word_embeddings.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Sukhman723/my_projects/blob/main/google_colab/word_embeddings.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lPNLDXs7qdFq",
        "outputId": "6b778b47-2672-418f-d619-e2af1cae5cf9"
      },
      "id": "lPNLDXs7qdFq",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqI2Dim-qQjQ"
      },
      "source": [
        "<a name='1'></a>\n",
        "## 1 - The Continuous Bag of Words Model\n",
        "\n",
        "Let's take a look at the following sentence: \n",
        ">**'I am happy because I am learning'**. \n",
        "\n",
        "- In continuous bag of words (CBOW) modeling, we try to predict the center word given a few context words (the words around the center word).\n",
        "- For example, if you were to choose a context half-size of say $C = 2$, then you would try to predict the word **happy** given the context that includes 2 words before and 2 words after the center word:\n",
        "\n",
        "> $C$ words before: [I, am] \n",
        "\n",
        "> $C$ words after: [because, I] \n",
        "\n",
        "- In other words:\n",
        "\n",
        "$$context = [I,am, because, I]$$\n",
        "$$target = happy$$\n",
        "\n",
        "The structure of your model will look like this:\n",
        "\n",
        "<div style=\"width:image width px; font-size:100%; text-align:center;\"><img src='images/word2.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:600px;height:250px;\" /> Figure 1 </div>\n",
        "\n",
        "Where $\\bar x$ is the average of all the one hot vectors of the context words. \n",
        "\n",
        "<div style=\"width:image width px; font-size:100%; text-align:center;\"><img src='images/mean_vec2.png' alt=\"alternate text\" width=\"width\" height=\"height\" style=\"width:600px;height:250px;\" /> Figure 2 </div>\n",
        "\n",
        "Once you have encoded all the context words, you can use $\\bar x$ as the input to your model. \n",
        "\n",
        "The architecture you will be implementing is as follows:\n",
        "\n",
        "\\begin{align}\n",
        " h &= W_1 \\  X + b_1  \\tag{1} \\\\\n",
        " a &= ReLU(h)  \\tag{2} \\\\\n",
        " z &= W_2 \\  a + b_2   \\tag{3} \\\\\n",
        " \\hat y &= softmax(z)   \\tag{4} \\\\\n",
        "\\end{align}"
      ],
      "id": "TqI2Dim-qQjQ"
    },
    {
      "cell_type": "code",
      "source": [
        "cd /content/drive/MyDrive/Code_files_and_data/"
      ],
      "metadata": {
        "id": "VofMkL6GqsFh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ecd67aef-ef2a-48e3-d978-34cc685bcf90"
      },
      "id": "VofMkL6GqsFh",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/content/drive/MyDrive/Code_files\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pwd"
      ],
      "metadata": {
        "id": "Sh5O_5N47XM2",
        "outputId": "8522d616-5695-4c18-c9e7-dfc2f4be054a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        }
      },
      "id": "Sh5O_5N47XM2",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'/content/drive/MyDrive/Code_files_and_data'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
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    {
      "cell_type": "code",
      "source": [
        "!ls"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CzelyBD2qxZp",
        "outputId": "76672b62-30b6-43e7-bb1c-d250950596bf"
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      "id": "CzelyBD2qxZp",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "data  utils2.py  w4_unittest.py\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HovIW0U5qQjS",
        "outputId": "2590f621-7a7c-4d01-e523-9daf0a35537d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "[nltk_data] Downloading package punkt to /root/nltk_data...\n",
            "[nltk_data]   Package punkt is already up-to-date!\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "# Import Python libraries and helper functions (in utils2) \n",
        "import nltk\n",
        "from nltk.tokenize import word_tokenize\n",
        "import numpy as np\n",
        "from collections import Counter\n",
        "from utils2 import sigmoid, get_batches, compute_pca, get_dict\n",
        "import w4_unittest\n",
        "\n",
        "nltk.download('punkt')"
      ],
      "id": "HovIW0U5qQjS"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fFFZNRfNqQjU"
      },
      "outputs": [],
      "source": [
        "# Download sentence tokenizer\n",
        "nltk.data.path.append('.')"
      ],
      "id": "fFFZNRfNqQjU"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jTA4VEhdqQjW",
        "outputId": "610eb7bc-500b-45d6-828e-b76293443005",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of tokens: 60976 \n",
            " ['o', 'for', 'a', 'muse', 'of', 'fire', '.', 'that', 'would', 'ascend', 'the', 'brightest', 'heaven', 'of', 'invention']\n"
          ]
        }
      ],
      "source": [
        "# Load, tokenize and process the data\n",
        "import re                                                           #  Load the Regex-modul\n",
        "with open('./data/shakespeare.txt') as f:\n",
        "    data = f.read()                                                 #  Read in the data\n",
        "data = re.sub(r'[,!?;-]', '.',data)                                 #  Punktuations are replaced by .\n",
        "data = nltk.word_tokenize(data)                                     #  Tokenize string to words\n",
        "data = [ ch.lower() for ch in data if ch.isalpha() or ch == '.']    #  Lower case and drop non-alphabetical tokens\n",
        "print(\"Number of tokens:\", len(data),'\\n', data[:15])               #  print data sample"
      ],
      "id": "jTA4VEhdqQjW"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qDUk4i7fqQja",
        "outputId": "2a807a20-5024-471f-d6ce-25c67244f9bd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Size of vocabulary:  5775\n",
            "Most frequent tokens:  [('.', 9630), ('the', 1521), ('and', 1394), ('i', 1257), ('to', 1159), ('of', 1093), ('my', 857), ('that', 781), ('in', 770), ('a', 752), ('you', 748), ('is', 630), ('not', 559), ('for', 467), ('it', 460), ('with', 441), ('his', 434), ('but', 417), ('me', 417), ('your', 397)]\n"
          ]
        }
      ],
      "source": [
        "# Compute the frequency distribution of the words in the dataset (vocabulary)\n",
        "fdist = nltk.FreqDist(word for word in data)\n",
        "print(\"Size of vocabulary: \",len(fdist) )\n",
        "print(\"Most frequent tokens: \",fdist.most_common(20) ) # print the 20 most frequent words and their freq."
      ],
      "id": "qDUk4i7fqQja"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M4MVrPJaqQjc"
      },
      "source": [
        "#### Mapping words to indices and indices to words\n",
        "We provide a helper function to create a dictionary that maps words to indices and indices to words."
      ],
      "id": "M4MVrPJaqQjc"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AytO6XJ-qQjd",
        "outputId": "a9e9b64d-7ddc-4273-faab-f781945c4a5f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Size of vocabulary:  5775\n"
          ]
        }
      ],
      "source": [
        "# get_dict creates two dictionaries, converting words to indices and viceversa.\n",
        "word2Ind, Ind2word = get_dict(data)\n",
        "V = len(word2Ind)\n",
        "print(\"Size of vocabulary: \", V)"
      ],
      "id": "AytO6XJ-qQjd"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1zQRovJBqQjf",
        "outputId": "832f9734-668a-4208-a6a8-6dd75c848516",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Index of the word 'king' :   2744\n",
            "Word which has index 2743:   kinds\n"
          ]
        }
      ],
      "source": [
        "# example of word to index mapping\n",
        "print(\"Index of the word 'king' :  \",word2Ind['king'] )\n",
        "print(\"Word which has index 2743:  \",Ind2word[2743] )"
      ],
      "id": "1zQRovJBqQjf"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_HI0zExdqQjh"
      },
      "outputs": [],
      "source": [
        "# UNIT TEST COMMENT: Candidate for Table Driven Tests\n",
        "# UNQ_C1 GRADED FUNCTION: initialize_model\n",
        "def initialize_model(N,V, random_seed=1):\n",
        "    '''\n",
        "    Inputs: \n",
        "        N:  dimension of hidden vector \n",
        "        V:  dimension of vocabulary\n",
        "        random_seed: random seed for consistent results in the unit tests\n",
        "     Outputs: \n",
        "        W1, W2, b1, b2: initialized weights and biases\n",
        "    '''\n",
        "    \n",
        "    ### START CODE HERE (Replace instances of 'None' with your code) ###\n",
        "    np.random.seed(random_seed)\n",
        "    # W1 has shape (N,V)\n",
        "    W1 = 1 * np.random.rand(N, V)\n",
        "    \n",
        "    # W2 has shape (V,N)\n",
        "    W2 = 1 * np.random.rand(V, N)\n",
        "    \n",
        "    # b1 has shape (N,1)\n",
        "    b1 = 1 * np.random.rand(N, 1)\n",
        "    \n",
        "    # b2 has shape (V,1)\n",
        "    b2 = 1 * np.random.rand(V, 1)\n",
        "    \n",
        "    ### END CODE HERE ###\n",
        "    return W1, W2, b1, b2"
      ],
      "id": "_HI0zExdqQjh"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ORemU9ZjqQji",
        "outputId": "00887aa6-5e76-4230-8060-1758f8f1f274",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tmp_W1.shape: (4, 10)\n",
            "tmp_W2.shape: (10, 4)\n",
            "tmp_b1.shape: (4, 1)\n",
            "tmp_b2.shape: (10, 1)\n"
          ]
        }
      ],
      "source": [
        "# Test your function example.\n",
        "tmp_N = 4\n",
        "tmp_V = 10\n",
        "tmp_W1, tmp_W2, tmp_b1, tmp_b2 = initialize_model(tmp_N,tmp_V)\n",
        "assert tmp_W1.shape == ((tmp_N,tmp_V))\n",
        "assert tmp_W2.shape == ((tmp_V,tmp_N))\n",
        "print(f\"tmp_W1.shape: {tmp_W1.shape}\")\n",
        "print(f\"tmp_W2.shape: {tmp_W2.shape}\")\n",
        "print(f\"tmp_b1.shape: {tmp_b1.shape}\")\n",
        "print(f\"tmp_b2.shape: {tmp_b2.shape}\")"
      ],
      "id": "ORemU9ZjqQji"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uixvFnQVqQjk"
      },
      "outputs": [],
      "source": [
        "# UNIT TEST COMMENT: Candidate for Table Driven Tests\n",
        "# UNQ_C2 GRADED FUNCTION: softmax\n",
        "def softmax(z):\n",
        "    '''\n",
        "    Inputs: \n",
        "        z: output scores from the hidden layer\n",
        "    Outputs: \n",
        "        yhat: prediction (estimate of y)\n",
        "    '''\n",
        "    ### START CODE HERE (Replace instances of 'None' with your own code) ###\n",
        "    # Calculate yhat (softmax)\n",
        "    e_z = np.exp(z)\n",
        "    sum_e_z = np.sum(e_z, axis=0, keepdims=True)\n",
        "    yhat = e_z / sum_e_z\n",
        "    ### END CODE HERE ###\n",
        "    return yhat"
      ],
      "id": "uixvFnQVqQjk"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UYPZ41jLqQjk",
        "outputId": "84695e59-3271-4144-dbe2-0291cb883e7e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "array([[0.5       , 0.73105858, 0.88079708],\n",
              "       [0.5       , 0.26894142, 0.11920292]])"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Test the function\n",
        "tmp = np.array([[1,2,3],\n",
        "                [1,1,1]\n",
        "               ])\n",
        "tmp_sm = softmax(tmp)\n",
        "display(tmp_sm)"
      ],
      "id": "UYPZ41jLqQjk"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z9RK4JhAqQjn"
      },
      "outputs": [],
      "source": [
        "# UNIT TEST COMMENT: Candidate for Table Driven Tests\n",
        "# UNQ_C3 GRADED FUNCTION: forward_prop\n",
        "def forward_prop(x, W1, W2, b1, b2):\n",
        "    '''\n",
        "    Inputs: \n",
        "        x:  average one hot vector for the context \n",
        "        W1, W2, b1, b2:  matrices and biases to be learned\n",
        "     Outputs: \n",
        "        z:  output score vector\n",
        "    '''\n",
        "    \n",
        "    ### START CODE HERE (Replace instances of 'None' with your own code) ###\n",
        "    # Calculate h\n",
        "    h = np.dot(W1, x) + b1\n",
        "  \n",
        "    # Apply the relu on h, \n",
        "    # store the relu in h\n",
        "    h[h < 0] = 0\n",
        "\n",
        "    # Calculate z\n",
        "    z = np.dot(W2, h) + b2\n",
        "\n",
        "    ### END CODE HERE ###\n",
        "\n",
        "    return z, h"
      ],
      "id": "z9RK4JhAqQjn"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bgo2lqKxqQjn",
        "outputId": "50e2b4bd-d040-4204-b407-30a5645c65e4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "tmp_x = np.array([[0,1,0]]).T\n",
        "tmp_x.shape"
      ],
      "id": "bgo2lqKxqQjn"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rnrvxBO6qQjo",
        "outputId": "febe7abd-857e-4d34-9a44-f24a4f2d3660",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x has shape (3, 1)\n",
            "N is 2 and vocabulary size V is 3\n",
            "call forward_prop\n",
            "\n",
            "z has shape (3, 1)\n",
            "z has values:\n",
            "[[0.55379268]\n",
            " [1.58960774]\n",
            " [1.50722933]]\n",
            "\n",
            "h has shape (2, 1)\n",
            "h has values:\n",
            "[[0.92477674]\n",
            " [1.02487333]]\n"
          ]
        }
      ],
      "source": [
        "# Test the function\n",
        "\n",
        "# Create some inputs\n",
        "tmp_N = 2\n",
        "tmp_V = 3\n",
        "tmp_x = np.array([[0,1,0]]).T\n",
        "#print(tmp_x)\n",
        "tmp_W1, tmp_W2, tmp_b1, tmp_b2 = initialize_model(N=tmp_N,V=tmp_V, random_seed=1)\n",
        "\n",
        "print(f\"x has shape {tmp_x.shape}\")\n",
        "print(f\"N is {tmp_N} and vocabulary size V is {tmp_V}\")\n",
        "\n",
        "# call function\n",
        "tmp_z, tmp_h = forward_prop(tmp_x, tmp_W1, tmp_W2, tmp_b1, tmp_b2)\n",
        "print(\"call forward_prop\")\n",
        "print()\n",
        "# Look at output\n",
        "print(f\"z has shape {tmp_z.shape}\")\n",
        "print(\"z has values:\")\n",
        "print(tmp_z)\n",
        "\n",
        "print()\n",
        "\n",
        "print(f\"h has shape {tmp_h.shape}\")\n",
        "print(\"h has values:\")\n",
        "print(tmp_h)"
      ],
      "id": "rnrvxBO6qQjo"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dDq6YbaoqQjp"
      },
      "source": [
        "<a name='2.4'></a>\n",
        "### 2.4 - Cost Function\n",
        "\n",
        "- We have implemented the *cross-entropy* cost function for you."
      ],
      "id": "dDq6YbaoqQjp"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "T2zHOvNUqQjp"
      },
      "outputs": [],
      "source": [
        "# compute_cost: cross-entropy cost function\n",
        "def compute_cost(y, yhat, batch_size):\n",
        "\n",
        "    # cost function \n",
        "    logprobs = np.multiply(np.log(yhat),y)\n",
        "    cost = - 1/batch_size * np.sum(logprobs)\n",
        "    cost = np.squeeze(cost)\n",
        "    return cost"
      ],
      "id": "T2zHOvNUqQjp"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YXkpzLs-qQjq",
        "outputId": "4da71839-e0de-4dca-ef14-6adf47091700",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tmp_x.shape (5775, 4)\n",
            "tmp_y.shape (5775, 4)\n",
            "tmp_W1.shape (50, 5775)\n",
            "tmp_W2.shape (5775, 50)\n",
            "tmp_b1.shape (50, 1)\n",
            "tmp_b2.shape (5775, 1)\n",
            "tmp_z.shape: (5775, 4)\n",
            "tmp_h.shape: (50, 4)\n",
            "tmp_yhat.shape: (5775, 4)\n",
            "call compute_cost\n",
            "tmp_cost 10.4074\n"
          ]
        }
      ],
      "source": [
        "# Test the function\n",
        "tmp_C = 2\n",
        "tmp_N = 50\n",
        "tmp_batch_size = 4\n",
        "tmp_word2Ind, tmp_Ind2word = get_dict(data)\n",
        "tmp_V = len(word2Ind)\n",
        "\n",
        "tmp_x, tmp_y = next(get_batches(data, tmp_word2Ind, tmp_V,tmp_C, tmp_batch_size))\n",
        "        \n",
        "print(f\"tmp_x.shape {tmp_x.shape}\")\n",
        "print(f\"tmp_y.shape {tmp_y.shape}\")\n",
        "\n",
        "tmp_W1, tmp_W2, tmp_b1, tmp_b2 = initialize_model(tmp_N,tmp_V)\n",
        "\n",
        "print(f\"tmp_W1.shape {tmp_W1.shape}\")\n",
        "print(f\"tmp_W2.shape {tmp_W2.shape}\")\n",
        "print(f\"tmp_b1.shape {tmp_b1.shape}\")\n",
        "print(f\"tmp_b2.shape {tmp_b2.shape}\")\n",
        "\n",
        "tmp_z, tmp_h = forward_prop(tmp_x, tmp_W1, tmp_W2, tmp_b1, tmp_b2)\n",
        "print(f\"tmp_z.shape: {tmp_z.shape}\")\n",
        "print(f\"tmp_h.shape: {tmp_h.shape}\")\n",
        "\n",
        "tmp_yhat = softmax(tmp_z)\n",
        "print(f\"tmp_yhat.shape: {tmp_yhat.shape}\")\n",
        "\n",
        "tmp_cost = compute_cost(tmp_y, tmp_yhat, tmp_batch_size)\n",
        "print(\"call compute_cost\")\n",
        "print(f\"tmp_cost {tmp_cost:.4f}\")"
      ],
      "id": "YXkpzLs-qQjq"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_ejcIzEXqQjr"
      },
      "source": [
        "<a name='2.5'></a>\n",
        "### 2.5 - Training the Model - Backpropagation\n",
        "\n",
        "<a name='ex-4'></a>\n",
        "### Exercise 4 - back_prop\n",
        "Now that you have understood how the CBOW model works, you will train it. <br>\n",
        "You created a function for the forward propagation. Now you will implement a function that computes the gradients to backpropagate the errors.\n"
      ],
      "id": "_ejcIzEXqQjr"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nyCr0bpeqQjs"
      },
      "outputs": [],
      "source": [
        "def relu(z):\n",
        "    result = z.copy()\n",
        "    result[result < 0] = 0\n",
        "    \n",
        "    return result"
      ],
      "id": "nyCr0bpeqQjs"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y4ZNWjhjqQjs"
      },
      "outputs": [],
      "source": [
        "# UNIT TEST COMMENT: Candidate for Table Driven Tests\n",
        "# UNQ_C4 GRADED FUNCTION: back_prop\n",
        "def back_prop(x, yhat, y, h, W1, W2, b1, b2, batch_size):\n",
        "    '''\n",
        "    Inputs: \n",
        "        x:  average one hot vector for the context \n",
        "        yhat: prediction (estimate of y)\n",
        "        y:  target vector\n",
        "        h:  hidden vector (see eq. 1)\n",
        "        W1, W2, b1, b2:  matrices and biases  \n",
        "        batch_size: batch size \n",
        "     Outputs: \n",
        "        grad_W1, grad_W2, grad_b1, grad_b2:  gradients of matrices and biases   \n",
        "    '''\n",
        "    ### START CODE HERE (Replace instanes of 'None' with your code) ###\n",
        "    # Compute l1 as W2^T (Yhat - Y)\n",
        "    # and re-use it whenever you see W2^T (Yhat - Y) used to compute a gradient\n",
        "    l1 = np.dot(W2.T, yhat - y)\n",
        "\n",
        "    # Apply relu to l1\n",
        "    l1 = relu(l1)\n",
        "\n",
        "    # compute the gradient for W1\n",
        "    grad_W1 = np.dot(l1, x.T)\n",
        "\n",
        "    # Compute gradient of W2\n",
        "    grad_W2 = np.dot(yhat - y, h.T)\n",
        "    \n",
        "    # compute gradient for b1\n",
        "    grad_b1 = l1\n",
        "\n",
        "    # compute gradient for b2\n",
        "    grad_b2 = yhat - y\n",
        "    ### END CODE HERE ####\n",
        "    \n",
        "    return grad_W1, grad_W2, grad_b1, grad_b2"
      ],
      "id": "Y4ZNWjhjqQjs"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xYnzT4aaqQjt",
        "outputId": "f84c3987-3009-46e6-d0ef-1f30bbe76ae1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "get a batch of data\n",
            "tmp_x.shape (5775, 4)\n",
            "tmp_y.shape (5775, 4)\n",
            "\n",
            "Initialize weights and biases\n",
            "tmp_W1.shape (50, 5775)\n",
            "tmp_W2.shape (5775, 50)\n",
            "tmp_b1.shape (50, 1)\n",
            "tmp_b2.shape (5775, 1)\n",
            "\n",
            "Forwad prop to get z and h\n",
            "tmp_z.shape: (5775, 4)\n",
            "tmp_h.shape: (50, 4)\n",
            "\n",
            "Get yhat by calling softmax\n",
            "tmp_yhat.shape: (5775, 4)\n",
            "\n",
            "call back_prop\n",
            "tmp_grad_W1.shape (50, 5775)\n",
            "tmp_grad_W2.shape (5775, 50)\n",
            "tmp_grad_b1.shape (50, 4)\n",
            "tmp_grad_b2.shape (5775, 4)\n"
          ]
        }
      ],
      "source": [
        "# Test the function\n",
        "tmp_C = 2\n",
        "tmp_N = 50\n",
        "tmp_batch_size = 4\n",
        "tmp_word2Ind, tmp_Ind2word = get_dict(data)\n",
        "tmp_V = len(word2Ind)\n",
        "\n",
        "\n",
        "# get a batch of data\n",
        "tmp_x, tmp_y = next(get_batches(data, tmp_word2Ind, tmp_V,tmp_C, tmp_batch_size))\n",
        "\n",
        "print(\"get a batch of data\")\n",
        "print(f\"tmp_x.shape {tmp_x.shape}\")\n",
        "print(f\"tmp_y.shape {tmp_y.shape}\")\n",
        "\n",
        "print()\n",
        "print(\"Initialize weights and biases\")\n",
        "tmp_W1, tmp_W2, tmp_b1, tmp_b2 = initialize_model(tmp_N,tmp_V)\n",
        "\n",
        "print(f\"tmp_W1.shape {tmp_W1.shape}\")\n",
        "print(f\"tmp_W2.shape {tmp_W2.shape}\")\n",
        "print(f\"tmp_b1.shape {tmp_b1.shape}\")\n",
        "print(f\"tmp_b2.shape {tmp_b2.shape}\")\n",
        "\n",
        "print()\n",
        "print(\"Forwad prop to get z and h\")\n",
        "tmp_z, tmp_h = forward_prop(tmp_x, tmp_W1, tmp_W2, tmp_b1, tmp_b2)\n",
        "print(f\"tmp_z.shape: {tmp_z.shape}\")\n",
        "print(f\"tmp_h.shape: {tmp_h.shape}\")\n",
        "\n",
        "print()\n",
        "print(\"Get yhat by calling softmax\")\n",
        "tmp_yhat = softmax(tmp_z)\n",
        "print(f\"tmp_yhat.shape: {tmp_yhat.shape}\")\n",
        "\n",
        "tmp_m = (2*tmp_C)\n",
        "tmp_grad_W1, tmp_grad_W2, tmp_grad_b1, tmp_grad_b2 = back_prop(tmp_x, tmp_yhat, tmp_y, tmp_h, tmp_W1, tmp_W2, tmp_b1, tmp_b2, tmp_batch_size)\n",
        "\n",
        "print()\n",
        "print(\"call back_prop\")\n",
        "print(f\"tmp_grad_W1.shape {tmp_grad_W1.shape}\")\n",
        "print(f\"tmp_grad_W2.shape {tmp_grad_W2.shape}\")\n",
        "print(f\"tmp_grad_b1.shape {tmp_grad_b1.shape}\")\n",
        "print(f\"tmp_grad_b2.shape {tmp_grad_b2.shape}\")"
      ],
      "id": "xYnzT4aaqQjt"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "So3jbgfQqQju"
      },
      "source": [
        "<a name='2.6'></a>\n",
        "### 2.6 - Gradient Descent\n",
        "\n",
        "<a name='ex-5'></a>\n",
        "### Exercise 5 - gradient_descent\n",
        "Now that you have implemented a function to compute the gradients, you will implement batch gradient descent over your training set. \n",
        "\n",
        "**Hint:** For that, you will use `initialize_model` and the `back_prop` functions which you just created (and the `compute_cost` function). You can also use the provided `get_batches` helper function:\n",
        "\n",
        "```for x, y in get_batches(data, word2Ind, V, C, batch_size):```\n",
        "\n",
        "```...```\n",
        "\n",
        "Also: print the cost after each batch is processed (use batch size = 128)"
      ],
      "id": "So3jbgfQqQju"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GVCwC6PjqQju"
      },
      "outputs": [],
      "source": [
        "# UNIT TEST COMMENT: Candidate for Table Driven Tests\n",
        "# UNQ_C5 GRADED FUNCTION: gradient_descent\n",
        "def gradient_descent(data, word2Ind, N, V, num_iters, alpha=0.03, \n",
        "                     random_seed=282, initialize_model=initialize_model, \n",
        "                     get_batches=get_batches, forward_prop=forward_prop, \n",
        "                     softmax=softmax, compute_cost=compute_cost, \n",
        "                     back_prop=back_prop):\n",
        "    \n",
        "    '''\n",
        "    This is the gradient_descent function\n",
        "    \n",
        "      Inputs: \n",
        "        data:      text\n",
        "        word2Ind:  words to Indices\n",
        "        N:         dimension of hidden vector  \n",
        "        V:         dimension of vocabulary \n",
        "        num_iters: number of iterations  \n",
        "        random_seed: random seed to initialize the model's matrices and vectors\n",
        "        initialize_model: your implementation of the function to initialize the model\n",
        "        get_batches: function to get the data in batches\n",
        "        forward_prop: your implementation of the function to perform forward propagation\n",
        "        softmax: your implementation of the softmax function\n",
        "        compute_cost: cost function (Cross entropy)\n",
        "        back_prop: your implementation of the function to perform backward propagation\n",
        "     Outputs: \n",
        "        W1, W2, b1, b2:  updated matrices and biases after num_iters iterations\n",
        "\n",
        "    '''\n",
        "    W1, W2, b1, b2 = initialize_model(N,V, random_seed=random_seed) #W1=(N,V) and W2=(V,N)\n",
        "\n",
        "    batch_size = 128\n",
        "#    batch_size = 512\n",
        "    iters = 0\n",
        "    C = 2 \n",
        "    \n",
        "    for x, y in get_batches(data, word2Ind, V, C, batch_size):\n",
        "        ### START CODE HERE (Replace instances of 'None' with your own code) ###                \n",
        "        # get z and h\n",
        "        z, h = forward_prop(x, W1, W2, b1, b2)\n",
        "                \n",
        "        # get yhat\n",
        "        yhat = softmax(z)\n",
        "        \n",
        "        # get cost\n",
        "        cost = compute_cost(y, yhat, batch_size)\n",
        "        if ( (iters+1) % 10 == 0):\n",
        "            print(f\"iters: {iters + 1} cost: {cost:.6f}\")\n",
        "            \n",
        "        # get gradients\n",
        "        grad_W1, grad_W2, grad_b1, grad_b2 = back_prop(x, yhat, y, h, W1, W2, b1, b2, batch_size)\n",
        "        \n",
        "        # update weights and biases\n",
        "        W1 = W1 - alpha * grad_W1\n",
        "        W2 = W2 - alpha * grad_W2\n",
        "        b1 = b1 - alpha * grad_b1\n",
        "        b2 = b2 - alpha * grad_b2\n",
        "\n",
        "        ### END CODE HERE ###\n",
        "        iters +=1 \n",
        "        if iters == num_iters: \n",
        "            break\n",
        "        if iters % 100 == 0:\n",
        "            alpha *= 0.66\n",
        "            \n",
        "    return W1, W2, b1, b2"
      ],
      "id": "GVCwC6PjqQju"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HBFXAbJ8qQjv",
        "outputId": "8555f7c6-0b57-405d-eac4-164172e20bf9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Call gradient_descent\n",
            "iters: 10 cost: 8.818361\n",
            "iters: 20 cost: 8.429526\n",
            "iters: 30 cost: 8.860088\n",
            "iters: 40 cost: 8.376004\n",
            "iters: 50 cost: 8.637915\n",
            "iters: 60 cost: 8.497060\n",
            "iters: 70 cost: 8.126808\n",
            "iters: 80 cost: 8.557430\n",
            "iters: 90 cost: 9.842446\n",
            "iters: 100 cost: 8.489021\n",
            "iters: 110 cost: 4.244449\n",
            "iters: 120 cost: 8.261117\n",
            "iters: 130 cost: 8.847587\n",
            "iters: 140 cost: 8.780203\n",
            "iters: 150 cost: 6.039174\n"
          ]
        }
      ],
      "source": [
        "# test your function\n",
        "# UNIT TEST COMMENT: Each time this cell is run the cost for each iteration changes slightly (the change is less dramatic after some iterations)\n",
        "# to have this into account let's accept an answer as correct if the cost of iter 15 = 41.6 (without caring about decimal points beyond the first decimal)\n",
        "# 41.66, 41.69778, 41.63, etc should all be valid answers.\n",
        "C = 2\n",
        "N = 50\n",
        "word2Ind, Ind2word = get_dict(data)\n",
        "V = len(word2Ind)\n",
        "num_iters = 150\n",
        "print(\"Call gradient_descent\")\n",
        "W1, W2, b1, b2 = gradient_descent(data, word2Ind, N, V, num_iters)"
      ],
      "id": "HBFXAbJ8qQjv"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MB6hnJ3IqQjw"
      },
      "source": [
        "<a name='3'></a>\n",
        "## 3 - Visualizing the Word Vectors\n",
        "\n",
        "In this part you will visualize the word vectors trained using the function you just coded above. "
      ],
      "id": "MB6hnJ3IqQjw"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Q4yqXCnYqQjw",
        "outputId": "fbaeba40-53ce-426a-fe23-ea7a0b21d802",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(10, 50) [2744, 3949, 2960, 3022, 5672, 1452, 5671, 4189, 2315, 4276]\n"
          ]
        }
      ],
      "source": [
        "# visualizing the word vectors here\n",
        "from matplotlib import pyplot\n",
        "%config InlineBackend.figure_format = 'svg'\n",
        "words = ['king', 'queen','lord','man', 'woman','dog','wolf',\n",
        "         'rich','happy','sad']\n",
        "\n",
        "embs = (W1.T + W2)/2.0\n",
        " \n",
        "# given a list of words and the embeddings, it returns a matrix with all the embeddings\n",
        "idx = [word2Ind[word] for word in words]\n",
        "X = embs[idx, :]\n",
        "print(X.shape, idx)  # X.shape:  Number of words of dimension N each "
      ],
      "id": "Q4yqXCnYqQjw"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "so0TKKW7qQjx",
        "outputId": "f513e9a7-6e43-47a2-8470-ab13ba802d2f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 353
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
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          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "result= compute_pca(X, 2)\n",
        "pyplot.scatter(result[:, 0], result[:, 1])\n",
        "for i, word in enumerate(words):\n",
        "    pyplot.annotate(word, xy=(result[i, 0], result[i, 1]))\n",
        "pyplot.show()"
      ],
      "id": "so0TKKW7qQjx"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9SMYYqP0qQjy",
        "outputId": "9c1afd79-e85c-4de9-9ed5-cb0a204ce593",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 352
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
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          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "result= compute_pca(X, 4)\n",
        "pyplot.scatter(result[:, 3], result[:, 1])\n",
        "for i, word in enumerate(words):\n",
        "    pyplot.annotate(word, xy=(result[i, 3], result[i, 1]))\n",
        "pyplot.show()"
      ],
      "id": "9SMYYqP0qQjy"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.6"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}