TF_Partial_Distance_Correlation_demo.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "d66468d6",
      "metadata": {
        "id": "d66468d6"
      },
      "source": [
        "# Partial Distance Correlation using TensorFlow😺"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "75788b94",
      "metadata": {
        "id": "75788b94"
      },
      "source": [
        "## Install required packages"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "469dd5e4",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "469dd5e4",
        "outputId": "dd6bc249-e7bc-4d6b-c2a7-47b38b4689fd",
        "scrolled": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
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            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.8/dist-packages (from matplotlib!=3.0.0,>=2.0.0->scikit-image>=0.16.1->albumentations) (0.11.0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.8/dist-packages (from python-dateutil>=2.1->matplotlib!=3.0.0,>=2.0.0->scikit-image>=0.16.1->albumentations) (1.15.0)\n",
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            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting transformers\n",
            "  Downloading transformers-4.25.1-py3-none-any.whl (5.8 MB)\n",
            "\u001b[K     |████████████████████████████████| 5.8 MB 14.8 MB/s \n",
            "\u001b[?25hCollecting huggingface-hub<1.0,>=0.10.0\n",
            "  Downloading huggingface_hub-0.11.1-py3-none-any.whl (182 kB)\n",
            "\u001b[K     |████████████████████████████████| 182 kB 74.0 MB/s \n",
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            "Collecting tokenizers!=0.11.3,<0.14,>=0.11.1\n",
            "  Downloading tokenizers-0.13.2-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (7.6 MB)\n",
            "\u001b[K     |████████████████████████████████| 7.6 MB 51.0 MB/s \n",
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            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (1.24.3)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (2.10)\n",
            "Installing collected packages: tokenizers, huggingface-hub, transformers\n",
            "Successfully installed huggingface-hub-0.11.1 tokenizers-0.13.2 transformers-4.25.1\n"
          ]
        }
      ],
      "source": [
        "#!pip install torch torchvision timm\n",
        "#!pip install transformers\n",
        "#!pip install torchshow\n",
        "%pip install albumentations\n",
        "%pip install transformers"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3c23b6e4",
      "metadata": {
        "id": "3c23b6e4"
      },
      "source": [
        "## Import all related packages"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "91e6649e",
      "metadata": {
        "id": "91e6649e"
      },
      "outputs": [],
      "source": [
        "import os\n",
        "import sys\n",
        "import time\n",
        "import math\n",
        "import numpy as np\n",
        "\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import figure\n",
        "from matplotlib.patches import Ellipse, Rectangle\n",
        "import matplotlib.transforms as transforms\n",
        "\n",
        "from scipy.stats import gaussian_kde\n",
        "#mute warnings\n",
        "os.environ[\"TF_CPP_MIN_LOG_LEVEL\"] = \"3\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "fbce5e02",
      "metadata": {
        "id": "fbce5e02"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "import tensorflow.keras as keras\n",
        "from tensorflow.keras import layers\n",
        "import albumentations as A\n",
        "import pandas as pd\n",
        "#set gpu memory dynamic growth\n",
        "gpus = tf.config.experimental.list_physical_devices('GPU')\n",
        "for gpu in gpus:\n",
        "  tf.config.experimental.set_memory_growth(gpu, True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "5616b6b4",
      "metadata": {
        "id": "5616b6b4"
      },
      "outputs": [],
      "source": [
        "plt.style.use('ggplot')\n",
        "#Avoid bug when latex package is not installed. Use default Latex in plt instead.\n",
        "matplotlib.rcParams['text.usetex'] = False\n",
        "# matplotlib.rcParams['text.latex.preamble'] = r'\\usepackage{{amsmath}}'"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6c9aa4c2",
      "metadata": {
        "id": "6c9aa4c2"
      },
      "source": [
        "## Define Distance Correlation\n",
        "Compute the distance matrices between the given samples\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cd1ac909",
      "metadata": {
        "id": "cd1ac909"
      },
      "source": [
        "Compute the correlation between those two distance matrices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "1d360b51",
      "metadata": {
        "id": "1d360b51"
      },
      "outputs": [],
      "source": [
        "class Loss_DC(tf.keras.losses.Loss):\n",
        "    def __init__(self):\n",
        "        super(Loss_DC, self).__init__()\n",
        "\n",
        "\n",
        "    def Distance_Correlation(self, latent, control):\n",
        "        matrix_a = tf.math.sqrt(tf.math.reduce_sum(tf.math.square(tf.expand_dims(latent,axis=0)  -  tf.expand_dims(latent,1)),axis=-1) + 1e-12)\n",
        "        matrix_b = tf.math.sqrt(tf.math.reduce_sum(tf.math.square(tf.expand_dims(control,axis=0) -  tf.expand_dims(control,1)),axis=-1) + 1e-12)\n",
        "        # print((tf.math.reduce_sum(tf.math.square(tf.expand_dims(latent,axis=0)  -  tf.expand_dims(latent,1)),axis=-1)).shape)\n",
        "        matrix_A = matrix_a - tf.math.reduce_mean(matrix_a, axis = 0, keepdims= True) - tf.math.reduce_mean(matrix_a, axis = 1, keepdims= True) + tf.math.reduce_mean(matrix_a)\n",
        "        matrix_B = matrix_b - tf.math.reduce_mean(matrix_b, axis = 0, keepdims= True) - tf.math.reduce_mean(matrix_b, axis = 1, keepdims= True) + tf.math.reduce_mean(matrix_b)\n",
        "        # print(tf.math.reduce_mean(matrix_a, axis = 0, keepdims= True).shape)\n",
        "        Gamma_XY = tf.math.reduce_sum(matrix_A * matrix_B)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
        "        Gamma_XX = tf.math.reduce_sum(matrix_A * matrix_A)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
        "        Gamma_YY = tf.math.reduce_sum(matrix_B * matrix_B)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
        "\n",
        "        correlation_r = Gamma_XY/tf.math.sqrt(Gamma_XX * Gamma_YY + 1e-9)\n",
        "        return correlation_r\n",
        "\n",
        "\n",
        "    def call(self, latent, control):\n",
        "        #Avoid OOE on GPU\n",
        "        # with tf.device('/cpu:0'):\n",
        "        dc_loss = self.Distance_Correlation(latent, control)\n",
        "\n",
        "        return dc_loss"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "faf9fcb4",
      "metadata": {
        "id": "faf9fcb4"
      },
      "source": [
        "## Pearson Correlation vs Distance Correlation\n",
        "This demo shows that Distance Correlation is better compared with Pearson Correlation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "ec292a5f",
      "metadata": {
        "id": "ec292a5f"
      },
      "outputs": [],
      "source": [
        "def Pearson_Correlation(latent, control):\n",
        "    batch_size = latent.shape[0]\n",
        "\n",
        "    up = (latent - tf.math.reduce_mean(latent, axis = 0, keepdims= True) ) * (control - tf.math.reduce_mean(control, axis = 0, keepdims= True) )\n",
        "    up = tf.math.reduce_sum(up) / batch_size\n",
        "\n",
        "    down = tf.math.reduce_sum((latent - tf.math.reduce_mean(latent, axis = 0, keepdims= True) ) ** 2 ) * tf.math.reduce_sum((control - tf.math.reduce_mean(control, axis = 0, keepdims= True) ) ** 2)\n",
        "    down = down / (batch_size ** 2)\n",
        "\n",
        "    return up/tf.math.sqrt(down)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3d8e3907",
      "metadata": {
        "id": "3d8e3907"
      },
      "source": [
        "Here, we will use a special case to obtain the eigenvalues of these two-dimensional datasets.\n",
        "Then, calculate the standard deviation of x and y from the square root of the variance and multiplaying with the given number of standard deviations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "c015333b",
      "metadata": {
        "id": "c015333b"
      },
      "outputs": [],
      "source": [
        "def confidence_ellipse(x, y, ax, n_std=2.9, facecolor='none', cov=None, **kwargs):\n",
        "    if x.size != y.size:\n",
        "        raise ValueError(\"x and y must be the same size\")\n",
        "\n",
        "    pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1, 1])\n",
        "    ell_radius_x = np.sqrt(1 + pearson)\n",
        "    ell_radius_y = np.sqrt(1 - pearson)\n",
        "    ellipse = Ellipse((0, 0), width=ell_radius_x * 2, height=ell_radius_y * 2,\n",
        "                      facecolor=facecolor, lw=3, **kwargs)\n",
        "    scale_x = np.sqrt(cov[0, 0]) * n_std\n",
        "    mean_x = np.mean(x)\n",
        "\n",
        "    scale_y = np.sqrt(cov[1, 1]) * n_std\n",
        "    mean_y = np.mean(y)\n",
        "\n",
        "    transf = transforms.Affine2D() \\\n",
        "        .rotate_deg(45) \\\n",
        "        .scale(scale_x, scale_y) \\\n",
        "        .translate(mean_x, mean_y)\n",
        "\n",
        "    ellipse.set_transform(transf + ax.transData)\n",
        "    return ax.add_patch(ellipse)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f55d4a3b",
      "metadata": {
        "id": "f55d4a3b"
      },
      "source": [
        "Now we compare Pearson Correlation and Distance Correlation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "69315f37",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 362
        },
        "id": "69315f37",
        "outputId": "2fb372d5-af46-4f2e-9f9f-f57a349c85dd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Pearson Correration: -0.004336792743168292\n",
            "Distance Correlation: 0.2072713453191376\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 240x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "batch_size=10000\n",
        "Distance_Correlation = Loss_DC()\n",
        "x = np.linspace(-3, 3, num=batch_size)\n",
        "y = np.random.randn(batch_size)\n",
        "\n",
        "y = y + x**2\n",
        "\n",
        "x = tf.constant(x)\n",
        "x = tf.reshape(x,[batch_size,-1])\n",
        "y = tf.constant(y)\n",
        "y = tf.reshape(y,[batch_size,-1])\n",
        "\n",
        "pc = Pearson_Correlation(x,y)\n",
        "dc = Distance_Correlation(x,y)\n",
        "print(f'Pearson Correration: {pc}')\n",
        "print(f'Distance Correlation: {dc}')\n",
        "\n",
        "outR = tf.concat([x,y], axis=-1).numpy()\n",
        "\n",
        "z = gaussian_kde(outR.transpose())(outR.transpose())\n",
        "figure(figsize=(3, 4.5), dpi=80)\n",
        "new_X = np.linspace(-3, 3, num=batch_size)\n",
        "new_Y_low = new_X**2 - 3\n",
        "new_Y_high = new_X**2 + 3\n",
        "plt.plot(new_X, new_X**2, 'b-', alpha=0.8)\n",
        "ax = plt.gca()\n",
        "ax.fill_between(new_X, new_Y_low, new_Y_high, color='b' , alpha=0.1)\n",
        "plt.scatter(x=x[::20], y = y[::20],c=z[::20],s=10,cmap='hot')\n",
        "ax.axis('equal')\n",
        "ax.set(xlim=(-5, 5), ylim=(-5, 15))\n",
        "# ax.set_title(r'$y=x^2+n,n\\sim \\mathcal{N}(0,1)$'))\n",
        "plt.text(0.05, 0.95, 'Pearson Cor : {:0.3f}\\nDistance Cor: {:0.3f}'.format(pc, dc) , horizontalalignment='left',verticalalignment='center', transform=ax.transAxes, size='x-large')\n",
        "plt.savefig('pearson_distance1.png', dpi=300)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "c23c3f13",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 362
        },
        "id": "c23c3f13",
        "outputId": "a8abbacf-70a0-415e-a96d-b084fc548ef5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Pearson Correration: 0.6656036725999988\n",
            "Distance Correlation: 0.3800003856064541\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 240x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "xy = np.random.multivariate_normal(mean=np.asarray([0,5]), cov = np.asarray([[1,1.5],[1.5,5]]), size=batch_size)\n",
        "x = xy[:,0]\n",
        "y = xy[:,1]\n",
        "\n",
        "x = tf.constant(x)\n",
        "x = tf.reshape(x,[batch_size,-1])\n",
        "y = tf.constant(y)\n",
        "y = tf.reshape(y,[batch_size,-1])\n",
        "\n",
        "pc = Pearson_Correlation(x,y)\n",
        "dc = Distance_Correlation(x,y)\n",
        "print(f'Pearson Correration: {pc}')\n",
        "print(f'Distance Correlation: {dc}')\n",
        "\n",
        "outR = tf.concat([x,y], axis=-1).numpy()\n",
        "z = gaussian_kde(outR.transpose())(outR.transpose())\n",
        "\n",
        "figure(figsize=(3, 4.5), dpi=80)\n",
        "plt.scatter(x=x[::10], y = y[::10],c=z[::10],s=10,cmap='hot')\n",
        "ax = plt.gca()\n",
        "confidence_ellipse(outR[:,0], outR[:,1],ax, cov=np.asarray([[1,1.5],[1.5,5]]), edgecolor=\"red\", facecolor='blue', alpha=0.1)\n",
        "ax.axis('equal')\n",
        "ax.set(xlim=(-5, 5), ylim=(-5, 15))\n",
        "plt.text(0.05, 0.95, 'Pearson Cor : {:0.3f}\\nDistance Cor: {:0.3f}'.format(pc, dc) , horizontalalignment='left',verticalalignment='center', transform=ax.transAxes, size='x-large')\n",
        "plt.savefig('pearson_distance2.png', dpi=300)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "5154cc53",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "5154cc53",
        "outputId": "99577e46-cde4-4555-c92e-65768b54c476"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Pearson Correration: 0.0039006626107336126\n",
            "Distance Correlation: 0.00018041871471347523\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 240x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "xy = np.random.multivariate_normal(mean=np.asarray([0,5]), cov = np.asarray([[1,0],[0,5]]), size=batch_size)\n",
        "x = xy[:,0]\n",
        "y = xy[:,1]\n",
        "\n",
        "x = tf.constant(x)\n",
        "x = tf.reshape(x,[batch_size,-1])\n",
        "y = tf.constant(y)\n",
        "y = tf.reshape(y,[batch_size,-1])\n",
        "\n",
        "pc = Pearson_Correlation(x,y)\n",
        "dc = Distance_Correlation(x,y)\n",
        "print(f'Pearson Correration: {pc}')\n",
        "print(f'Distance Correlation: {dc}')\n",
        "\n",
        "outR = tf.concat([x,y], axis=-1).numpy()\n",
        "z = gaussian_kde(outR.transpose())(outR.transpose())\n",
        "\n",
        "figure(figsize=(3, 4.5), dpi=80)\n",
        "plt.scatter(x=x[::10], y = y[::10],c=z[::10],s=10,cmap='hot')\n",
        "ax = plt.gca()\n",
        "confidence_ellipse(outR[:,0], outR[:,1],ax, cov=np.asarray([[1,0],[0,5]]), edgecolor=None, facecolor='blue', alpha=0.1)\n",
        "ax.axis('equal')\n",
        "ax.set(xlim=(-5, 5), ylim=(-5, 15))\n",
        "plt.text(0.05, 0.95, 'Pearson Cor : {:0.3f}\\nDistance Cor: {:0.3f}'.format(pc.numpy(), dc) , horizontalalignment='left',verticalalignment='center', transform=ax.transAxes, size='x-large')\n",
        "plt.savefig('pearson_distance3.png', dpi=300)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d5a56ff5",
      "metadata": {
        "id": "d5a56ff5"
      },
      "source": [
        "## Define Models\n",
        "We only use the features to evaluate the similarity between networks"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "c8f8c054",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c8f8c054",
        "outputId": "0572760f-a0a2-40e0-f55b-a1cc7014393a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Downloading data from https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz\n",
            "170498071/170498071 [==============================] - 6s 0us/step\n",
            "mean after normalization: [-2.71552120e-14  1.88792759e-15  4.94816688e-15]\n",
            "std after normalization: [1. 1. 1.]\n"
          ]
        }
      ],
      "source": [
        "\n",
        "def normalize(x):\n",
        "  #scale range to [0,1] first, in consistence with Pytorch implementation\n",
        "  x=x/255.0\n",
        "  mean = x.mean(axis=(0,1,2)).reshape(1,1,-1)\n",
        "  std = x.std(axis=(0,1,2)).reshape(1,1,-1)\n",
        "  return (x-mean)/std\n",
        "    \n",
        "transforms=A.Compose([\n",
        "    A.augmentations.RandomCrop(width=32,height=32),#tensorflow does not support RandomCrop with padding\n",
        "    A.augmentations.HorizontalFlip(0.5)    \n",
        "])\n",
        "classes = ('plane', 'car', 'bird', 'cat', 'deer',\n",
        "           'dog', 'frog', 'horse', 'ship', 'truck')\n",
        "(x_train,y_train),(x_test,y_test)=keras.datasets.cifar10.load_data()\n",
        "transform = lambda x: transforms(image=x)['image']\n",
        "\n",
        "for i in range(x_test.shape[0]):\n",
        "    x_test[i]==transform(x_test[i])\n",
        "for i in range(x_train.shape[0]):\n",
        "    x_train[i]==transform(x_train[i])\n",
        "    \n",
        "x_train=normalize(x_train)\n",
        "x_test=normalize(x_test)\n",
        "print(\"mean after normalization:\",x_train.mean(axis=(0,1,2)))\n",
        "print(\"std after normalization:\",x_train.std(axis=(0,1,2)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "id": "a88a6a19",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a88a6a19",
        "outputId": "7626d2d5-1360-4c55-9361-f6563c286f6f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1563/1563 [==============================] - 40s 24ms/step\n",
            "1563/1563 [==============================] - 15s 9ms/step\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "((50000, 2048), (50000, 2048))"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#tensorflow doesn't implement ResNet18\n",
        "model1=keras.applications.ResNet152(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "model2=keras.applications.ResNet50(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "features1 = model1.predict(x_train)\n",
        "features2 = model2.predict(x_train)\n",
        "features1 = features1.reshape(features1.shape[0],-1)\n",
        "features2 = features2.reshape(features2.shape[0],-1)\n",
        "features1.shape,features2.shape\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "58285ec9",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "58285ec9",
        "outputId": "d0898d6e-9f87-4730-e278-354fa3718356"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Similarity between model1 and model2: 0.571228593673706\n"
          ]
        }
      ],
      "source": [
        "similarity = Loss_DC()\n",
        "batch_size=128\n",
        "sim = 0\n",
        "\n",
        "for i in range(batch_size,x_train.shape[0],batch_size):\n",
        "  print(f\"\\rbatch {int(i/batch_size)}\",end=\"\")\n",
        "\n",
        "  idx = np.arange(i-batch_size,i)\n",
        "  sim+=similarity(features1[idx],features2[idx]).numpy()\n",
        "\n",
        "\n",
        "print(f'\\rSimilarity between model1 and model2: {sim/len(x_train)*batch_size}')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9352e2ca",
      "metadata": {
        "id": "9352e2ca"
      },
      "source": [
        "## A simple example for partial distance correlation"
      ]
    },
    {
      "cell_type": "code",
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      "id": "59b89b89",
      "metadata": {
        "colab": {
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        "id": "59b89b89",
        "outputId": "92b7b6e4-7f1e-4354-d227-835649ec9fd7"
      },
      "outputs": [
        {
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            "text/plain": [
              "Downloading:   0%|          | 0.00/232k [00:00<?, ?B/s]"
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          "output_type": "display_data"
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        {
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        {
          "name": "stderr",
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          "text": [
            "Some layers from the model checkpoint at bert-base-uncased were not used when initializing TFBertModel: ['mlm___cls', 'nsp___cls']\n",
            "- This IS expected if you are initializing TFBertModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
            "- This IS NOT expected if you are initializing TFBertModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n",
            "All the layers of TFBertModel were initialized from the model checkpoint at bert-base-uncased.\n",
            "If your task is similar to the task the model of the checkpoint was trained on, you can already use TFBertModel for predictions without further training.\n"
          ]
        },
        {
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>plane</th>\n",
              "      <th>car</th>\n",
              "      <th>bird</th>\n",
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              "      <th>0</th>\n",
              "      <td>-0.778572</td>\n",
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              "      <td>-0.729765</td>\n",
              "      <td>-0.821767</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.185883</td>\n",
              "      <td>-0.168564</td>\n",
              "      <td>-0.290150</td>\n",
              "      <td>-0.169207</td>\n",
              "      <td>-0.527162</td>\n",
              "      <td>-0.316793</td>\n",
              "      <td>-0.291923</td>\n",
              "      <td>-0.362023</td>\n",
              "      <td>-0.193511</td>\n",
              "      <td>-0.164111</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.546288</td>\n",
              "      <td>0.245530</td>\n",
              "      <td>0.357177</td>\n",
              "      <td>0.490521</td>\n",
              "      <td>-0.837614</td>\n",
              "      <td>-0.094327</td>\n",
              "      <td>0.263216</td>\n",
              "      <td>-0.061634</td>\n",
              "      <td>0.524687</td>\n",
              "      <td>0.292495</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.596004</td>\n",
              "      <td>0.655340</td>\n",
              "      <td>0.735480</td>\n",
              "      <td>0.570933</td>\n",
              "      <td>0.909102</td>\n",
              "      <td>0.786214</td>\n",
              "      <td>0.742419</td>\n",
              "      <td>0.792160</td>\n",
              "      <td>0.550749</td>\n",
              "      <td>0.696199</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.394308</td>\n",
              "      <td>-0.091688</td>\n",
              "      <td>-0.045644</td>\n",
              "      <td>-0.370888</td>\n",
              "      <td>0.744903</td>\n",
              "      <td>0.057494</td>\n",
              "      <td>0.010459</td>\n",
              "      <td>0.054226</td>\n",
              "      <td>-0.389657</td>\n",
              "      <td>-0.173794</td>\n",
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              "      plane       car      bird       cat      deer       dog      frog  \\\n",
              "0 -0.778572 -0.787241 -0.858110 -0.751022 -0.968879 -0.865062 -0.883761   \n",
              "1 -0.185883 -0.168564 -0.290150 -0.169207 -0.527162 -0.316793 -0.291923   \n",
              "2  0.546288  0.245530  0.357177  0.490521 -0.837614 -0.094327  0.263216   \n",
              "3  0.596004  0.655340  0.735480  0.570933  0.909102  0.786214  0.742419   \n",
              "4 -0.394308 -0.091688 -0.045644 -0.370888  0.744903  0.057494  0.010459   \n",
              "\n",
              "      horse      ship     truck  \n",
              "0 -0.862523 -0.729765 -0.821767  \n",
              "1 -0.362023 -0.193511 -0.164111  \n",
              "2 -0.061634  0.524687  0.292495  \n",
              "3  0.792160  0.550749  0.696199  \n",
              "4  0.054226 -0.389657 -0.173794  "
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from transformers import BertTokenizer, TFBertModel\n",
        "tokenizer = BertTokenizer.from_pretrained('bert-base-uncased')\n",
        "embed_model = TFBertModel.from_pretrained(\"bert-base-uncased\")\n",
        "\n",
        "class_embedding = []\n",
        "for cifar_class in classes:\n",
        "    encoded_input = tokenizer(cifar_class.lower(), return_tensors='tf')\n",
        "    output = embed_model(**encoded_input)\n",
        "    class_embedding.append(output[1])\n",
        "class_embedding = tf.concat(class_embedding,axis=0)\n",
        "class_embedding_DF = pd.DataFrame(class_embedding.numpy())\n",
        "class_embedding_tranp_DF = class_embedding_DF.transpose()\n",
        "class_embedding_tranp_DF.columns = classes\n",
        "class_embedding_tranp_DF.head()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "19eae044",
      "metadata": {
        "id": "19eae044"
      },
      "source": [
        "## Definition of the Partial Distance Correlation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "471d94fb",
      "metadata": {
        "id": "471d94fb"
      },
      "outputs": [],
      "source": [
        "def P_Distance_Matrix(latent):\n",
        "    n = latent.shape[0]\n",
        "    matrix_a = tf.math.sqrt(tf.math.reduce_sum(tf.square(tf.expand_dims(latent,axis=0) - tf.expand_dims(latent,axis=1) ), axis = -1) + 1e-18)\n",
        "    matrix_A = matrix_a - tf.math.reduce_sum(matrix_a, axis = 0, keepdims= True)/(n-2) - tf.math.reduce_sum(matrix_a, axis = 1, keepdims= True)/(n-2) \\\n",
        "                + tf.math.reduce_sum(matrix_a)/((n-1)*(n-2))\n",
        "\n",
        "    diag_A = tf.linalg.diag(tf.linalg.diag(matrix_A) ) \n",
        "    matrix_A = matrix_A - diag_A\n",
        "    return matrix_A\n",
        "\n",
        "\n",
        "def bracket_op(matrix_A, matrix_B):\n",
        "    n = matrix_A.shape[0]\n",
        "    return tf.math.reduce_sum(matrix_A * matrix_B)/(n*(n-3))\n",
        "\n",
        "\n",
        "def P_removal(matrix_A, matrix_C):\n",
        "    result = matrix_A - bracket_op(matrix_A, matrix_C) / bracket_op(matrix_C, matrix_C) * matrix_C\n",
        "    return result\n",
        "\n",
        "def Correlation(matrix_A, matrix_B):\n",
        "    Gamma_XY = bracket_op(matrix_A, matrix_B)\n",
        "    Gamma_XX = bracket_op(matrix_A, matrix_A)\n",
        "    Gamma_YY = bracket_op(matrix_B, matrix_B)\n",
        "\n",
        "    correlation_r = Gamma_XY/tf.math.sqrt(Gamma_XX * Gamma_YY + 1e-18)\n",
        "\n",
        "    return correlation_r\n",
        "\n",
        "\n",
        "def P_DC(latent_A, latent_B, ground_truth):\n",
        "    matrix_A = P_Distance_Matrix(latent_A)\n",
        "    matrix_B = P_Distance_Matrix(latent_B)\n",
        "    matrix_GT = P_Distance_Matrix(ground_truth)\n",
        "\n",
        "    matrix_A_B = P_removal(matrix_A, matrix_B)\n",
        "\n",
        "    cr = Correlation(matrix_A_B, matrix_GT)\n",
        "\n",
        "    return cr\n",
        "\n",
        "\n",
        "def New_DC(latent_A, ground_truth):\n",
        "    matrix_A = P_Distance_Matrix(latent_A)\n",
        "    matrix_GT = P_Distance_Matrix(ground_truth)\n",
        "    cr = Correlation(matrix_A, matrix_GT)\n",
        "\n",
        "    return cr"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d0f4b8be",
      "metadata": {
        "id": "d0f4b8be"
      },
      "source": [
        "Unit test 1:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "id": "900b28b7",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "900b28b7",
        "outputId": "26729835-3891-4aee-f26d-4efb9e112d97"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Actual result from the paper:0.003\n",
            " Partial Distance after removing resnet152 from resnet50: 0.057866757746934894\n"
          ]
        }
      ],
      "source": [
        "def compute_P_DC(features1,features2,name1,name2):\n",
        "  total_pdc = 0\n",
        "  batch_size=128\n",
        "\n",
        "  for i in range(batch_size,x_train.shape[0],batch_size):\n",
        "    print(f\"\\rbatch {int(i/batch_size)}\",end=\"\")\n",
        "\n",
        "    idx = np.arange(i-batch_size,i)\n",
        "    targets = tf.squeeze(y_train[idx].astype('int32'))\n",
        "    ground_truth = tf.gather(class_embedding,targets)#uint8 not allowed as index\n",
        "    total_pdc+=P_DC(features1[idx],features2[idx],ground_truth).numpy()\n",
        "\n",
        "  print(f\"\\r Partial Distance after removing {name1} from {name2}:\",total_pdc/len(x_train)*batch_size)\n",
        "print(\"Actual result from the paper:0.003\")\n",
        "compute_P_DC(features1,features2,model1._name,model2._name)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "maEoo63P4obf",
      "metadata": {
        "id": "maEoo63P4obf"
      },
      "source": [
        "Unit test 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "id": "Lw71RNr3SBRu",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Lw71RNr3SBRu",
        "outputId": "9d266007-35e8-4b39-c557-3236c96d94b2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1563/1563 [==============================] - 16s 10ms/step\n",
            "1563/1563 [==============================] - 15s 10ms/step\n",
            "Actual result from the paper: 0.02\n",
            " Partial Distance after removing resnet50 from vgg19: 0.03058003036714159\n"
          ]
        }
      ],
      "source": [
        "model1=keras.applications.ResNet50(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "model2=keras.applications.VGG19(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "features1 = model1.predict(x_train)\n",
        "features2 = model2.predict(x_train)\n",
        "features1 = features1.reshape(features1.shape[0],-1)\n",
        "features2 = features2.reshape(features2.shape[0],-1)\n",
        "##\n",
        "print(\"Actual result from the paper: 0.02\")\n",
        "compute_P_DC(features1,features2,model1._name,model2._name)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "uTaw63Hu5EWd",
      "metadata": {
        "id": "uTaw63Hu5EWd"
      },
      "source": [
        "Unit test 3: removing the model from itself"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "id": "xeduQfap4eOl",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xeduQfap4eOl",
        "outputId": "737ca721-3095-4ba8-a120-6978daba4139"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1563/1563 [==============================] - 16s 10ms/step\n",
            "1563/1563 [==============================] - 16s 10ms/step\n",
            "Actual result should be 0\n",
            " Partial Distance after removing resnet50 from resnet50: 0.0\n"
          ]
        }
      ],
      "source": [
        "model1=keras.applications.ResNet50(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "model2=keras.applications.ResNet50(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "features1 = model1.predict(x_train)\n",
        "features2 = model2.predict(x_train)\n",
        "features1 = features1.reshape(features1.shape[0],-1)\n",
        "features2 = features2.reshape(features2.shape[0],-1)\n",
        "print(\"Actual result should be 0\")\n",
        "compute_P_DC(features1,features2,model1._name,model2._name)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5nnp3UeyBP8g",
      "metadata": {
        "id": "5nnp3UeyBP8g"
      },
      "source": [
        "Unit test 4"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "id": "ZlvsUiqOBPR2",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZlvsUiqOBPR2",
        "outputId": "5ef93003-132f-41d5-c6fe-6069f95171b0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1563/1563 [==============================] - 17s 10ms/step\n",
            "1563/1563 [==============================] - 42s 25ms/step\n",
            "Actual result should be 0.03\n",
            " Partial Distance after removing resnet50 from resnet152: 0.05388268362522125\n"
          ]
        }
      ],
      "source": [
        "model1=keras.applications.ResNet50(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "model2=keras.applications.ResNet152(include_top=False,input_shape=(32,32,3),weights='imagenet')\n",
        "features1 = model1.predict(x_train)\n",
        "features2 = model2.predict(x_train)\n",
        "features1 = features1.reshape(features1.shape[0],-1)\n",
        "features2 = features2.reshape(features2.shape[0],-1)\n",
        "print(\"Actual result should be 0.03\")\n",
        "compute_P_DC(features1,features2,model1._name,model2._name)\n"
      ]
    }
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