gp.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled24.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMH9gzbe6I0NZ7nHg2x8s1e",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/kierandidi/ml_advanced_hd/blob/main/gp.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Exercise sheet 6"
      ],
      "metadata": {
        "id": "ylpIlbngsbKV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##1 GP Optimization of a Toy Problem"
      ],
      "metadata": {
        "id": "-htSB0r5sc-z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install Optunity GPy sobol sobol-seq"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HbmIuGCPsaIJ",
        "outputId": "a7d9e50f-30dd-4fff-dc54-64a6fbd46b37"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting Optunity\n",
            "  Downloading Optunity-1.1.1.tar.gz (4.6 MB)\n",
            "\u001b[K     |████████████████████████████████| 4.6 MB 22.3 MB/s \n",
            "\u001b[?25hCollecting GPy\n",
            "  Downloading GPy-1.10.0.tar.gz (959 kB)\n",
            "\u001b[K     |████████████████████████████████| 959 kB 35.1 MB/s \n",
            "\u001b[?25hCollecting sobol\n",
            "  Downloading sobol-0.9.tar.gz (6.4 kB)\n",
            "Collecting sobol-seq\n",
            "  Downloading sobol_seq-0.2.0-py3-none-any.whl (9.2 kB)\n",
            "Requirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.7/dist-packages (from GPy) (1.21.6)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from GPy) (1.15.0)\n",
            "Collecting paramz>=0.9.0\n",
            "  Downloading paramz-0.9.5.tar.gz (71 kB)\n",
            "\u001b[K     |████████████████████████████████| 71 kB 5.1 MB/s \n",
            "\u001b[?25hRequirement already satisfied: cython>=0.29 in /usr/local/lib/python3.7/dist-packages (from GPy) (0.29.30)\n",
            "Requirement already satisfied: scipy>=1.3.0 in /usr/local/lib/python3.7/dist-packages (from GPy) (1.7.3)\n",
            "Requirement already satisfied: decorator>=4.0.10 in /usr/local/lib/python3.7/dist-packages (from paramz>=0.9.0->GPy) (4.4.2)\n",
            "Building wheels for collected packages: Optunity, GPy, paramz, sobol\n",
            "  Building wheel for Optunity (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for Optunity: filename=Optunity-1.1.1-py3-none-any.whl size=72032 sha256=5d29d9cf1d6aec0e27375460df9a8db3850530d69024a9ba8172be31660aefdd\n",
            "  Stored in directory: /root/.cache/pip/wheels/0d/0e/31/a4763ff822a20f88a61dd3bb1c8b78a8f25c605392fe956d07\n",
            "  Building wheel for GPy (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for GPy: filename=GPy-1.10.0-cp37-cp37m-linux_x86_64.whl size=2565121 sha256=cb22418a5f2dbcd0ff8cc40152f36d14206d58b540be1d1933ccc4ff62360a14\n",
            "  Stored in directory: /root/.cache/pip/wheels/f7/18/28/dd1ce0192a81b71a3b086fd952511d088b21e8359ea496860a\n",
            "  Building wheel for paramz (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for paramz: filename=paramz-0.9.5-py3-none-any.whl size=102566 sha256=0048c952c679de50ad7767b7f9949efde077a82eb68e04d1c830fd42f624f402\n",
            "  Stored in directory: /root/.cache/pip/wheels/c8/95/f5/ce28482da28162e6028c4b3a32c41d147395825b3cd62bc810\n",
            "  Building wheel for sobol (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for sobol: filename=sobol-0.9-py3-none-any.whl size=7925 sha256=dbbf17d885365a334e6fdb285672441a09bea94edf8c2a98b7251627b2b50f90\n",
            "  Stored in directory: /root/.cache/pip/wheels/0a/c1/07/ade158173d250d010973cd0e0592fb63e2a2ad3c96d45106e7\n",
            "Successfully built Optunity GPy paramz sobol\n",
            "Installing collected packages: paramz, sobol-seq, sobol, Optunity, GPy\n",
            "Successfully installed GPy-1.10.0 Optunity-1.1.1 paramz-0.9.5 sobol-0.9 sobol-seq-0.2.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy.sparse\n",
        "import scipy.sparse.linalg\n",
        "import scipy.spatial\n",
        "import scipy.stats\n",
        "import math\n",
        "import sobol"
      ],
      "metadata": {
        "id": "GVLfx-aEs4l8"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def func(x, y):\n",
        "  return x**2 - x + y**2 + y - (np.cos(2 * math.pi * (x - 0.5)) + np.cos(2 * math.pi * (y + 0.5))) + 2.5"
      ],
      "metadata": {
        "id": "A63OmtNttWVe"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def toy_plot():\n",
        "  x = np.linspace(-6, 6, 100)\n",
        "  y = np.linspace(-6, 6, 100)\n",
        "  xx, yy = np.meshgrid(x, y, sparse=True)\n",
        "  z = func(xx,yy)\n",
        "  plt.imshow(z, extent =(-6,6,-6,6))\n",
        "  plt.colorbar()\n",
        "  plt.gca().set_aspect(1)\n",
        "  plt.xlabel(\"$x$\")\n",
        "  plt.ylabel(\"$y$\")\n",
        "  plt.title(\"toy function\")"
      ],
      "metadata": {
        "id": "o6IO1RZKtWXp"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "toy_plot()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "9gglp5LHtWZs",
        "outputId": "5650b960-546c-44f6-a4f6-0b8eb6bdaa80"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#get random points in interval [-6,6]\n",
        "points_rand = np.random.rand(60,2)\n",
        "output = func(points_rand[:,0], points_rand[:,1])\n",
        "print(scipy.stats.describe(output))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IHyFpHQu1JaS",
        "outputId": "d3188f5a-42c1-4b52-80b0-2b240430f774"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "DescribeResult(nobs=60, minmax=(0.962191114776044, 5.682392487267582), mean=3.301108126243248, variance=1.2432913291673964, skewness=0.1283447180050109, kurtosis=-0.5790585159066137)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sample_num = 30\n",
        "paramUpperLim = np.array([6,6])\n",
        "paramLowerLim = np.array([-6,-6])\n",
        "for i in range(sample_num):\n",
        "  x,y = sobol.i4_sobol(2,i)[0] * (paramUpperLim - paramLowerLim) +paramLowerLim"
      ],
      "metadata": {
        "id": "YAZl6pXV3QdT"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##2 "
      ],
      "metadata": {
        "id": "IguDvKs9sdB7"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZcVcv4tLsX2a"
      },
      "outputs": [],
      "source": [
        "opt_print = lambda *args, **kwargs: None  # silence output\n",
        "\n",
        "\n",
        "# opt_print = print # for debugging\n",
        "\n",
        "def gaussian_kernel(data, sigma, max_distance):\n",
        "    \"\"\"Compute the gaussian kernel matrix.\n",
        "\n",
        "    :param data: data matrix\n",
        "    :param sigma: parameter sigma of the gaussian kernel\n",
        "    :return: gaussian kernel matrix\n",
        "    \"\"\"\n",
        "    assert len(data.shape) == 2\n",
        "    assert sigma > 0\n",
        "\n",
        "    factor = -0.5 / (sigma ** 2)\n",
        "    limit = np.exp(factor * max_distance ** 2)\n",
        "    # Find the pairwise squared distances and compute the Gaussian kernel.\n",
        "    K = []\n",
        "    for k in data:\n",
        "        d = np.exp(factor * np.sum((data - k) ** 2, axis=1))\n",
        "        d[d < limit] = 0.0  # truncate the Gaussian\n",
        "        d = scipy.sparse.csc_matrix(d[:, None])\n",
        "        K.append(d)\n",
        "    K = scipy.sparse.hstack(K)\n",
        "    return K\n",
        "\n",
        "\n",
        "def compute_alpha(train_x, train_y, tau, sigma, max_distance, verbose=False):\n",
        "    \"\"\"Compute the alpha vector of the ridge regressor.\n",
        "\n",
        "    :param train_x: training x data\n",
        "    :param train_y: training y data\n",
        "    :param tau: parameter tau of the ridge regressor\n",
        "    :param sigma: parameter sigma of the gaussian kernel\n",
        "    :param verbose: Print debugging information?\n",
        "    :return: alpha vector\n",
        "    \"\"\"\n",
        "    if verbose: print(\"Building input kernel matrix\")\n",
        "    K = gaussian_kernel(train_x, sigma, max_distance)\n",
        "    if verbose: print(\"Sparsity is: %.2f%%\" % (\n",
        "            float(100 * K.nnz) / (K.shape[0] * K.shape[1])))\n",
        "    M = K + tau * scipy.sparse.identity(train_x.shape[0])\n",
        "    y = scipy.sparse.csc_matrix(train_y[:, None])\n",
        "    if verbose: print(\"Solving sparse system\")\n",
        "    alpha = scipy.sparse.linalg.cg(M, train_y)\n",
        "    if verbose: print(\"Done computing alpha\")\n",
        "    return alpha[0]\n",
        "\n",
        "\n",
        "class KernelRidgeRegressor(object):\n",
        "    \"\"\"Kernel Ridge Regressor.\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(self, tau, sigma):\n",
        "        self.dim = None\n",
        "        self.train_x = None\n",
        "        self.alpha = None\n",
        "        self.mean_y = None\n",
        "        self.std_y = None\n",
        "        self.tau = tau\n",
        "        self.sigma = sigma\n",
        "        self.scale = -0.5 / sigma**2\n",
        "        self.max_distance = 4.0*sigma\n",
        "\n",
        "    def train(self, train_x, train_y, verbose=False):\n",
        "        \"\"\"Train the kernel ridge regressor.\n",
        "\n",
        "        :param train_x: training x data\n",
        "        :param train_y: training y data\n",
        "        \"\"\"\n",
        "        assert len(train_x.shape) == 2\n",
        "        assert len(train_y.shape) == 1\n",
        "        assert train_x.shape[0] == train_y.shape[0]\n",
        "\n",
        "        self.dim = train_x.shape[1]\n",
        "        self.train_x = train_x.astype(np.float32)\n",
        "        self.tree = scipy.spatial.cKDTree(self.train_x)\n",
        "\n",
        "        self.mean_y = train_y.mean()\n",
        "        self.std_y = train_y.std()\n",
        "        train_y_std = (train_y - self.mean_y) / self.std_y\n",
        "\n",
        "        self.alpha = compute_alpha(self.train_x, train_y_std, self.tau,\n",
        "                                   self.sigma, self.max_distance,\n",
        "                                   verbose=verbose)\n",
        "\n",
        "\n",
        "    def predict_single(self, pred_x):\n",
        "        \"\"\"Predict the value of a single instance.\n",
        "\n",
        "        :param pred_x: x data\n",
        "        :return: predicted value of pred_x\n",
        "        \"\"\"\n",
        "        assert len(pred_x.shape) == 1\n",
        "        assert pred_x.shape[0] == self.dim\n",
        "        indices = np.asarray(\n",
        "            self.tree.query_ball_point(pred_x, self.max_distance),\n",
        "            dtype=np.dtype(\"i8\"))\n",
        "        dist = np.sum((self.train_x[indices] - pred_x) ** 2, axis=1)\n",
        "        kappa = np.exp(self.scale * dist)\n",
        "        pred_y = np.dot(kappa, self.alpha[indices])\n",
        "        return self.std_y * pred_y + self.mean_y\n",
        "\n",
        "    def predict(self, pred_x):\n",
        "        \"\"\"Predict the values of pred_x.\n",
        "\n",
        "        :param pred_x: x data\n",
        "        :return: predicted values of pred_x\n",
        "        \"\"\"\n",
        "        assert len(pred_x.shape) == 2\n",
        "        assert pred_x.shape[1] == self.dim\n",
        "        pred_x = pred_x.astype(np.float32)\n",
        "        return np.array([self.predict_single(x) for x in pred_x])\n",
        "\n",
        "\n",
        "def kernel_ridge_regression(tau, sigma, verbose=False):\n",
        "    # Load the image.\n",
        "    im_orig = np.squeeze(plt.imread(\"cc_90.png\"))\n",
        "\n",
        "    # Make a copy, so both the original and the regressed image can be shown afterwards.\n",
        "    im = np.array(im_orig)\n",
        "\n",
        "    # Find the known pixels and the pixels that shall be predicted.\n",
        "    known_ind = np.where(im != 0)\n",
        "    # predict everywhere, use im == 0 to predict only unfilled values\n",
        "    unknown_ind = np.where(im >= 0)\n",
        "    known_x = np.array(known_ind).transpose()\n",
        "    known_y = np.array(im[known_ind])\n",
        "    pred_x = np.array(unknown_ind).transpose()\n",
        "\n",
        "    # Train and predict with the given regressor.\n",
        "    start = time.time()\n",
        "    if verbose: print(\"Training...\")\n",
        "    r = KernelRidgeRegressor(tau, sigma)\n",
        "    r.train(known_x, known_y, verbose=verbose)\n",
        "    if verbose: print(\"Done training.\")\n",
        "\n",
        "    if verbose: print(\"Predicting... \", end=\"\")\n",
        "    pred_y = r.predict(pred_x)\n",
        "    if verbose: print(\"Done.\")\n",
        "\n",
        "    # Write the predicted values back into the image and show the result.\n",
        "    im[unknown_ind] = pred_y\n",
        "    stop = time.time()\n",
        "    if verbose: print(\"Train and predict took %.02f seconds.\" % (stop - start))\n",
        "    if verbose: print(im.shape)\n",
        "\n",
        "    return im\n"
      ]
    }
  ]
}