637\", 'University of Chicago'],\n",
    "    [\"Yale, New Haven, CT 06520\", 'Yale'],\n",
    "    [\"116th St & Broadway, New York, NY 10027\", 'Columbia University'],\n",
    "    [\"450 Serra Mall, Stanford, CA 94305\", 'Stanford'],\n",
    "    [\"77 Massachusetts Ave, Cambridge, MA 02139\", 'MIT'],\n",
    "    [\"Duke University, Durham, NC 27708\", 'Duke University'],\n",
    "    [\"University of Pennsylvania, Philadelphia, PA 19104\", 'University of Pennsylvania'],\n",
    "    [\"Johns Hopkins University, Baltimore, MD 21218\", 'Johns Hopkins']\n",
    "]\n",
    "\n",
    "lat1, lng1 = lookup_lat_lng(\"1 Brookings Dr, St. Louis, MO 63130\")\n",
    "\n",
    "for address, name in schools:\n",
    "    lat2,lng2 = lookup_lat_lng(address)\n",
    "    dist = distance_lat_lng(lat1,lng1,lat2,lng2)\n",
    "    print(\"School '{}', distance to wustl is: {}\".format(name,dist))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Training with a Validation Set and Early Stopping\n",
    "\n",
    "**Overfitting** occurs when a neural network is trained to the point that it begins to memorize rather than generalize.  \n",
    "\n",
    "![Training vs Validation Error for Overfitting](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_3_training_val.png \"Training vs Validation Error for Overfitting\")\n",
    "\n",
    "It is important to segment the original dataset into several datasets:\n",
    "\n",
    "* **Training Set**\n",
    "* **Validation Set**\n",
    "* **Holdout Set**\n",
    "\n",
    "There are several different ways that these sets can be constructed.  The following programs demonstrate some of these.\n",
    "\n",
    "The first method is a training and validation set.  The training data are used to train the neural network until the validation set no longer improves.  This attempts to stop at a near optimal training point.  This method will only give accurate \"out of sample\" predictions for the validation set, this is usually 20% or so of the data.  The predictions for the training data will be overly optimistic, as these were the data that the neural network was trained on.  \n",
    "\n",
    "![Training with a Validation Set](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_1_train_val.png \"Training with a Validation Set\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 112 samples, validate on 38 samples\n",
      "Epoch 1/1000\n",
      " - 0s - loss: 1.3263 - val_loss: 1.2906\n",
      "Epoch 2/1000\n",
      " - 0s - loss: 1.2794 - val_loss: 1.2567\n",
      "Epoch 3/1000\n",
      " - 0s - loss: 1.2460 - val_loss: 1.2247\n",
      "Epoch 4/1000\n",
      " - 0s - loss: 1.2107 - val_loss: 1.1960\n",
      "Epoch 5/1000\n",
      " - 0s - loss: 1.1801 - val_loss: 1.1701\n",
      "Epoch 6/1000\n",
      " - 0s - loss: 1.1508 - val_loss: 1.1459\n",
      "Epoch 7/1000\n",
      " - 0s - loss: 1.1215 - val_loss: 1.1228\n",
      "Epoch 8/1000\n",
      " - 0s - loss: 1.0963 - val_loss: 1.1018\n",
      "Epoch 9/1000\n",
      " - 0s - loss: 1.0758 - val_loss: 1.0819\n",
      "Epoch 10/1000\n",
      " - 0s - loss: 1.0532 - val_loss: 1.0643\n",
      "Epoch 11/1000\n",
      " - 0s - loss: 1.0373 - val_loss: 1.0476\n",
      "Epoch 12/1000\n",
      " - 0s - loss: 1.0190 - val_loss: 1.0318\n",
      "Epoch 13/1000\n",
      " - 0s - loss: 1.0040 - val_loss: 1.0179\n",
      "Epoch 14/1000\n",
      " - 0s - loss: 0.9891 - val_loss: 1.0050\n",
      "Epoch 15/1000\n",
      " - 0s - loss: 0.9773 - val_loss: 0.9942\n",
      "Epoch 16/1000\n",
      " - 0s - loss: 0.9670 - val_loss: 0.9834\n",
      "Epoch 17/1000\n",
      " - 0s - loss: 0.9578 - val_loss: 0.9715\n",
      "Epoch 18/1000\n",
      " - 0s - loss: 0.9484 - val_loss: 0.9593\n",
      "Epoch 19/1000\n",
      " - 0s - loss: 0.9386 - val_loss: 0.9464\n",
      "Epoch 20/1000\n",
      " - 0s - loss: 0.9286 - val_loss: 0.9332\n",
      "Epoch 21/1000\n",
      " - 0s - loss: 0.9197 - val_loss: 0.9201\n",
      "Epoch 22/1000\n",
      " - 0s - loss: 0.9111 - val_loss: 0.9085\n",
      "Epoch 23/1000\n",
      " - 0s - loss: 0.9025 - val_loss: 0.8979\n",
      "Epoch 24/1000\n",
      " - 0s - loss: 0.8940 - val_loss: 0.8879\n",
      "Epoch 25/1000\n",
      " - 0s - loss: 0.8861 - val_loss: 0.8780\n",
      "Epoch 26/1000\n",
      " - 0s - loss: 0.8788 - val_loss: 0.8682\n",
      "Epoch 27/1000\n",
      " - 0s - loss: 0.8707 - val_loss: 0.8590\n",
      "Epoch 28/1000\n",
      " - 0s - loss: 0.8632 - val_loss: 0.8496\n",
      "Epoch 29/1000\n",
      " - 0s - loss: 0.8555 - val_loss: 0.8404\n",
      "Epoch 30/1000\n",
      " - 0s - loss: 0.8480 - val_loss: 0.8309\n",
      "Epoch 31/1000\n",
      " - 0s - loss: 0.8404 - val_loss: 0.8215\n",
      "Epoch 32/1000\n",
      " - 0s - loss: 0.8323 - val_loss: 0.8122\n",
      "Epoch 33/1000\n",
      " - 0s - loss: 0.8244 - val_loss: 0.8031\n",
      "Epoch 34/1000\n",
      " - 0s - loss: 0.8164 - val_loss: 0.7938\n",
      "Epoch 35/1000\n",
      " - 0s - loss: 0.8086 - val_loss: 0.7842\n",
      "Epoch 36/1000\n",
      " - 0s - loss: 0.8002 - val_loss: 0.7748\n",
      "Epoch 37/1000\n",
      " - 0s - loss: 0.7920 - val_loss: 0.7651\n",
      "Epoch 38/1000\n",
      " - 0s - loss: 0.7834 - val_loss: 0.7556\n",
      "Epoch 39/1000\n",
      " - 0s - loss: 0.7753 - val_loss: 0.7457\n",
      "Epoch 40/1000\n",
      " - 0s - loss: 0.7666 - val_loss: 0.7362\n",
      "Epoch 41/1000\n",
      " - 0s - loss: 0.7580 - val_loss: 0.7264\n",
      "Epoch 42/1000\n",
      " - 0s - loss: 0.7496 - val_loss: 0.7163\n",
      "Epoch 43/1000\n",
      " - 0s - loss: 0.7409 - val_loss: 0.7067\n",
      "Epoch 44/1000\n",
      " - 0s - loss: 0.7323 - val_loss: 0.6974\n",
      "Epoch 45/1000\n",
      " - 0s - loss: 0.7239 - val_loss: 0.6875\n",
      "Epoch 46/1000\n",
      " - 0s - loss: 0.7152 - val_loss: 0.6779\n",
      "Epoch 47/1000\n",
      " - 0s - loss: 0.7067 - val_loss: 0.6685\n",
      "Epoch 48/1000\n",
      " - 0s - loss: 0.6982 - val_loss: 0.6593\n",
      "Epoch 49/1000\n",
      " - 0s - loss: 0.6901 - val_loss: 0.6497\n",
      "Epoch 50/1000\n",
      " - 0s - loss: 0.6816 - val_loss: 0.6406\n",
      "Epoch 51/1000\n",
      " - 0s - loss: 0.6737 - val_loss: 0.6315\n",
      "Epoch 52/1000\n",
      " - 0s - loss: 0.6660 - val_loss: 0.6228\n",
      "Epoch 53/1000\n",
      " - 0s - loss: 0.6584 - val_loss: 0.6142\n",
      "Epoch 54/1000\n",
      " - 0s - loss: 0.6509 - val_loss: 0.6064\n",
      "Epoch 55/1000\n",
      " - 0s - loss: 0.6440 - val_loss: 0.5982\n",
      "Epoch 56/1000\n",
      " - 0s - loss: 0.6369 - val_loss: 0.5902\n",
      "Epoch 57/1000\n",
      " - 0s - loss: 0.6300 - val_loss: 0.5828\n",
      "Epoch 58/1000\n",
      " - 0s - loss: 0.6231 - val_loss: 0.5754\n",
      "Epoch 59/1000\n",
      " - 0s - loss: 0.6166 - val_loss: 0.5686\n",
      "Epoch 60/1000\n",
      " - 0s - loss: 0.6102 - val_loss: 0.5621\n",
      "Epoch 61/1000\n",
      " - 0s - loss: 0.6043 - val_loss: 0.5559\n",
      "Epoch 62/1000\n",
      " - 0s - loss: 0.5984 - val_loss: 0.5503\n",
      "Epoch 63/1000\n",
      " - 0s - loss: 0.5924 - val_loss: 0.5448\n",
      "Epoch 64/1000\n",
      " - 0s - loss: 0.5870 - val_loss: 0.5398\n",
      "Epoch 65/1000\n",
      " - 0s - loss: 0.5818 - val_loss: 0.5345\n",
      "Epoch 66/1000\n",
      " - 0s - loss: 0.5767 - val_loss: 0.5292\n",
      "Epoch 67/1000\n",
      " - 0s - loss: 0.5719 - val_loss: 0.5238\n",
      "Epoch 68/1000\n",
      " - 0s - loss: 0.5670 - val_loss: 0.5187\n",
      "Epoch 69/1000\n",
      " - 0s - loss: 0.5622 - val_loss: 0.5141\n",
      "Epoch 70/1000\n",
      " - 0s - loss: 0.5576 - val_loss: 0.5093\n",
      "Epoch 71/1000\n",
      " - 0s - loss: 0.5529 - val_loss: 0.5050\n",
      "Epoch 72/1000\n",
      " - 0s - loss: 0.5478 - val_loss: 0.5012\n",
      "Epoch 73/1000\n",
      " - 0s - loss: 0.5435 - val_loss: 0.4972\n",
      "Epoch 74/1000\n",
      " - 0s - loss: 0.5393 - val_loss: 0.4931\n",
      "Epoch 75/1000\n",
      " - 0s - loss: 0.5349 - val_loss: 0.4892\n",
      "Epoch 76/1000\n",
      " - 0s - loss: 0.5307 - val_loss: 0.4850\n",
      "Epoch 77/1000\n",
      " - 0s - loss: 0.5269 - val_loss: 0.4812\n",
      "Epoch 78/1000\n",
      " - 0s - loss: 0.5226 - val_loss: 0.4772\n",
      "Epoch 79/1000\n",
      " - 0s - loss: 0.5191 - val_loss: 0.4735\n",
      "Epoch 80/1000\n",
      " - 0s - loss: 0.5148 - val_loss: 0.4692\n",
      "Epoch 81/1000\n",
      " - 0s - loss: 0.5102 - val_loss: 0.4645\n",
      "Epoch 82/1000\n",
      " - 0s - loss: 0.5068 - val_loss: 0.4596\n",
      "Epoch 83/1000\n",
      " - 0s - loss: 0.5027 - val_loss: 0.4547\n",
      "Epoch 84/1000\n",
      " - 0s - loss: 0.4990 - val_loss: 0.4502\n",
      "Epoch 85/1000\n",
      " - 0s - loss: 0.4954 - val_loss: 0.4460\n",
      "Epoch 86/1000\n",
      " - 0s - loss: 0.4916 - val_loss: 0.4420\n",
      "Epoch 87/1000\n",
      " - 0s - loss: 0.4880 - val_loss: 0.4386\n",
      "Epoch 88/1000\n",
      " - 0s - loss: 0.4841 - val_loss: 0.4353\n",
      "Epoch 89/1000\n",
      " - 0s - loss: 0.4814 - val_loss: 0.4327\n",
      "Epoch 90/1000\n",
      " - 0s - loss: 0.4769 - val_loss: 0.4297\n",
      "Epoch 91/1000\n",
      " - 0s - loss: 0.4733 - val_loss: 0.4264\n",
      "Epoch 92/1000\n",
      " - 0s - loss: 0.4701 - val_loss: 0.4228\n",
      "Epoch 93/1000\n",
      " - 0s - loss: 0.4663 - val_loss: 0.4193\n",
      "Epoch 94/1000\n",
      " - 0s - loss: 0.4632 - val_loss: 0.4157\n",
      "Epoch 95/1000\n",
      " - 0s - loss: 0.4591 - val_loss: 0.4123\n",
      "Epoch 96/1000\n",
      " - 0s - loss: 0.4558 - val_loss: 0.4089\n",
      "Epoch 97/1000\n",
      " - 0s - loss: 0.4534 - val_loss: 0.4063\n",
      "Epoch 98/1000\n",
      " - 0s - loss: 0.4499 - val_loss: 0.4032\n",
      "Epoch 99/1000\n",
      " - 0s - loss: 0.4465 - val_loss: 0.4002\n",
      "Epoch 100/1000\n",
      " - 0s - loss: 0.4427 - val_loss: 0.3974\n",
      "Epoch 101/1000\n",
      " - 0s - loss: 0.4395 - val_loss: 0.3943\n",
      "Epoch 102/1000\n",
      " - 0s - loss: 0.4364 - val_loss: 0.3910\n",
      "Epoch 103/1000\n",
      " - 0s - loss: 0.4327 - val_loss: 0.3874\n",
      "Epoch 104/1000\n",
      " - 0s - loss: 0.4295 - val_loss: 0.3840\n",
      "Epoch 105/1000\n",
      " - 0s - loss: 0.4265 - val_loss: 0.3806\n",
      "Epoch 106/1000\n",
      " - 0s - loss: 0.4236 - val_loss: 0.3770\n",
      "Epoch 107/1000\n",
      " - 0s - loss: 0.4200 - val_loss: 0.3734\n",
      "Epoch 108/1000\n",
      " - 0s - loss: 0.4173 - val_loss: 0.3703\n",
      "Epoch 109/1000\n",
      " - 0s - loss: 0.4139 - val_loss: 0.3674\n",
      "Epoch 110/1000\n",
      " - 0s - loss: 0.4111 - val_loss: 0.3650\n",
      "Epoch 111/1000\n",
      " - 0s - loss: 0.4075 - val_loss: 0.3623\n",
      "Epoch 112/1000\n",
      " - 0s - loss: 0.4045 - val_loss: 0.3594\n",
      "Epoch 113/1000\n",
      " - 0s - loss: 0.4017 - val_loss: 0.3564\n",
      "Epoch 114/1000\n",
      " - 0s - loss: 0.3997 - val_loss: 0.3533\n",
      "Epoch 115/1000\n",
      " - 0s - loss: 0.3961 - val_loss: 0.3494\n",
      "Epoch 116/1000\n",
      " - 0s - loss: 0.3926 - val_loss: 0.3458\n",
      "Epoch 117/1000\n",
      " - 0s - loss: 0.3895 - val_loss: 0.3434\n",
      "Epoch 118/1000\n",
      " - 0s - loss: 0.3864 - val_loss: 0.3411\n",
      "Epoch 119/1000\n",
      " - 0s - loss: 0.3838 - val_loss: 0.3390\n",
      "Epoch 120/1000\n",
      " - 0s - loss: 0.3803 - val_loss: 0.3370\n",
      "Epoch 121/1000\n",
      " - 0s - loss: 0.3772 - val_loss: 0.3347\n",
      "Epoch 122/1000\n",
      " - 0s - loss: 0.3745 - val_loss: 0.3319\n",
      "Epoch 123/1000\n",
      " - 0s - loss: 0.3716 - val_loss: 0.3286\n",
      "Epoch 124/1000\n",
      " - 0s - loss: 0.3687 - val_loss: 0.3255\n",
      "Epoch 125/1000\n",
      " - 0s - loss: 0.3657 - val_loss: 0.3228\n",
      "Epoch 126/1000\n",
      " - 0s - loss: 0.3626 - val_loss: 0.3202\n",
      "Epoch 127/1000\n",
      " - 0s - loss: 0.3596 - val_loss: 0.3176\n",
      "Epoch 128/1000\n",
      " - 0s - loss: 0.3568 - val_loss: 0.3152\n",
      "Epoch 129/1000\n",
      " - 0s - loss: 0.3545 - val_loss: 0.3130\n",
      "Epoch 130/1000\n",
      " - 0s - loss: 0.3516 - val_loss: 0.3105\n",
      "Epoch 131/1000\n",
      " - 0s - loss: 0.3484 - val_loss: 0.3078\n",
      "Epoch 132/1000\n",
      " - 0s - loss: 0.3454 - val_loss: 0.3049\n",
      "Epoch 133/1000\n",
      " - 0s - loss: 0.3431 - val_loss: 0.3019\n",
      "Epoch 134/1000\n",
      " - 0s - loss: 0.3394 - val_loss: 0.2993\n",
      "Epoch 135/1000\n",
      " - 0s - loss: 0.3368 - val_loss: 0.2967\n",
      "Epoch 136/1000\n",
      " - 0s - loss: 0.3377 - val_loss: 0.2950\n",
      "Epoch 137/1000\n",
      " - 0s - loss: 0.3307 - val_loss: 0.2919\n",
      "Epoch 138/1000\n",
      " - 0s - loss: 0.3307 - val_loss: 0.2905\n",
      "Epoch 139/1000\n",
      " - 0s - loss: 0.3276 - val_loss: 0.2867\n",
      "Epoch 140/1000\n",
      " - 0s - loss: 0.3242 - val_loss: 0.2838\n",
      "Epoch 141/1000\n",
      " - 0s - loss: 0.3208 - val_loss: 0.2811\n",
      "Epoch 142/1000\n",
      " - 0s - loss: 0.3182 - val_loss: 0.2785\n",
      "Epoch 143/1000\n",
      " - 0s - loss: 0.3157 - val_loss: 0.2760\n",
      "Epoch 144/1000\n",
      " - 0s - loss: 0.3140 - val_loss: 0.2740\n",
      "Epoch 145/1000\n",
      " - 0s - loss: 0.3107 - val_loss: 0.2715\n",
      "Epoch 146/1000\n",
      " - 0s - loss: 0.3078 - val_loss: 0.2692\n",
      "Epoch 147/1000\n",
      " - 0s - loss: 0.3053 - val_loss: 0.2671\n",
      "Epoch 148/1000\n",
      " - 0s - loss: 0.3028 - val_loss: 0.2648\n",
      "Epoch 149/1000\n",
      " - 0s - loss: 0.3002 - val_loss: 0.2624\n",
      "Epoch 150/1000\n",
      " - 0s - loss: 0.2978 - val_loss: 0.2602\n",
      "Epoch 151/1000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " - 0s - loss: 0.2953 - val_loss: 0.2580\n",
      "Epoch 152/1000\n",
      " - 0s - loss: 0.2929 - val_loss: 0.2557\n",
      "Epoch 153/1000\n",
      " - 0s - loss: 0.2906 - val_loss: 0.2534\n",
      "Epoch 154/1000\n",
      " - 0s - loss: 0.2898 - val_loss: 0.2512\n",
      "Epoch 155/1000\n",
      " - 0s - loss: 0.2863 - val_loss: 0.2491\n",
      "Epoch 156/1000\n",
      " - 0s - loss: 0.2832 - val_loss: 0.2466\n",
      "Epoch 157/1000\n",
      " - 0s - loss: 0.2806 - val_loss: 0.2443\n",
      "Epoch 158/1000\n",
      " - 0s - loss: 0.2783 - val_loss: 0.2423\n",
      "Epoch 159/1000\n",
      " - 0s - loss: 0.2760 - val_loss: 0.2403\n",
      "Epoch 160/1000\n",
      " - 0s - loss: 0.2735 - val_loss: 0.2381\n",
      "Epoch 161/1000\n",
      " - 0s - loss: 0.2710 - val_loss: 0.2361\n",
      "Epoch 162/1000\n",
      " - 0s - loss: 0.2688 - val_loss: 0.2341\n",
      "Epoch 163/1000\n",
      " - 0s - loss: 0.2668 - val_loss: 0.2319\n",
      "Epoch 164/1000\n",
      " - 0s - loss: 0.2643 - val_loss: 0.2298\n",
      "Epoch 165/1000\n",
      " - 0s - loss: 0.2626 - val_loss: 0.2276\n",
      "Epoch 166/1000\n",
      " - 0s - loss: 0.2599 - val_loss: 0.2256\n",
      "Epoch 167/1000\n",
      " - 0s - loss: 0.2574 - val_loss: 0.2235\n",
      "Epoch 168/1000\n",
      " - 0s - loss: 0.2553 - val_loss: 0.2215\n",
      "Epoch 169/1000\n",
      " - 0s - loss: 0.2533 - val_loss: 0.2195\n",
      "Epoch 170/1000\n",
      " - 0s - loss: 0.2506 - val_loss: 0.2175\n",
      "Epoch 171/1000\n",
      " - 0s - loss: 0.2488 - val_loss: 0.2158\n",
      "Epoch 172/1000\n",
      " - 0s - loss: 0.2471 - val_loss: 0.2141\n",
      "Epoch 173/1000\n",
      " - 0s - loss: 0.2439 - val_loss: 0.2121\n",
      "Epoch 174/1000\n",
      " - 0s - loss: 0.2425 - val_loss: 0.2104\n",
      "Epoch 175/1000\n",
      " - 0s - loss: 0.2406 - val_loss: 0.2083\n",
      "Epoch 176/1000\n",
      " - 0s - loss: 0.2398 - val_loss: 0.2069\n",
      "Epoch 177/1000\n",
      " - 0s - loss: 0.2373 - val_loss: 0.2045\n",
      "Epoch 178/1000\n",
      " - 0s - loss: 0.2358 - val_loss: 0.2033\n",
      "Epoch 179/1000\n",
      " - 0s - loss: 0.2340 - val_loss: 0.2009\n",
      "Epoch 180/1000\n",
      " - 0s - loss: 0.2307 - val_loss: 0.1992\n",
      "Epoch 181/1000\n",
      " - 0s - loss: 0.2282 - val_loss: 0.1973\n",
      "Epoch 182/1000\n",
      " - 0s - loss: 0.2263 - val_loss: 0.1957\n",
      "Epoch 183/1000\n",
      " - 0s - loss: 0.2247 - val_loss: 0.1940\n",
      "Epoch 184/1000\n",
      " - 0s - loss: 0.2234 - val_loss: 0.1923\n",
      "Epoch 185/1000\n",
      " - 0s - loss: 0.2214 - val_loss: 0.1919\n",
      "Epoch 186/1000\n",
      " - 0s - loss: 0.2202 - val_loss: 0.1916\n",
      "Epoch 187/1000\n",
      " - 0s - loss: 0.2188 - val_loss: 0.1885\n",
      "Epoch 188/1000\n",
      " - 0s - loss: 0.2156 - val_loss: 0.1864\n",
      "Epoch 189/1000\n",
      " - 0s - loss: 0.2141 - val_loss: 0.1846\n",
      "Epoch 190/1000\n",
      " - 0s - loss: 0.2127 - val_loss: 0.1831\n",
      "Epoch 191/1000\n",
      " - 0s - loss: 0.2108 - val_loss: 0.1817\n",
      "Epoch 192/1000\n",
      " - 0s - loss: 0.2089 - val_loss: 0.1802\n",
      "Epoch 193/1000\n",
      " - 0s - loss: 0.2082 - val_loss: 0.1788\n",
      "Epoch 194/1000\n",
      " - 0s - loss: 0.2066 - val_loss: 0.1770\n",
      "Epoch 195/1000\n",
      " - 0s - loss: 0.2047 - val_loss: 0.1756\n",
      "Epoch 196/1000\n",
      " - 0s - loss: 0.2025 - val_loss: 0.1748\n",
      "Epoch 197/1000\n",
      " - 0s - loss: 0.2012 - val_loss: 0.1738\n",
      "Epoch 198/1000\n",
      " - 0s - loss: 0.1994 - val_loss: 0.1721\n",
      "Epoch 199/1000\n",
      " - 0s - loss: 0.1978 - val_loss: 0.1703\n",
      "Epoch 200/1000\n",
      " - 0s - loss: 0.1963 - val_loss: 0.1690\n",
      "Epoch 201/1000\n",
      " - 0s - loss: 0.1946 - val_loss: 0.1676\n",
      "Epoch 202/1000\n",
      " - 0s - loss: 0.1935 - val_loss: 0.1664\n",
      "Epoch 203/1000\n",
      " - 0s - loss: 0.1922 - val_loss: 0.1654\n",
      "Epoch 204/1000\n",
      " - 0s - loss: 0.1906 - val_loss: 0.1639\n",
      "Epoch 205/1000\n",
      " - 0s - loss: 0.1885 - val_loss: 0.1624\n",
      "Epoch 206/1000\n",
      " - 0s - loss: 0.1892 - val_loss: 0.1613\n",
      "Epoch 207/1000\n",
      " - 0s - loss: 0.1860 - val_loss: 0.1601\n",
      "Epoch 208/1000\n",
      " - 0s - loss: 0.1858 - val_loss: 0.1612\n",
      "Epoch 209/1000\n",
      " - 0s - loss: 0.1844 - val_loss: 0.1601\n",
      "Epoch 210/1000\n",
      " - 0s - loss: 0.1830 - val_loss: 0.1574\n",
      "Epoch 211/1000\n",
      " - 0s - loss: 0.1805 - val_loss: 0.1548\n",
      "Epoch 212/1000\n",
      " - 0s - loss: 0.1832 - val_loss: 0.1540\n",
      "Epoch 213/1000\n",
      " - 0s - loss: 0.1799 - val_loss: 0.1531\n",
      "Epoch 214/1000\n",
      " - 0s - loss: 0.1772 - val_loss: 0.1527\n",
      "Epoch 215/1000\n",
      " - 0s - loss: 0.1759 - val_loss: 0.1512\n",
      "Epoch 216/1000\n",
      " - 0s - loss: 0.1749 - val_loss: 0.1502\n",
      "Epoch 217/1000\n",
      " - 0s - loss: 0.1734 - val_loss: 0.1502\n",
      "Epoch 218/1000\n",
      " - 0s - loss: 0.1724 - val_loss: 0.1485\n",
      "Epoch 219/1000\n",
      " - 0s - loss: 0.1706 - val_loss: 0.1463\n",
      "Epoch 220/1000\n",
      " - 0s - loss: 0.1706 - val_loss: 0.1453\n",
      "Epoch 221/1000\n",
      " - 0s - loss: 0.1683 - val_loss: 0.1449\n",
      "Epoch 222/1000\n",
      " - 0s - loss: 0.1673 - val_loss: 0.1454\n",
      "Epoch 223/1000\n",
      " - 0s - loss: 0.1672 - val_loss: 0.1439\n",
      "Epoch 224/1000\n",
      " - 0s - loss: 0.1661 - val_loss: 0.1428\n",
      "Epoch 225/1000\n",
      " - 0s - loss: 0.1641 - val_loss: 0.1413\n",
      "Epoch 226/1000\n",
      " - 0s - loss: 0.1628 - val_loss: 0.1395\n",
      "Epoch 227/1000\n",
      " - 0s - loss: 0.1624 - val_loss: 0.1383\n",
      "Epoch 228/1000\n",
      " - 0s - loss: 0.1611 - val_loss: 0.1375\n",
      "Epoch 229/1000\n",
      " - 0s - loss: 0.1601 - val_loss: 0.1365\n",
      "Epoch 230/1000\n",
      " - 0s - loss: 0.1587 - val_loss: 0.1368\n",
      "Epoch 231/1000\n",
      " - 0s - loss: 0.1601 - val_loss: 0.1372\n",
      "Epoch 232/1000\n",
      " - 0s - loss: 0.1572 - val_loss: 0.1343\n",
      "Epoch 233/1000\n",
      " - 0s - loss: 0.1559 - val_loss: 0.1325\n",
      "Epoch 234/1000\n",
      " - 0s - loss: 0.1552 - val_loss: 0.1316\n",
      "Epoch 235/1000\n",
      " - 0s - loss: 0.1539 - val_loss: 0.1312\n",
      "Epoch 236/1000\n",
      " - 0s - loss: 0.1527 - val_loss: 0.1314\n",
      "Epoch 237/1000\n",
      " - 0s - loss: 0.1520 - val_loss: 0.1308\n",
      "Epoch 238/1000\n",
      " - 0s - loss: 0.1511 - val_loss: 0.1298\n",
      "Epoch 239/1000\n",
      " - 0s - loss: 0.1499 - val_loss: 0.1281\n",
      "Epoch 240/1000\n",
      " - 0s - loss: 0.1499 - val_loss: 0.1266\n",
      "Epoch 241/1000\n",
      " - 0s - loss: 0.1490 - val_loss: 0.1259\n",
      "Epoch 242/1000\n",
      " - 0s - loss: 0.1467 - val_loss: 0.1276\n",
      "Epoch 243/1000\n",
      " - 0s - loss: 0.1478 - val_loss: 0.1288\n",
      "Epoch 244/1000\n",
      " - 0s - loss: 0.1469 - val_loss: 0.1256\n",
      "Epoch 245/1000\n",
      " - 0s - loss: 0.1471 - val_loss: 0.1227\n",
      "Epoch 246/1000\n",
      " - 0s - loss: 0.1461 - val_loss: 0.1219\n",
      "Epoch 247/1000\n",
      " - 0s - loss: 0.1456 - val_loss: 0.1243\n",
      "Epoch 248/1000\n",
      " - 0s - loss: 0.1450 - val_loss: 0.1247\n",
      "Epoch 249/1000\n",
      " - 0s - loss: 0.1427 - val_loss: 0.1209\n",
      "Epoch 250/1000\n",
      " - 0s - loss: 0.1409 - val_loss: 0.1194\n",
      "Epoch 251/1000\n",
      " - 0s - loss: 0.1403 - val_loss: 0.1186\n",
      "Epoch 252/1000\n",
      " - 0s - loss: 0.1394 - val_loss: 0.1180\n",
      "Epoch 253/1000\n",
      " - 0s - loss: 0.1387 - val_loss: 0.1174\n",
      "Epoch 254/1000\n",
      " - 0s - loss: 0.1381 - val_loss: 0.1171\n",
      "Epoch 255/1000\n",
      " - 0s - loss: 0.1391 - val_loss: 0.1157\n",
      "Epoch 256/1000\n",
      " - 0s - loss: 0.1360 - val_loss: 0.1171\n",
      "Epoch 257/1000\n",
      " - 0s - loss: 0.1403 - val_loss: 0.1204\n",
      "Epoch 258/1000\n",
      " - 0s - loss: 0.1365 - val_loss: 0.1157\n",
      "Epoch 259/1000\n",
      " - 0s - loss: 0.1337 - val_loss: 0.1134\n",
      "Epoch 260/1000\n",
      " - 0s - loss: 0.1335 - val_loss: 0.1124\n",
      "Epoch 261/1000\n",
      " - 0s - loss: 0.1359 - val_loss: 0.1117\n",
      "Epoch 262/1000\n",
      " - 0s - loss: 0.1321 - val_loss: 0.1129\n",
      "Epoch 263/1000\n",
      " - 0s - loss: 0.1310 - val_loss: 0.1155\n",
      "Epoch 264/1000\n",
      " - 0s - loss: 0.1327 - val_loss: 0.1150\n",
      "Epoch 265/1000\n",
      " - 0s - loss: 0.1315 - val_loss: 0.1113\n",
      "Epoch 266/1000\n",
      " - 0s - loss: 0.1295 - val_loss: 0.1094\n",
      "Epoch 267/1000\n",
      " - 0s - loss: 0.1296 - val_loss: 0.1086\n",
      "Epoch 268/1000\n",
      " - 0s - loss: 0.1291 - val_loss: 0.1098\n",
      "Epoch 269/1000\n",
      " - 0s - loss: 0.1280 - val_loss: 0.1088\n",
      "Epoch 270/1000\n",
      " - 0s - loss: 0.1280 - val_loss: 0.1082\n",
      "Epoch 271/1000\n",
      " - 0s - loss: 0.1274 - val_loss: 0.1061\n",
      "Epoch 272/1000\n",
      " - 0s - loss: 0.1261 - val_loss: 0.1064\n",
      "Epoch 273/1000\n",
      " - 0s - loss: 0.1251 - val_loss: 0.1069\n",
      "Epoch 274/1000\n",
      " - 0s - loss: 0.1250 - val_loss: 0.1078\n",
      "Epoch 275/1000\n",
      " - 0s - loss: 0.1249 - val_loss: 0.1080\n",
      "Epoch 276/1000\n",
      " - 0s - loss: 0.1244 - val_loss: 0.1055\n",
      "Epoch 00276: early stopping\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1a26629e48>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import io\n",
    "import requests\n",
    "import numpy as np\n",
    "import os\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Activation\n",
    "from keras.callbacks import EarlyStopping\n",
    "\n",
    "path = \"./data/\"\n",
    "    \n",
    "filename = os.path.join(path,\"iris.csv\")    \n",
    "df = pd.read_csv(filename,na_values=['NA','?'])\n",
    "\n",
    "species = encode_text_index(df,\"species\")\n",
    "x,y = to_xy(df,\"species\")\n",
    "\n",
    "# Split into train/test\n",
    "x_train, x_test, y_train, y_test = train_test_split(    \n",
    "    x, y, test_size=0.25, random_state=42)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Dense(10, input_dim=x.shape[1], activation='relu'))\n",
    "model.add(Dense(5,activation='relu'))\n",
    "model.add(Dense(y.shape[1],activation='softmax'))\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam')\n",
    "monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "\n",
    "model.fit(x_train, y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=2,epochs=1000)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the neural network is trained, we can make predictions about the test set.  The following code predicts the type of iris for test set and displays the first five irises. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.0973369e-03 8.7977165e-01 1.1613102e-01]\n",
      " [9.8989701e-01 1.0103002e-02 1.7175730e-09]\n",
      " [3.6760881e-07 2.0157052e-02 9.7984260e-01]\n",
      " [3.0534274e-03 8.1347972e-01 1.8346678e-01]\n",
      " [3.0218584e-03 9.0403229e-01 9.2945851e-02]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "import tensorflow as tf\n",
    "\n",
    "pred = model.predict(x_test)\n",
    "print(pred[0:5]) # print first five predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These numbers are in scientific notation.  Each line provides the probability that the iris is one of the 3 types of iris in the data set.  For the first line, the second type of iris has a 91% probability of being the species of iris."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Early Stopping and the Best Weights\n",
    "\n",
    "In the previous section we used early stopping so that the training would halt once the validation set no longer saw score improvements for a number of epoch.  This number of epochs that early stopping will tolerate no improvement is called *patience*.  If the patience value is large, the neural network's error may continue to worsen while early stopping is patiently waiting.  At some point earlier in the training the optimal set of weights was obtained for the neural network.  However, at the end of training we will have the weights for the neural network that finally exhausted the patience of early stopping.  The weights of this neural network might not be bad, but it would be better to have the most optimal weights during the entire training operation.  \n",
    "\n",
    "The code presented below does this.  An additional monitor is used and saves a copy of the neural network to **best_weights.hdf5** each time the validation score of the neural network improves.  Once training is done, we just reload this file and we have the optimal training weights that were found.\n",
    "\n",
    "This technique is slight overkill for many of the examples for this class.  It can also introduce an occasional issue (as described in the next section).  Because of this, most of the examples in this course will not use this code to obtain the absolute best weights.  However, for the larger, more complex datasets in this course, we will save the absolute best weights as demonstrated here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 112 samples, validate on 38 samples\n",
      "Epoch 1/1000\n",
      " - 0s - loss: 1.0611 - val_loss: 1.0936\n",
      "Epoch 2/1000\n",
      " - 0s - loss: 1.0387 - val_loss: 1.0672\n",
      "Epoch 3/1000\n",
      " - 0s - loss: 1.0185 - val_loss: 1.0400\n",
      "Epoch 4/1000\n",
      " - 0s - loss: 0.9983 - val_loss: 1.0172\n",
      "Epoch 5/1000\n",
      " - 0s - loss: 0.9834 - val_loss: 0.9984\n",
      "Epoch 6/1000\n",
      " - 0s - loss: 0.9694 - val_loss: 0.9816\n",
      "Epoch 7/1000\n",
      " - 0s - loss: 0.9582 - val_loss: 0.9654\n",
      "Epoch 8/1000\n",
      " - 0s - loss: 0.9470 - val_loss: 0.9503\n",
      "Epoch 9/1000\n",
      " - 0s - loss: 0.9353 - val_loss: 0.9359\n",
      "Epoch 10/1000\n",
      " - 0s - loss: 0.9254 - val_loss: 0.9212\n",
      "Epoch 11/1000\n",
      " - 0s - loss: 0.9138 - val_loss: 0.9073\n",
      "Epoch 12/1000\n",
      " - 0s - loss: 0.9030 - val_loss: 0.8937\n",
      "Epoch 13/1000\n",
      " - 0s - loss: 0.8923 - val_loss: 0.8800\n",
      "Epoch 14/1000\n",
      " - 0s - loss: 0.8808 - val_loss: 0.8668\n",
      "Epoch 15/1000\n",
      " - 0s - loss: 0.8699 - val_loss: 0.8534\n",
      "Epoch 16/1000\n",
      " - 0s - loss: 0.8590 - val_loss: 0.8406\n",
      "Epoch 17/1000\n",
      " - 0s - loss: 0.8490 - val_loss: 0.8283\n",
      "Epoch 18/1000\n",
      " - 0s - loss: 0.8389 - val_loss: 0.8172\n",
      "Epoch 19/1000\n",
      " - 0s - loss: 0.8295 - val_loss: 0.8064\n",
      "Epoch 20/1000\n",
      " - 0s - loss: 0.8196 - val_loss: 0.7959\n",
      "Epoch 21/1000\n",
      " - 0s - loss: 0.8104 - val_loss: 0.7856\n",
      "Epoch 22/1000\n",
      " - 0s - loss: 0.8017 - val_loss: 0.7755\n",
      "Epoch 23/1000\n",
      " - 0s - loss: 0.7925 - val_loss: 0.7663\n",
      "Epoch 24/1000\n",
      " - 0s - loss: 0.7848 - val_loss: 0.7572\n",
      "Epoch 25/1000\n",
      " - 0s - loss: 0.7763 - val_loss: 0.7485\n",
      "Epoch 26/1000\n",
      " - 0s - loss: 0.7685 - val_loss: 0.7394\n",
      "Epoch 27/1000\n",
      " - 0s - loss: 0.7602 - val_loss: 0.7309\n",
      "Epoch 28/1000\n",
      " - 0s - loss: 0.7526 - val_loss: 0.7223\n",
      "Epoch 29/1000\n",
      " - 0s - loss: 0.7445 - val_loss: 0.7141\n",
      "Epoch 30/1000\n",
      " - 0s - loss: 0.7367 - val_loss: 0.7060\n",
      "Epoch 31/1000\n",
      " - 0s - loss: 0.7289 - val_loss: 0.6971\n",
      "Epoch 32/1000\n",
      " - 0s - loss: 0.7212 - val_loss: 0.6888\n",
      "Epoch 33/1000\n",
      " - 0s - loss: 0.7130 - val_loss: 0.6807\n",
      "Epoch 34/1000\n",
      " - 0s - loss: 0.7055 - val_loss: 0.6721\n",
      "Epoch 35/1000\n",
      " - 0s - loss: 0.6976 - val_loss: 0.6639\n",
      "Epoch 36/1000\n",
      " - 0s - loss: 0.6903 - val_loss: 0.6555\n",
      "Epoch 37/1000\n",
      " - 0s - loss: 0.6830 - val_loss: 0.6473\n",
      "Epoch 38/1000\n",
      " - 0s - loss: 0.6756 - val_loss: 0.6399\n",
      "Epoch 39/1000\n",
      " - 0s - loss: 0.6683 - val_loss: 0.6325\n",
      "Epoch 40/1000\n",
      " - 0s - loss: 0.6609 - val_loss: 0.6251\n",
      "Epoch 41/1000\n",
      " - 0s - loss: 0.6539 - val_loss: 0.6175\n",
      "Epoch 42/1000\n",
      " - 0s - loss: 0.6467 - val_loss: 0.6098\n",
      "Epoch 43/1000\n",
      " - 0s - loss: 0.6397 - val_loss: 0.6021\n",
      "Epoch 44/1000\n",
      " - 0s - loss: 0.6325 - val_loss: 0.5948\n",
      "Epoch 45/1000\n",
      " - 0s - loss: 0.6259 - val_loss: 0.5868\n",
      "Epoch 46/1000\n",
      " - 0s - loss: 0.6189 - val_loss: 0.5796\n",
      "Epoch 47/1000\n",
      " - 0s - loss: 0.6124 - val_loss: 0.5720\n",
      "Epoch 48/1000\n",
      " - 0s - loss: 0.6055 - val_loss: 0.5650\n",
      "Epoch 49/1000\n",
      " - 0s - loss: 0.5988 - val_loss: 0.5580\n",
      "Epoch 50/1000\n",
      " - 0s - loss: 0.5923 - val_loss: 0.5508\n",
      "Epoch 51/1000\n",
      " - 0s - loss: 0.5858 - val_loss: 0.5438\n",
      "Epoch 52/1000\n",
      " - 0s - loss: 0.5795 - val_loss: 0.5369\n",
      "Epoch 53/1000\n",
      " - 0s - loss: 0.5730 - val_loss: 0.5303\n",
      "Epoch 54/1000\n",
      " - 0s - loss: 0.5668 - val_loss: 0.5237\n",
      "Epoch 55/1000\n",
      " - 0s - loss: 0.5608 - val_loss: 0.5169\n",
      "Epoch 56/1000\n",
      " - 0s - loss: 0.5546 - val_loss: 0.5100\n",
      "Epoch 57/1000\n",
      " - 0s - loss: 0.5487 - val_loss: 0.5031\n",
      "Epoch 58/1000\n",
      " - 0s - loss: 0.5425 - val_loss: 0.4970\n",
      "Epoch 59/1000\n",
      " - 0s - loss: 0.5368 - val_loss: 0.4908\n",
      "Epoch 60/1000\n",
      " - 0s - loss: 0.5311 - val_loss: 0.4848\n",
      "Epoch 61/1000\n",
      " - 0s - loss: 0.5255 - val_loss: 0.4792\n",
      "Epoch 62/1000\n",
      " - 0s - loss: 0.5197 - val_loss: 0.4734\n",
      "Epoch 63/1000\n",
      " - 0s - loss: 0.5142 - val_loss: 0.4675\n",
      "Epoch 64/1000\n",
      " - 0s - loss: 0.5090 - val_loss: 0.4616\n",
      "Epoch 65/1000\n",
      " - 0s - loss: 0.5037 - val_loss: 0.4560\n",
      "Epoch 66/1000\n",
      " - 0s - loss: 0.4982 - val_loss: 0.4509\n",
      "Epoch 67/1000\n",
      " - 0s - loss: 0.4928 - val_loss: 0.4458\n",
      "Epoch 68/1000\n",
      " - 0s - loss: 0.4875 - val_loss: 0.4406\n",
      "Epoch 69/1000\n",
      " - 0s - loss: 0.4826 - val_loss: 0.4351\n",
      "Epoch 70/1000\n",
      " - 0s - loss: 0.4777 - val_loss: 0.4298\n",
      "Epoch 71/1000\n",
      " - 0s - loss: 0.4725 - val_loss: 0.4247\n",
      "Epoch 72/1000\n",
      " - 0s - loss: 0.4681 - val_loss: 0.4197\n",
      "Epoch 73/1000\n",
      " - 0s - loss: 0.4631 - val_loss: 0.4149\n",
      "Epoch 74/1000\n",
      " - 0s - loss: 0.4585 - val_loss: 0.4104\n",
      "Epoch 75/1000\n",
      " - 0s - loss: 0.4537 - val_loss: 0.4056\n",
      "Epoch 76/1000\n",
      " - 0s - loss: 0.4491 - val_loss: 0.4009\n",
      "Epoch 77/1000\n",
      " - 0s - loss: 0.4448 - val_loss: 0.3963\n",
      "Epoch 78/1000\n",
      " - 0s - loss: 0.4400 - val_loss: 0.3920\n",
      "Epoch 79/1000\n",
      " - 0s - loss: 0.4361 - val_loss: 0.3877\n",
      "Epoch 80/1000\n",
      " - 0s - loss: 0.4321 - val_loss: 0.3836\n",
      "Epoch 81/1000\n",
      " - 0s - loss: 0.4278 - val_loss: 0.3793\n",
      "Epoch 82/1000\n",
      " - 0s - loss: 0.4237 - val_loss: 0.3750\n",
      "Epoch 83/1000\n",
      " - 0s - loss: 0.4195 - val_loss: 0.3709\n",
      "Epoch 84/1000\n",
      " - 0s - loss: 0.4155 - val_loss: 0.3670\n",
      "Epoch 85/1000\n",
      " - 0s - loss: 0.4117 - val_loss: 0.3633\n",
      "Epoch 86/1000\n",
      " - 0s - loss: 0.4076 - val_loss: 0.3596\n",
      "Epoch 87/1000\n",
      " - 0s - loss: 0.4038 - val_loss: 0.3558\n",
      "Epoch 88/1000\n",
      " - 0s - loss: 0.4000 - val_loss: 0.3516\n",
      "Epoch 89/1000\n",
      " - 0s - loss: 0.3961 - val_loss: 0.3481\n",
      "Epoch 90/1000\n",
      " - 0s - loss: 0.3923 - val_loss: 0.3448\n",
      "Epoch 91/1000\n",
      " - 0s - loss: 0.3884 - val_loss: 0.3414\n",
      "Epoch 92/1000\n",
      " - 0s - loss: 0.3849 - val_loss: 0.3381\n",
      "Epoch 93/1000\n",
      " - 0s - loss: 0.3815 - val_loss: 0.3347\n",
      "Epoch 94/1000\n",
      " - 0s - loss: 0.3777 - val_loss: 0.3312\n",
      "Epoch 95/1000\n",
      " - 0s - loss: 0.3745 - val_loss: 0.3279\n",
      "Epoch 96/1000\n",
      " - 0s - loss: 0.3706 - val_loss: 0.3245\n",
      "Epoch 97/1000\n",
      " - 0s - loss: 0.3668 - val_loss: 0.3217\n",
      "Epoch 98/1000\n",
      " - 0s - loss: 0.3642 - val_loss: 0.3186\n",
      "Epoch 99/1000\n",
      " - 0s - loss: 0.3608 - val_loss: 0.3149\n",
      "Epoch 100/1000\n",
      " - 0s - loss: 0.3566 - val_loss: 0.3109\n",
      "Epoch 101/1000\n",
      " - 0s - loss: 0.3530 - val_loss: 0.3078\n",
      "Epoch 102/1000\n",
      " - 0s - loss: 0.3503 - val_loss: 0.3050\n",
      "Epoch 103/1000\n",
      " - 0s - loss: 0.3470 - val_loss: 0.3018\n",
      "Epoch 104/1000\n",
      " - 0s - loss: 0.3428 - val_loss: 0.2990\n",
      "Epoch 105/1000\n",
      " - 0s - loss: 0.3399 - val_loss: 0.2962\n",
      "Epoch 106/1000\n",
      " - 0s - loss: 0.3365 - val_loss: 0.2934\n",
      "Epoch 107/1000\n",
      " - 0s - loss: 0.3332 - val_loss: 0.2901\n",
      "Epoch 108/1000\n",
      " - 0s - loss: 0.3305 - val_loss: 0.2867\n",
      "Epoch 109/1000\n",
      " - 0s - loss: 0.3264 - val_loss: 0.2838\n",
      "Epoch 110/1000\n",
      " - 0s - loss: 0.3234 - val_loss: 0.2808\n",
      "Epoch 111/1000\n",
      " - 0s - loss: 0.3198 - val_loss: 0.2779\n",
      "Epoch 112/1000\n",
      " - 0s - loss: 0.3165 - val_loss: 0.2752\n",
      "Epoch 113/1000\n",
      " - 0s - loss: 0.3133 - val_loss: 0.2725\n",
      "Epoch 114/1000\n",
      " - 0s - loss: 0.3099 - val_loss: 0.2695\n",
      "Epoch 115/1000\n",
      " - 0s - loss: 0.3068 - val_loss: 0.2666\n",
      "Epoch 116/1000\n",
      " - 0s - loss: 0.3039 - val_loss: 0.2639\n",
      "Epoch 117/1000\n",
      " - 0s - loss: 0.3010 - val_loss: 0.2610\n",
      "Epoch 118/1000\n",
      " - 0s - loss: 0.2973 - val_loss: 0.2581\n",
      "Epoch 119/1000\n",
      " - 0s - loss: 0.2947 - val_loss: 0.2555\n",
      "Epoch 120/1000\n",
      " - 0s - loss: 0.2913 - val_loss: 0.2530\n",
      "Epoch 121/1000\n",
      " - 0s - loss: 0.2888 - val_loss: 0.2502\n",
      "Epoch 122/1000\n",
      " - 0s - loss: 0.2850 - val_loss: 0.2477\n",
      "Epoch 123/1000\n",
      " - 0s - loss: 0.2822 - val_loss: 0.2452\n",
      "Epoch 124/1000\n",
      " - 0s - loss: 0.2789 - val_loss: 0.2427\n",
      "Epoch 125/1000\n",
      " - 0s - loss: 0.2761 - val_loss: 0.2402\n",
      "Epoch 126/1000\n",
      " - 0s - loss: 0.2742 - val_loss: 0.2377\n",
      "Epoch 127/1000\n",
      " - 0s - loss: 0.2705 - val_loss: 0.2350\n",
      "Epoch 128/1000\n",
      " - 0s - loss: 0.2680 - val_loss: 0.2327\n",
      "Epoch 129/1000\n",
      " - 0s - loss: 0.2653 - val_loss: 0.2304\n",
      "Epoch 130/1000\n",
      " - 0s - loss: 0.2628 - val_loss: 0.2279\n",
      "Epoch 131/1000\n",
      " - 0s - loss: 0.2598 - val_loss: 0.2257\n",
      "Epoch 132/1000\n",
      " - 0s - loss: 0.2574 - val_loss: 0.2234\n",
      "Epoch 133/1000\n",
      " - 0s - loss: 0.2551 - val_loss: 0.2214\n",
      "Epoch 134/1000\n",
      " - 0s - loss: 0.2523 - val_loss: 0.2189\n",
      "Epoch 135/1000\n",
      " - 0s - loss: 0.2493 - val_loss: 0.2167\n",
      "Epoch 136/1000\n",
      " - 0s - loss: 0.2467 - val_loss: 0.2145\n",
      "Epoch 137/1000\n",
      " - 0s - loss: 0.2441 - val_loss: 0.2125\n",
      "Epoch 138/1000\n",
      " - 0s - loss: 0.2417 - val_loss: 0.2104\n",
      "Epoch 139/1000\n",
      " - 0s - loss: 0.2394 - val_loss: 0.2083\n",
      "Epoch 140/1000\n",
      " - 0s - loss: 0.2371 - val_loss: 0.2063\n",
      "Epoch 141/1000\n",
      " - 0s - loss: 0.2346 - val_loss: 0.2044\n",
      "Epoch 142/1000\n",
      " - 0s - loss: 0.2324 - val_loss: 0.2024\n",
      "Epoch 143/1000\n",
      " - 0s - loss: 0.2304 - val_loss: 0.2005\n",
      "Epoch 144/1000\n",
      " - 0s - loss: 0.2277 - val_loss: 0.1985\n",
      "Epoch 145/1000\n",
      " - 0s - loss: 0.2256 - val_loss: 0.1966\n",
      "Epoch 146/1000\n",
      " - 0s - loss: 0.2233 - val_loss: 0.1947\n",
      "Epoch 147/1000\n",
      " - 0s - loss: 0.2211 - val_loss: 0.1929\n",
      "Epoch 148/1000\n",
      " - 0s - loss: 0.2192 - val_loss: 0.1911\n",
      "Epoch 149/1000\n",
      " - 0s - loss: 0.2174 - val_loss: 0.1895\n",
      "Epoch 150/1000\n",
      " - 0s - loss: 0.2150 - val_loss: 0.1877\n",
      "Epoch 151/1000\n",
      " - 0s - loss: 0.2129 - val_loss: 0.1861\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 152/1000\n",
      " - 0s - loss: 0.2111 - val_loss: 0.1845\n",
      "Epoch 153/1000\n",
      " - 0s - loss: 0.2088 - val_loss: 0.1829\n",
      "Epoch 154/1000\n",
      " - 0s - loss: 0.2075 - val_loss: 0.1812\n",
      "Epoch 155/1000\n",
      " - 0s - loss: 0.2051 - val_loss: 0.1797\n",
      "Epoch 156/1000\n",
      " - 0s - loss: 0.2030 - val_loss: 0.1781\n",
      "Epoch 157/1000\n",
      " - 0s - loss: 0.2012 - val_loss: 0.1765\n",
      "Epoch 158/1000\n",
      " - 0s - loss: 0.1992 - val_loss: 0.1749\n",
      "Epoch 159/1000\n",
      " - 0s - loss: 0.1981 - val_loss: 0.1734\n",
      "Epoch 160/1000\n",
      " - 0s - loss: 0.1958 - val_loss: 0.1719\n",
      "Epoch 161/1000\n",
      " - 0s - loss: 0.1940 - val_loss: 0.1704\n",
      "Epoch 162/1000\n",
      " - 0s - loss: 0.1923 - val_loss: 0.1690\n",
      "Epoch 163/1000\n",
      " - 0s - loss: 0.1905 - val_loss: 0.1677\n",
      "Epoch 164/1000\n",
      " - 0s - loss: 0.1888 - val_loss: 0.1665\n",
      "Epoch 165/1000\n",
      " - 0s - loss: 0.1882 - val_loss: 0.1655\n",
      "Epoch 166/1000\n",
      " - 0s - loss: 0.1858 - val_loss: 0.1638\n",
      "Epoch 167/1000\n",
      " - 0s - loss: 0.1838 - val_loss: 0.1624\n",
      "Epoch 168/1000\n",
      " - 0s - loss: 0.1826 - val_loss: 0.1612\n",
      "Epoch 169/1000\n",
      " - 0s - loss: 0.1815 - val_loss: 0.1599\n",
      "Epoch 170/1000\n",
      " - 0s - loss: 0.1794 - val_loss: 0.1584\n",
      "Epoch 171/1000\n",
      " - 0s - loss: 0.1780 - val_loss: 0.1579\n",
      "Epoch 172/1000\n",
      " - 0s - loss: 0.1772 - val_loss: 0.1573\n",
      "Epoch 173/1000\n",
      " - 0s - loss: 0.1754 - val_loss: 0.1554\n",
      "Epoch 174/1000\n",
      " - 0s - loss: 0.1732 - val_loss: 0.1538\n",
      "Epoch 175/1000\n",
      " - 0s - loss: 0.1717 - val_loss: 0.1526\n",
      "Epoch 176/1000\n",
      " - 0s - loss: 0.1716 - val_loss: 0.1515\n",
      "Epoch 177/1000\n",
      " - 0s - loss: 0.1694 - val_loss: 0.1503\n",
      "Epoch 178/1000\n",
      " - 0s - loss: 0.1677 - val_loss: 0.1494\n",
      "Epoch 179/1000\n",
      " - 0s - loss: 0.1666 - val_loss: 0.1487\n",
      "Epoch 180/1000\n",
      " - 0s - loss: 0.1657 - val_loss: 0.1473\n",
      "Epoch 181/1000\n",
      " - 0s - loss: 0.1638 - val_loss: 0.1462\n",
      "Epoch 182/1000\n",
      " - 0s - loss: 0.1630 - val_loss: 0.1456\n",
      "Epoch 183/1000\n",
      " - 0s - loss: 0.1614 - val_loss: 0.1442\n",
      "Epoch 184/1000\n",
      " - 0s - loss: 0.1601 - val_loss: 0.1430\n",
      "Epoch 185/1000\n",
      " - 0s - loss: 0.1586 - val_loss: 0.1422\n",
      "Epoch 186/1000\n",
      " - 0s - loss: 0.1574 - val_loss: 0.1412\n",
      "Epoch 187/1000\n",
      " - 0s - loss: 0.1567 - val_loss: 0.1405\n",
      "Epoch 188/1000\n",
      " - 0s - loss: 0.1553 - val_loss: 0.1395\n",
      "Epoch 189/1000\n",
      " - 0s - loss: 0.1542 - val_loss: 0.1387\n",
      "Epoch 190/1000\n",
      " - 0s - loss: 0.1530 - val_loss: 0.1375\n",
      "Epoch 191/1000\n",
      " - 0s - loss: 0.1518 - val_loss: 0.1366\n",
      "Epoch 192/1000\n",
      " - 0s - loss: 0.1508 - val_loss: 0.1357\n",
      "Epoch 193/1000\n",
      " - 0s - loss: 0.1496 - val_loss: 0.1351\n",
      "Epoch 194/1000\n",
      " - 0s - loss: 0.1485 - val_loss: 0.1341\n",
      "Epoch 195/1000\n",
      " - 0s - loss: 0.1477 - val_loss: 0.1330\n",
      "Epoch 196/1000\n",
      " - 0s - loss: 0.1468 - val_loss: 0.1321\n",
      "Epoch 197/1000\n",
      " - 0s - loss: 0.1461 - val_loss: 0.1312\n",
      "Epoch 198/1000\n",
      " - 0s - loss: 0.1448 - val_loss: 0.1304\n",
      "Epoch 199/1000\n",
      " - 0s - loss: 0.1437 - val_loss: 0.1296\n",
      "Epoch 200/1000\n",
      " - 0s - loss: 0.1428 - val_loss: 0.1288\n",
      "Epoch 201/1000\n",
      " - 0s - loss: 0.1415 - val_loss: 0.1281\n",
      "Epoch 202/1000\n",
      " - 0s - loss: 0.1406 - val_loss: 0.1274\n",
      "Epoch 203/1000\n",
      " - 0s - loss: 0.1409 - val_loss: 0.1265\n",
      "Epoch 204/1000\n",
      " - 0s - loss: 0.1388 - val_loss: 0.1258\n",
      "Epoch 205/1000\n",
      " - 0s - loss: 0.1377 - val_loss: 0.1252\n",
      "Epoch 206/1000\n",
      " - 0s - loss: 0.1367 - val_loss: 0.1245\n",
      "Epoch 207/1000\n",
      " - 0s - loss: 0.1365 - val_loss: 0.1237\n",
      "Epoch 208/1000\n",
      " - 0s - loss: 0.1357 - val_loss: 0.1234\n",
      "Epoch 209/1000\n",
      " - 0s - loss: 0.1344 - val_loss: 0.1226\n",
      "Epoch 210/1000\n",
      " - 0s - loss: 0.1331 - val_loss: 0.1217\n",
      "Epoch 211/1000\n",
      " - 0s - loss: 0.1325 - val_loss: 0.1209\n",
      "Epoch 212/1000\n",
      " - 0s - loss: 0.1325 - val_loss: 0.1203\n",
      "Epoch 213/1000\n",
      " - 0s - loss: 0.1316 - val_loss: 0.1197\n",
      "Epoch 214/1000\n",
      " - 0s - loss: 0.1300 - val_loss: 0.1195\n",
      "Epoch 215/1000\n",
      " - 0s - loss: 0.1293 - val_loss: 0.1190\n",
      "Epoch 216/1000\n",
      " - 0s - loss: 0.1294 - val_loss: 0.1187\n",
      "Epoch 217/1000\n",
      " - 0s - loss: 0.1279 - val_loss: 0.1173\n",
      "Epoch 218/1000\n",
      " - 0s - loss: 0.1271 - val_loss: 0.1167\n",
      "Epoch 219/1000\n",
      " - 0s - loss: 0.1269 - val_loss: 0.1160\n",
      "Epoch 220/1000\n",
      " - 0s - loss: 0.1264 - val_loss: 0.1159\n",
      "Epoch 221/1000\n",
      " - 0s - loss: 0.1248 - val_loss: 0.1152\n",
      "Epoch 222/1000\n",
      " - 0s - loss: 0.1247 - val_loss: 0.1143\n",
      "Epoch 223/1000\n",
      " - 0s - loss: 0.1238 - val_loss: 0.1138\n",
      "Epoch 224/1000\n",
      " - 0s - loss: 0.1232 - val_loss: 0.1132\n",
      "Epoch 225/1000\n",
      " - 0s - loss: 0.1225 - val_loss: 0.1127\n",
      "Epoch 226/1000\n",
      " - 0s - loss: 0.1217 - val_loss: 0.1121\n",
      "Epoch 227/1000\n",
      " - 0s - loss: 0.1210 - val_loss: 0.1117\n",
      "Epoch 228/1000\n",
      " - 0s - loss: 0.1202 - val_loss: 0.1113\n",
      "Epoch 229/1000\n",
      " - 0s - loss: 0.1197 - val_loss: 0.1111\n",
      "Epoch 230/1000\n",
      " - 0s - loss: 0.1188 - val_loss: 0.1104\n",
      "Epoch 231/1000\n",
      " - 0s - loss: 0.1183 - val_loss: 0.1098\n",
      "Epoch 232/1000\n",
      " - 0s - loss: 0.1188 - val_loss: 0.1091\n",
      "Epoch 233/1000\n",
      " - 0s - loss: 0.1172 - val_loss: 0.1091\n",
      "Epoch 234/1000\n",
      " - 0s - loss: 0.1165 - val_loss: 0.1097\n",
      "Epoch 235/1000\n",
      " - 0s - loss: 0.1170 - val_loss: 0.1090\n",
      "Epoch 236/1000\n",
      " - 0s - loss: 0.1168 - val_loss: 0.1102\n",
      "Epoch 00236: early stopping\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import io\n",
    "import requests\n",
    "import numpy as np\n",
    "import os\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import metrics\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Activation\n",
    "from keras.callbacks import EarlyStopping\n",
    "from keras.callbacks import ModelCheckpoint\n",
    "\n",
    "path = \"./data/\"\n",
    "    \n",
    "filename = os.path.join(path,\"iris.csv\")    \n",
    "df = pd.read_csv(filename,na_values=['NA','?'])\n",
    "\n",
    "species = encode_text_index(df,\"species\")\n",
    "x,y = to_xy(df,\"species\")\n",
    "\n",
    "# Split into train/test\n",
    "x_train, x_test, y_train, y_test = train_test_split(    \n",
    "    x, y, test_size=0.25, random_state=42)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Dense(10, input_dim=x.shape[1], activation='relu'))\n",
    "model.add(Dense(5,activation='relu'))\n",
    "model.add(Dense(y.shape[1],activation='softmax'))\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam')\n",
    "monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "checkpointer = ModelCheckpoint(filepath=\"best_weights.hdf5\", verbose=0, save_best_only=True) # save best model\n",
    "\n",
    "model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor,checkpointer],verbose=2,epochs=1000)\n",
    "model.load_weights('best_weights.hdf5') # load weights from best model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Potential Keras Issue on Small Networks and Early Stopping\n",
    "\n",
    "You might occasionally see this error:\n",
    "\n",
    "```\n",
    "OSError: Unable to create file (Unable to open file: name = 'best_weights.hdf5', errno = 22, error message = 'invalid argument', flags = 13, o_flags = 302)\n",
    "```\n",
    "\n",
    "Usually you can just run rerun the code and it goes away.  This is an unfortnuate result of saving a file each time the validation score improves (as described in the previous section).  If the errors improve two rapidly, you might try to save the file twice and get an error from these two saves overlapping.  For larger neural networks this will not be a problem because each training step will take longer, allowing for plenty of time for the previous save to complete.  Because of this potential issue, this code is not used with every neural network in this course.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Classification Accuracy\n",
    " \n",
    "Accuracy is the number of rows where the neural network correctly predicted the target class.  Accuracy is only used for classification, not regression.\n",
    "\n",
    "$ accuracy = \\frac{\\textit{#} \\ correct}{N} $\n",
    "\n",
    "Where $N$ is the size of the evaluted set (training or validation). Higher accuracy numbers are desired.\n",
    "\n",
    "As we just saw, by default, Keras will return the percent probability for each class. We can change these prediction probabilities into the actual iris predicted with **argmax**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 2 1 1 0 1 2 1 1 2 0 0 0 0 1 2 1 1 2 0 2 0 2 2 2 2 2 0 0 0 0 1 0 0 2 1\n",
      " 0]\n"
     ]
    }
   ],
   "source": [
    "pred = np.argmax(pred,axis=1) # raw probabilities to chosen class (highest probability)\n",
    "print(pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the actual iris flower predicted, we can calculate the percent accuracy (how many were correctly classified)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy score: 1.0\n"
     ]
    }
   ],
   "source": [
    "y_compare = np.argmax(y_test,axis=1) \n",
    "score = metrics.accuracy_score(y_compare, pred)\n",
    "print(\"Accuracy score: {}\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Classification Log Loss\n",
    "\n",
    "Accuracy is like a final exam with no partial credit.  However, neural networks can predict a probability of each of the target classes.  Neural networks will give high probabilities to predictions that are more likely.  Log loss is an error metric that penalizes confidence in wrong answers. Lower log loss values are desired.\n",
    "\n",
    "The following code shows the output of predict_proba:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numpy array of predictions\n",
      "[ 0.4971 91.1698  8.333 ]\n",
      "As percent probability\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.005 , 0.9117, 0.0833],\n",
       "       [0.9892, 0.0108, 0.    ],\n",
       "       [0.    , 0.004 , 0.996 ],\n",
       "       [0.0044, 0.8406, 0.155 ],\n",
       "       [0.0031, 0.8727, 0.1242]], dtype=float32)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log loss score: 0.1090184848902649\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import display\n",
    "\n",
    "# Don't display numpy in scientific notation\n",
    "np.set_printoptions(precision=4)\n",
    "np.set_printoptions(suppress=True)\n",
    "\n",
    "# Generate predictions\n",
    "pred = model.predict(x_test)\n",
    "\n",
    "print(\"Numpy array of predictions\")\n",
    "print(pred[0]*100)\n",
    "\n",
    "print(\"As percent probability\")\n",
    "display(pred[0:5])\n",
    "\n",
    "score = metrics.log_loss(y_test, pred)\n",
    "print(\"Log loss score: {}\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Log loss](https://www.kaggle.com/wiki/LogarithmicLoss) is calculated as follows:\n",
    "\n",
    "$ \\text{log loss} = -\\frac{1}{N}\\sum_{i=1}^N {( {y}_i\\log(\\hat{y}_i) + (1 - {y}_i)\\log(1 - \\hat{y}_i))} $\n",
    "\n",
    "The log function is useful to penalizing wrong answers.  The following code demonstrates the utility of the log function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jheaton/miniconda3/envs/wustl/lib/python3.6/site-packages/ipykernel_launcher.py:12: RuntimeWarning: divide by zero encountered in log\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib.pyplot import figure, show\n",
    "from numpy import arange, sin, pi\n",
    "\n",
    "#t = arange(1e-5, 5.0, 0.00001)\n",
    "#t = arange(1.0, 5.0, 0.00001) # computer scientists\n",
    "t = arange(0.0, 1.0, 0.00001)  # data     scientists\n",
    "\n",
    "fig = figure(1,figsize=(12, 10))\n",
    "\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax1.plot(t, np.log(t))\n",
    "ax1.grid(True)\n",
    "ax1.set_ylim((-8, 1.5))\n",
    "ax1.set_xlim((-0.1, 2))\n",
    "ax1.set_xlabel('x')\n",
    "ax1.set_ylabel('y')\n",
    "ax1.set_title('log(x)')\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluating Regression Results\n",
    "\n",
    "Regression results are evaluated differently than classification.  Consider the following code that trains a neural network for the [MPG dataset](https://github.com/jeffheaton/t81_558_deep_learning/blob/master/datasets_mpg.ipynb). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 298 samples, validate on 100 samples\n",
      "Epoch 1/1000\n",
      " - 0s - loss: 142034.0649 - val_loss: 22125.5094\n",
      "Epoch 2/1000\n",
      " - 0s - loss: 5822.5145 - val_loss: 7864.1312\n",
      "Epoch 3/1000\n",
      " - 0s - loss: 10037.8172 - val_loss: 5982.6624\n",
      "Epoch 4/1000\n",
      " - 0s - loss: 2253.3492 - val_loss: 232.4389\n",
      "Epoch 5/1000\n",
      " - 0s - loss: 796.3646 - val_loss: 990.3266\n",
      "Epoch 6/1000\n",
      " - 0s - loss: 653.7929 - val_loss: 174.5293\n",
      "Epoch 7/1000\n",
      " - 0s - loss: 277.1220 - val_loss: 275.1542\n",
      "Epoch 8/1000\n",
      " - 0s - loss: 283.4258 - val_loss: 168.5874\n",
      "Epoch 9/1000\n",
      " - 0s - loss: 231.6704 - val_loss: 173.7314\n",
      "Epoch 10/1000\n",
      " - 0s - loss: 232.5294 - val_loss: 164.0449\n",
      "Epoch 11/1000\n",
      " - 0s - loss: 225.1893 - val_loss: 165.6957\n",
      "Epoch 12/1000\n",
      " - 0s - loss: 224.6920 - val_loss: 162.9912\n",
      "Epoch 13/1000\n",
      " - 0s - loss: 224.6847 - val_loss: 162.3074\n",
      "Epoch 14/1000\n",
      " - 0s - loss: 224.6661 - val_loss: 162.8305\n",
      "Epoch 15/1000\n",
      " - 0s - loss: 220.2555 - val_loss: 160.3870\n",
      "Epoch 16/1000\n",
      " - 0s - loss: 224.4560 - val_loss: 160.0171\n",
      "Epoch 17/1000\n",
      " - 0s - loss: 219.7174 - val_loss: 163.3100\n",
      "Epoch 18/1000\n",
      " - 0s - loss: 217.7110 - val_loss: 158.1695\n",
      "Epoch 19/1000\n",
      " - 0s - loss: 217.1406 - val_loss: 158.2402\n",
      "Epoch 20/1000\n",
      " - 0s - loss: 216.6037 - val_loss: 157.4796\n",
      "Epoch 21/1000\n",
      " - 0s - loss: 214.4612 - val_loss: 156.1508\n",
      "Epoch 22/1000\n",
      " - 0s - loss: 215.7526 - val_loss: 155.2971\n",
      "Epoch 23/1000\n",
      " - 0s - loss: 213.0326 - val_loss: 154.7822\n",
      "Epoch 24/1000\n",
      " - 0s - loss: 211.1509 - val_loss: 153.7669\n",
      "Epoch 25/1000\n",
      " - 0s - loss: 210.9135 - val_loss: 153.1265\n",
      "Epoch 26/1000\n",
      " - 0s - loss: 209.8571 - val_loss: 152.3891\n",
      "Epoch 27/1000\n",
      " - 0s - loss: 209.1727 - val_loss: 153.8275\n",
      "Epoch 28/1000\n",
      " - 0s - loss: 208.5483 - val_loss: 150.9563\n",
      "Epoch 29/1000\n",
      " - 0s - loss: 205.5773 - val_loss: 150.9820\n",
      "Epoch 30/1000\n",
      " - 0s - loss: 204.9097 - val_loss: 150.7043\n",
      "Epoch 31/1000\n",
      " - 0s - loss: 204.6076 - val_loss: 149.7102\n",
      "Epoch 32/1000\n",
      " - 0s - loss: 203.8169 - val_loss: 148.1554\n",
      "Epoch 33/1000\n",
      " - 0s - loss: 201.9095 - val_loss: 149.3679\n",
      "Epoch 34/1000\n",
      " - 0s - loss: 201.0487 - val_loss: 146.5900\n",
      "Epoch 35/1000\n",
      " - 0s - loss: 199.6612 - val_loss: 146.4136\n",
      "Epoch 36/1000\n",
      " - 0s - loss: 198.5718 - val_loss: 145.1680\n",
      "Epoch 37/1000\n",
      " - 0s - loss: 198.5341 - val_loss: 144.9321\n",
      "Epoch 38/1000\n",
      " - 0s - loss: 196.2664 - val_loss: 143.7364\n",
      "Epoch 39/1000\n",
      " - 0s - loss: 195.4598 - val_loss: 143.1398\n",
      "Epoch 40/1000\n",
      " - 0s - loss: 194.4302 - val_loss: 142.1545\n",
      "Epoch 41/1000\n",
      " - 0s - loss: 193.8097 - val_loss: 141.7574\n",
      "Epoch 42/1000\n",
      " - 0s - loss: 193.0254 - val_loss: 140.9950\n",
      "Epoch 43/1000\n",
      " - 0s - loss: 191.9874 - val_loss: 139.9543\n",
      "Epoch 44/1000\n",
      " - 0s - loss: 191.6853 - val_loss: 141.1604\n",
      "Epoch 45/1000\n",
      " - 0s - loss: 190.9116 - val_loss: 138.5242\n",
      "Epoch 46/1000\n",
      " - 0s - loss: 190.0719 - val_loss: 138.5930\n",
      "Epoch 47/1000\n",
      " - 0s - loss: 189.0179 - val_loss: 137.2141\n",
      "Epoch 48/1000\n",
      " - 0s - loss: 186.3961 - val_loss: 136.8059\n",
      "Epoch 49/1000\n",
      " - 0s - loss: 185.0528 - val_loss: 135.8020\n",
      "Epoch 50/1000\n",
      " - 0s - loss: 184.4299 - val_loss: 136.4859\n",
      "Epoch 51/1000\n",
      " - 0s - loss: 183.6499 - val_loss: 134.5718\n",
      "Epoch 52/1000\n",
      " - 0s - loss: 181.9594 - val_loss: 133.7869\n",
      "Epoch 53/1000\n",
      " - 0s - loss: 183.6123 - val_loss: 133.1585\n",
      "Epoch 54/1000\n",
      " - 0s - loss: 181.2779 - val_loss: 132.5634\n",
      "Epoch 55/1000\n",
      " - 0s - loss: 181.6672 - val_loss: 131.8075\n",
      "Epoch 56/1000\n",
      " - 0s - loss: 182.7708 - val_loss: 131.2811\n",
      "Epoch 57/1000\n",
      " - 0s - loss: 177.0549 - val_loss: 130.5512\n",
      "Epoch 58/1000\n",
      " - 0s - loss: 177.5336 - val_loss: 129.9046\n",
      "Epoch 59/1000\n",
      " - 0s - loss: 177.2632 - val_loss: 130.3021\n",
      "Epoch 60/1000\n",
      " - 0s - loss: 175.4082 - val_loss: 128.5698\n",
      "Epoch 61/1000\n",
      " - 0s - loss: 174.7606 - val_loss: 127.8705\n",
      "Epoch 62/1000\n",
      " - 0s - loss: 172.7900 - val_loss: 127.2126\n",
      "Epoch 63/1000\n",
      " - 0s - loss: 172.3382 - val_loss: 126.8519\n",
      "Epoch 64/1000\n",
      " - 0s - loss: 171.0638 - val_loss: 126.0986\n",
      "Epoch 65/1000\n",
      " - 0s - loss: 170.0569 - val_loss: 125.4111\n",
      "Epoch 66/1000\n",
      " - 0s - loss: 168.5925 - val_loss: 124.8196\n",
      "Epoch 67/1000\n",
      " - 0s - loss: 167.8108 - val_loss: 124.8052\n",
      "Epoch 68/1000\n",
      " - 0s - loss: 168.1371 - val_loss: 123.6412\n",
      "Epoch 69/1000\n",
      " - 0s - loss: 166.4577 - val_loss: 122.9636\n",
      "Epoch 70/1000\n",
      " - 0s - loss: 170.1499 - val_loss: 124.1808\n",
      "Epoch 71/1000\n",
      " - 0s - loss: 170.1017 - val_loss: 122.2284\n",
      "Epoch 72/1000\n",
      " - 0s - loss: 165.6222 - val_loss: 121.2260\n",
      "Epoch 73/1000\n",
      " - 0s - loss: 170.8798 - val_loss: 122.0269\n",
      "Epoch 74/1000\n",
      " - 0s - loss: 163.9266 - val_loss: 120.0923\n",
      "Epoch 75/1000\n",
      " - 0s - loss: 162.0813 - val_loss: 119.6166\n",
      "Epoch 76/1000\n",
      " - 0s - loss: 160.1972 - val_loss: 119.0086\n",
      "Epoch 77/1000\n",
      " - 0s - loss: 159.2485 - val_loss: 119.4080\n",
      "Epoch 78/1000\n",
      " - 0s - loss: 158.0934 - val_loss: 118.0012\n",
      "Epoch 79/1000\n",
      " - 0s - loss: 159.6465 - val_loss: 118.9654\n",
      "Epoch 80/1000\n",
      " - 0s - loss: 160.9290 - val_loss: 119.2042\n",
      "Epoch 81/1000\n",
      " - 0s - loss: 164.2418 - val_loss: 122.2335\n",
      "Epoch 82/1000\n",
      " - 0s - loss: 156.8419 - val_loss: 117.4512\n",
      "Epoch 83/1000\n",
      " - 0s - loss: 155.8224 - val_loss: 116.8696\n",
      "Epoch 84/1000\n",
      " - 0s - loss: 154.9614 - val_loss: 115.0544\n",
      "Epoch 85/1000\n",
      " - 0s - loss: 152.7481 - val_loss: 116.4831\n",
      "Epoch 86/1000\n",
      " - 0s - loss: 151.9418 - val_loss: 114.0089\n",
      "Epoch 87/1000\n",
      " - 0s - loss: 152.8164 - val_loss: 113.4692\n",
      "Epoch 88/1000\n",
      " - 0s - loss: 150.9029 - val_loss: 113.0737\n",
      "Epoch 89/1000\n",
      " - 0s - loss: 150.2323 - val_loss: 112.8490\n",
      "Epoch 90/1000\n",
      " - 0s - loss: 148.7399 - val_loss: 112.3980\n",
      "Epoch 91/1000\n",
      " - 0s - loss: 148.6017 - val_loss: 111.6046\n",
      "Epoch 92/1000\n",
      " - 0s - loss: 148.2058 - val_loss: 111.0807\n",
      "Epoch 93/1000\n",
      " - 0s - loss: 147.2340 - val_loss: 110.6369\n",
      "Epoch 94/1000\n",
      " - 0s - loss: 147.8878 - val_loss: 112.5986\n",
      "Epoch 95/1000\n",
      " - 0s - loss: 146.5648 - val_loss: 111.0576\n",
      "Epoch 96/1000\n",
      " - 0s - loss: 149.7013 - val_loss: 112.0264\n",
      "Epoch 97/1000\n",
      " - 0s - loss: 144.0471 - val_loss: 108.9845\n",
      "Epoch 98/1000\n",
      " - 0s - loss: 145.0954 - val_loss: 111.0829\n",
      "Epoch 99/1000\n",
      " - 0s - loss: 142.8315 - val_loss: 108.0753\n",
      "Epoch 100/1000\n",
      " - 0s - loss: 141.5716 - val_loss: 108.3696\n",
      "Epoch 101/1000\n",
      " - 0s - loss: 144.2942 - val_loss: 115.1858\n",
      "Epoch 102/1000\n",
      " - 0s - loss: 146.4098 - val_loss: 111.3486\n",
      "Epoch 103/1000\n",
      " - 0s - loss: 143.7554 - val_loss: 107.9643\n",
      "Epoch 104/1000\n",
      " - 0s - loss: 141.1339 - val_loss: 106.1514\n",
      "Epoch 105/1000\n",
      " - 0s - loss: 138.8331 - val_loss: 105.7181\n",
      "Epoch 106/1000\n",
      " - 0s - loss: 141.4276 - val_loss: 107.7319\n",
      "Epoch 107/1000\n",
      " - 0s - loss: 142.8513 - val_loss: 109.6068\n",
      "Epoch 108/1000\n",
      " - 0s - loss: 140.1378 - val_loss: 106.9414\n",
      "Epoch 109/1000\n",
      " - 0s - loss: 138.4703 - val_loss: 107.1609\n",
      "Epoch 110/1000\n",
      " - 0s - loss: 140.9187 - val_loss: 107.8843\n",
      "Epoch 00110: early stopping\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1a26b079e8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "cars = df['name']\n",
    "df.drop('name',1,inplace=True)\n",
    "missing_median(df, 'horsepower')\n",
    "x,y = to_xy(df,\"mpg\")\n",
    "# Split into train/test\n",
    "x_train, x_test, y_train, y_test = train_test_split(    \n",
    "    x, y, test_size=0.25, random_state=45)\n",
    "model = Sequential()\n",
    "model.add(Dense(10, input_dim=x.shape[1], activation='relu'))\n",
    "model.add(Dense(10))\n",
    "model.add(Dense(10))\n",
    "model.add(Dense(10))\n",
    "model.add(Dense(1))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=2,epochs=1000)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Square Error\n",
    "\n",
    "The mean square error is the sum of the squared differences between the prediction ($\\hat{y}$) and the expected ($y$).  MSE values are not of a particular unit.  If an MSE value has decreased for a model, that is good.  However, beyond this, there is not much more you can determine.  Low MSE values are desired.\n",
    "\n",
    "$ \\text{MSE} = \\frac{1}{n} \\sum_{i=1}^n \\left(\\hat{y}_i - y_i\\right)^2 $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final score (MSE): 107.88433837890625\n"
     ]
    }
   ],
   "source": [
    "# Predict\n",
    "pred = model.predict(x_test)\n",
    "\n",
    "# Measure MSE error.  \n",
    "score = metrics.mean_squared_error(pred,y_test)\n",
    "print(\"Final score (MSE): {}\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Root Mean Square Error\n",
    "\n",
    "The root mean square (RMSE) is essentially the square root of the MSE.  Because of this, the RMSE error is in the same units as the training data outcome. Low RMSE values are desired.\n",
    "\n",
    "$ \\text{RMSE} = \\sqrt{\\frac{1}{n} \\sum_{i=1}^n \\left(\\hat{y}_i - y_i\\right)^2} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final score (RMSE): 10.386738777160645\n"
     ]
    }
   ],
   "source": [
    "# Measure RMSE error.  RMSE is common for regression.\n",
    "score = np.sqrt(metrics.mean_squared_error(pred,y_test))\n",
    "print(\"Final score (RMSE): {}\".format(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training with Cross-Validation\n",
    "\n",
    "Cross-Validation uses a number of folds, and multiple models, to generate out of sample predictions on the entire dataset.  It is important to note that there will be one model (neural network) for each fold. Each model contributes part of the final out-of-sample prediction.\n",
    "\n",
    "![K-Fold Crossvalidation](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_1_kfold.png \"K-Fold Crossvalidation\")\n",
    "\n",
    "For new data, which is data not present in the training set, predictions from the fold models can be handled in several ways.\n",
    "\n",
    "* Choose the model that had the highest validation score as the final model.\n",
    "* Preset new data to the 5 models and average the result (this is an [enesmble](https://en.wikipedia.org/wiki/Ensemble_learning)).\n",
    "* Retrain a new model (using the same settings as the cross-validation) on the entire dataset.  Train for as many epochs, and with the same hidden layer structure.\n",
    "\n",
    "## Regression with Cross-Validation\n",
    "\n",
    "The following code trains the MPG dataset using a 5-fold cross-validation.  The expected performance of a neural network, of the type trained here, would be the score for the generated out-of-sample predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fold #1\n",
      "Epoch 00161: early stopping\n",
      "Fold score (RMSE): 10.870452880859375\n",
      "Fold #2\n",
      "Epoch 00160: early stopping\n",
      "Fold score (RMSE): 4.573093414306641\n",
      "Fold #3\n",
      "Epoch 00034: early stopping\n",
      "Fold score (RMSE): 4.168812274932861\n",
      "Fold #4\n",
      "Epoch 00317: early stopping\n",
      "Fold score (RMSE): 5.540182113647461\n",
      "Fold #5\n",
      "Epoch 00248: early stopping\n",
      "Fold score (RMSE): 4.2834153175354\n",
      "Final, out of sample score (RMSE): 6.417425632476807\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "from sklearn.model_selection import KFold\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Activation\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "filename_write = os.path.join(path,\"auto-mpg-out-of-sample.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "# Shuffle\n",
    "np.random.seed(42)\n",
    "df = df.reindex(np.random.permutation(df.index))\n",
    "df.reset_index(inplace=True, drop=True)\n",
    "\n",
    "# Preprocess\n",
    "cars = df['name']\n",
    "df.drop('name',1,inplace=True)\n",
    "missing_median(df, 'horsepower')\n",
    "\n",
    "# Encode to a 2D matrix for training\n",
    "x,y = to_xy(df,'mpg')\n",
    "\n",
    "# Cross-Validate\n",
    "kf = KFold(5)\n",
    "    \n",
    "oos_y = []\n",
    "oos_pred = []\n",
    "fold = 0\n",
    "for train, test in kf.split(x):\n",
    "    fold+=1\n",
    "    print(\"Fold #{}\".format(fold))\n",
    "        \n",
    "    x_train = x[train]\n",
    "    y_train = y[train]\n",
    "    x_test = x[test]\n",
    "    y_test = y[test]\n",
    "    \n",
    "    model = Sequential()\n",
    "    model.add(Dense(20, input_dim=x.shape[1], activation='relu'))\n",
    "    model.add(Dense(10, activation='relu'))\n",
    "    model.add(Dense(1))\n",
    "    model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "    \n",
    "    monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "    model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=0,epochs=1000)\n",
    "    \n",
    "    pred = model.predict(x_test)\n",
    "    \n",
    "    oos_y.append(y_test)\n",
    "    oos_pred.append(pred)        \n",
    "\n",
    "    # Measure this fold's RMSE\n",
    "    score = np.sqrt(metrics.mean_squared_error(pred,y_test))\n",
    "    print(\"Fold score (RMSE): {}\".format(score))\n",
    "\n",
    "\n",
    "# Build the oos prediction list and calculate the error.\n",
    "oos_y = np.concatenate(oos_y)\n",
    "oos_pred = np.concatenate(oos_pred)\n",
    "score = np.sqrt(metrics.mean_squared_error(oos_pred,oos_y))\n",
    "print(\"Final, out of sample score (RMSE): {}\".format(score))    \n",
    "    \n",
    "# Write the cross-validated prediction\n",
    "oos_y = pd.DataFrame(oos_y)\n",
    "oos_pred = pd.DataFrame(oos_pred)\n",
    "oosDF = pd.concat( [df, oos_y, oos_pred],axis=1 )\n",
    "oosDF.to_csv(filename_write,index=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification with Cross-Validation\n",
    "\n",
    "The following code trains and fits the iris dataset with Cross-Validation.  It also writes out the out of sample (predictions on the test set) results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fold #1\n",
      "Epoch 00207: early stopping\n",
      "Fold score (accuracy): 1.0\n",
      "Fold #2\n",
      "Epoch 00255: early stopping\n",
      "Fold score (accuracy): 0.9666666666666667\n",
      "Fold #3\n",
      "Epoch 00233: early stopping\n",
      "Fold score (accuracy): 0.9666666666666667\n",
      "Fold #4\n",
      "Epoch 00150: early stopping\n",
      "Fold score (accuracy): 0.9333333333333333\n",
      "Fold #5\n",
      "Epoch 00304: early stopping\n",
      "Fold score (accuracy): 1.0\n",
      "Final score (accuracy): 0.9733333333333334\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "from sklearn.model_selection import KFold\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Activation\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"iris.csv\")\n",
    "filename_write = os.path.join(path,\"iris-out-of-sample.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "# Shuffle\n",
    "np.random.seed(42)\n",
    "df = df.reindex(np.random.permutation(df.index))\n",
    "df.reset_index(inplace=True, drop=True)\n",
    "\n",
    "# Encode to a 2D matrix for training\n",
    "species = encode_text_index(df,\"species\")\n",
    "x,y = to_xy(df,\"species\")\n",
    "\n",
    "# Cross-validate\n",
    "kf = KFold(5)\n",
    "    \n",
    "oos_y = []\n",
    "oos_pred = []\n",
    "fold = 0\n",
    "\n",
    "for train, test in kf.split(x):\n",
    "    fold+=1\n",
    "    print(\"Fold #{}\".format(fold))\n",
    "        \n",
    "    x_train = x[train]\n",
    "    y_train = y[train]\n",
    "    x_test = x[test]\n",
    "    y_test = y[test]\n",
    "    \n",
    "    model = Sequential()\n",
    "    model.add(Dense(50, input_dim=x.shape[1], activation='relu')) # Hidden 1\n",
    "    model.add(Dense(25, activation='relu')) # Hidden 2\n",
    "    model.add(Dense(y.shape[1],activation='softmax')) # Output\n",
    "    model.compile(loss='categorical_crossentropy', optimizer='adam')\n",
    "    monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=25, verbose=1, mode='auto')\n",
    "\n",
    "    model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=0,epochs=1000)\n",
    "    \n",
    "    pred = model.predict(x_test)\n",
    "    \n",
    "    oos_y.append(y_test)\n",
    "    pred = np.argmax(pred,axis=1) # raw probabilities to chosen class (highest probability)\n",
    "    oos_pred.append(pred)        \n",
    "\n",
    "    # Measure this fold's accuracy\n",
    "    y_compare = np.argmax(y_test,axis=1) # For accuracy calculation\n",
    "    score = metrics.accuracy_score(y_compare, pred)\n",
    "    print(\"Fold score (accuracy): {}\".format(score))\n",
    "\n",
    "\n",
    "# Build the oos prediction list and calculate the error.\n",
    "oos_y = np.concatenate(oos_y)\n",
    "oos_pred = np.concatenate(oos_pred)\n",
    "oos_y_compare = np.argmax(oos_y,axis=1) # For accuracy calculation\n",
    "\n",
    "score = metrics.accuracy_score(oos_y_compare, oos_pred)\n",
    "print(\"Final score (accuracy): {}\".format(score))    \n",
    "    \n",
    "# Write the cross-validated prediction\n",
    "oos_y = pd.DataFrame(oos_y)\n",
    "oos_pred = pd.DataFrame(oos_pred)\n",
    "oosDF = pd.concat( [df, oos_y, oos_pred],axis=1 )\n",
    "oosDF.to_csv(filename_write,index=False)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training with both a Cross-Validation and a Holdout Set\n",
    "\n",
    "If you have a considerable amount of data, it is always valuable to set aside a holdout set before you cross-validate.  This hold out set will be the final evaluation before you make use of your model for its real-world use.\n",
    "\n",
    "![Cross Validation and a Holdout Set](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_3_hold_train_val.png \"Cross Validation and a Holdout Set\")\n",
    "\n",
    "The following program makes use of a holdout set, and then still cross-validates.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fold #1\n",
      "Epoch 00059: early stopping\n",
      "Fold score (RMSE): 15.734644889831543\n",
      "Fold #2\n",
      "Fold score (RMSE): 18.667470932006836\n",
      "Fold #3\n",
      "Epoch 00224: early stopping\n",
      "Fold score (RMSE): 3.864037036895752\n",
      "Fold #4\n",
      "Epoch 00020: early stopping\n",
      "Fold score (RMSE): 8.148503303527832\n",
      "Fold #5\n",
      "Epoch 00154: early stopping\n",
      "Fold score (RMSE): 3.963421583175659\n",
      "\n",
      "Cross-validated score (RMSE): 11.796749114990234\n",
      "Holdout score (RMSE): 3.031569242477417\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "from sklearn.model_selection import KFold\n",
    "from keras.callbacks import EarlyStopping\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "filename_write = os.path.join(path,\"auto-mpg-holdout.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "# create feature vector\n",
    "missing_median(df, 'horsepower')\n",
    "df.drop('name',1,inplace=True)\n",
    "encode_text_dummy(df, 'origin')\n",
    "\n",
    "# Shuffle\n",
    "np.random.seed(42)\n",
    "df = df.reindex(np.random.permutation(df.index))\n",
    "df.reset_index(inplace=True, drop=True)\n",
    "\n",
    "# Encode to a 2D matrix for training\n",
    "x,y = to_xy(df,'mpg')\n",
    "\n",
    "\n",
    "# Keep a 10% holdout\n",
    "x_main, x_holdout, y_main, y_holdout = train_test_split(    \n",
    "    x, y, test_size=0.10) \n",
    "\n",
    "\n",
    "# Cross-validate\n",
    "kf = KFold(5)\n",
    "    \n",
    "oos_y = []\n",
    "oos_pred = []\n",
    "fold = 0\n",
    "for train, test in kf.split(x_main):        \n",
    "    fold+=1\n",
    "    print(\"Fold #{}\".format(fold))\n",
    "        \n",
    "    x_train = x_main[train]\n",
    "    y_train = y_main[train]\n",
    "    x_test = x_main[test]\n",
    "    y_test = y_main[test]\n",
    "    \n",
    "    model = Sequential()\n",
    "    model.add(Dense(20, input_dim=x.shape[1], activation='relu'))\n",
    "    model.add(Dense(5, activation='relu'))\n",
    "    model.add(Dense(1))\n",
    "    model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "    \n",
    "    monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "    model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=0,epochs=1000)\n",
    "    \n",
    "    pred = model.predict(x_test)\n",
    "    \n",
    "    oos_y.append(y_test)\n",
    "    oos_pred.append(pred) \n",
    "\n",
    "    # Measure accuracy\n",
    "    score = np.sqrt(metrics.mean_squared_error(pred,y_test))\n",
    "    print(\"Fold score (RMSE): {}\".format(score))\n",
    "\n",
    "\n",
    "# Build the oos prediction list and calculate the error.\n",
    "oos_y = np.concatenate(oos_y)\n",
    "oos_pred = np.concatenate(oos_pred)\n",
    "score = np.sqrt(metrics.mean_squared_error(oos_pred,oos_y))\n",
    "print()\n",
    "print(\"Cross-validated score (RMSE): {}\".format(score))    \n",
    "    \n",
    "# Write the cross-validated prediction (from the last neural network)\n",
    "holdout_pred = model.predict(x_holdout)\n",
    "\n",
    "score = np.sqrt(metrics.mean_squared_error(holdout_pred,y_holdout))\n",
    "print(\"Holdout score (RMSE): {}\".format(score))    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scikit-Learn Versions: model_selection vs cross_validation\n",
    "\n",
    "Scikit-Learn changed a bit in how cross-validation is handled.  Both versions still work, but you should use the **sklearn.model_selection** import, rather than **sklearn.cross_validation**.  The following shows both the new and old forms of cross-validation.  All examples from this class will use the newer form.\n",
    "\n",
    "The following two sections show both forms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: 2018-12-14: sklearn.cross_validation is now totally gone from sklearn, if the code\n",
    "# below still works on your system, you REALLY need to update your software. :-)\n",
    "\n",
    "# Older scikit-learn syntax for splits/cross-validation\n",
    "# Still valid, but going away.  Do not use.\n",
    "# (Note the red box warning below)\n",
    "\n",
    "#from sklearn.cross_validation import train_test_split\n",
    "#from sklearn.cross_validation import KFold\n",
    "\n",
    "#path = \"./data/\"\n",
    "\n",
    "#filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "#df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "#kf = KFold(len(df), n_folds=5)\n",
    "\n",
    "#fold = 0\n",
    "#for train, test in kf:        \n",
    "#    fold+=1\n",
    "#    print(\"Fold #{}: train={}, test={}\".format(fold,len(train),len(test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fold #1: train=318, test=80\n",
      "Fold #2: train=318, test=80\n",
      "Fold #3: train=318, test=80\n",
      "Fold #4: train=319, test=79\n",
      "Fold #5: train=319, test=79\n"
     ]
    }
   ],
   "source": [
    "# Newer scikit-learn syntax for splits/cross-validation\n",
    "# Use this method (as shown above)\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import KFold\n",
    "\n",
    "path = \"./data/\"\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "kf = KFold(5)\n",
    "\n",
    "fold = 0\n",
    "for train, test in kf.split(df):        \n",
    "    fold+=1\n",
    "    print(\"Fold #{}: train={}, test={}\".format(fold,len(train),len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How Kaggle Competitions are Scored\n",
    "\n",
    "[Kaggle](https://www.kaggle.com/) is a platform for competitive data science. Competitions are posted onto Kaggle by companies seeking the best model for their data.  Competing in a Kaggle competition is quite a bit of work, I've [competed in one Kaggle competition](https://www.kaggle.com/jeffheaton).   \n",
    "\n",
    "Kaggle awards \"tiers\", such as:\n",
    "\n",
    "* Kaggle Grandmaster\n",
    "* Kaggle Master\n",
    "* Kaggle Expert\n",
    "\n",
    "Your [tier](https://www.kaggle.com/progression) is based on your performance in past competitions.  \n",
    "\n",
    "To compete in Kaggle you simply provide predictions for a dataset that they post.  You do not need to submit any code.  Your prediction output will place you onto the [leaderboard of a competition](https://www.kaggle.com/c/otto-group-product-classification-challenge/leaderboard/public).\n",
    "\n",
    "![How Kaggle Competitions are Scored](https://raw.githubusercontent.com/jeffheaton/t81_558_deep_learning/master/images/class_3_kaggle.png \"How Kaggle Competitions are Scored\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "An original dataset is sent to Kaggle by the company.  From this dataset, Kaggle posts public data that includes \"train\" and \"test.  For the \"train\" data, the outcomes (y) are provided.  For the test data, no outcomes are provided.  Your submission file contains your predictions for the \"test data\".  When you submit your results, Kaggle will calculate a score on part of your prediction data.  They do not publish want part of the submission data are used for the public and private leaderboard scores (this is a secret to prevent overfitting).  While the competition is still running, Kaggle publishes the public leaderboard ranks.  Once the competition ends, the private leaderboard is revealed to designate the true winners.  Due to overfitting, there is sometimes an upset in positions when the final private leaderboard is revealed.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Managing Hyperparameters\n",
    "\n",
    "There are many different settings that you can use for a neural network.  These can affect performance.  The following code changes some of these, beyond their default values:\n",
    "\n",
    "* **activation:** relu, sigmoid, tanh\n",
    "* Layers/Neuron Counts\n",
    "* **optimizer:** adam, sgd, rmsprop, and [others](https://keras.io/optimizers/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 00042: early stopping\n",
      "Score (RMSE): 8.010347366333008\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib.pyplot import figure, show\n",
    "from sklearn.model_selection import train_test_split\n",
    "import pandas as pd\n",
    "import os\n",
    "import numpy as np\n",
    "from sklearn import metrics\n",
    "from scipy.stats import zscore\n",
    "import tensorflow as tf\n",
    "\n",
    "path = \"./data/\"\n",
    "preprocess = False\n",
    "\n",
    "filename_read = os.path.join(path,\"auto-mpg.csv\")\n",
    "df = pd.read_csv(filename_read,na_values=['NA','?'])\n",
    "\n",
    "# create feature vector\n",
    "missing_median(df, 'horsepower')\n",
    "encode_text_dummy(df, 'origin')\n",
    "df.drop('name',1,inplace=True)\n",
    "if preprocess:\n",
    "    encode_numeric_zscore(df, 'horsepower')\n",
    "    encode_numeric_zscore(df, 'weight')\n",
    "    encode_numeric_zscore(df, 'cylinders')\n",
    "    encode_numeric_zscore(df, 'displacement')\n",
    "    encode_numeric_zscore(df, 'acceleration')\n",
    "\n",
    "# Encode to a 2D matrix for training\n",
    "x,y = to_xy(df,'mpg')\n",
    "\n",
    "# Split into train/test\n",
    "x_train, x_test, y_train, y_test = train_test_split(\n",
    "    x, y, test_size=0.20, random_state=42)\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Dense(100, input_dim=x.shape[1], activation='relu'))\n",
    "model.add(Dense(50, activation='relu'))\n",
    "model.add(Dense(25, activation='relu'))\n",
    "model.add(Dense(1))\n",
    "model.compile(loss='mean_squared_error', optimizer='adam')\n",
    "monitor = EarlyStopping(monitor='val_loss', min_delta=1e-3, patience=5, verbose=1, mode='auto')\n",
    "model.fit(x_train,y_train,validation_data=(x_test,y_test),callbacks=[monitor],verbose=0,epochs=1000)\n",
    "\n",
    "# Predict and measure RMSE\n",
    "pred = model.predict(x_test)\n",
    "score = np.sqrt(metrics.mean_squared_error(pred,y_test))\n",
    "print(\"Score (RMSE): {}\".format(score))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Error Calculation from Scratch\n",
    "\n",
    "We will now look at how to calculate RMSE and logloss by hand.  You will need to be able to perform this for the midterm.\n",
    "\n",
    "\n",
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score (MSE): 0.14200000000000007\n",
      "Score (RMSE): 0.37682887362833556\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "import numpy as np\n",
    "\n",
    "predicted = [1.1,1.9,3.4,4.2,4.3]\n",
    "expected = [1,2,3,4,5]\n",
    "\n",
    "score_mse = metrics.mean_squared_error(predicted,expected)\n",
    "score_rmse = np.sqrt(score_mse)\n",
    "print(\"Score (MSE): {}\".format(score_mse))\n",
    "print(\"Score (RMSE): {}\".format(score_rmse))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score (MSE): 0.14200000000000007\n",
      "Score (RMSE): 0.37682887362833556\n"
     ]
    }
   ],
   "source": [
    "score_mse = ((predicted[0]-expected[0])**2 + (predicted[1]-expected[1])**2 \n",
    "+ (predicted[2]-expected[2])**2 + (predicted[3]-expected[3])**2\n",
    "+ (predicted[4]-expected[4])**2)/len(predicted)\n",
    "score_rmse = np.sqrt(score_mse)\n",
    "    \n",
    "print(\"Score (MSE): {}\".format(score_mse))\n",
    "print(\"Score (RMSE): {}\".format(score_rmse))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "We will now look at how to calculate a logloss by hand. For this we look at a binary prediction. The expected is always 0 or 1. The predicted is some number between 0-1 that indicates the probability true (1). Therefore a prediction of 1.0 is completely correct if the expected is 1 and completely wrong if the expected is 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06678801305495843\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "expected = [1,1,0,0,0]\n",
    "predicted = [0.9,0.99,0.1,0.05,0.06]\n",
    "\n",
    "print(metrics.log_loss(expected,predicted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we attempt to calculate the same logloss manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score Logloss 0.06678801305495843\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "score_logloss = (np.log(1.0-np.abs(expected[0]-predicted[0]))+\\\n",
    "np.log(1.0-np.abs(expected[1]-predicted[1]))+\\\n",
    "np.log(1.0-np.abs(expected[2]-predicted[2]))+\\\n",
    "np.log(1.0-np.abs(expected[3]-predicted[3]))+\\\n",
    "np.log(1.0-np.abs(expected[4]-predicted[4])))\\\n",
    "*(-1/len(predicted))\n",
    "\n",
    "print(f'Score Logloss {score_logloss}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Module 4 Assignment\n",
    "\n",
    "You can find the first assignmeht here: [assignment 4](https://github.com/jeffheaton/t81_558_deep_learning/blob/master/assignments/assignment_yourname_class1.ipynb)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3.6 (wustl)",
   "language": "python",
   "name": "wustl"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}