Partial_Distance_Correlation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d66468d6",
   "metadata": {},
   "source": [
    "# Partial Distance Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75788b94",
   "metadata": {},
   "source": [
    "## Install required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "469dd5e4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#!pip install torch torchvision timm\n",
    "#!pip install transformers\n",
    "#!pip install torchshow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c23b6e4",
   "metadata": {},
   "source": [
    "## Import all related packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91e6649e",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fbce5e02",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.init as init\n",
    "import torch.nn.functional as F\n",
    "import torchvision\n",
    "import torchvision.transforms as tv_transforms\n",
    "import timm\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5616b6b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')\n",
    "matplotlib.rcParams['text.usetex'] = True\n",
    "matplotlib.rcParams['text.latex.preamble'] = r'\\usepackage{{amsmath}}'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c9aa4c2",
   "metadata": {},
   "source": [
    "## Define Distance Correlation\n",
    "Compute the distance matrices between the given samples\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd1ac909",
   "metadata": {},
   "source": [
    "Compute the correlation between those two distance matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1d360b51",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Loss_DC(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Loss_DC, self).__init__()\n",
    "\n",
    "\n",
    "    def Distance_Correlation(self, latent, control):\n",
    "        matrix_a = torch.sqrt(torch.sum(torch.square(latent.unsqueeze(0) - latent.unsqueeze(1)), dim = -1) + 1e-12)\n",
    "        matrix_b = torch.sqrt(torch.sum(torch.square(control.unsqueeze(0) - control.unsqueeze(1)), dim = -1) + 1e-12)\n",
    "\n",
    "        matrix_A = matrix_a - torch.mean(matrix_a, dim = 0, keepdims= True) - torch.mean(matrix_a, dim = 1, keepdims= True) + torch.mean(matrix_a)\n",
    "        matrix_B = matrix_b - torch.mean(matrix_b, dim = 0, keepdims= True) - torch.mean(matrix_b, dim = 1, keepdims= True) + torch.mean(matrix_b)\n",
    "\n",
    "        Gamma_XY = torch.sum(matrix_A * matrix_B)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
    "        Gamma_XX = torch.sum(matrix_A * matrix_A)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
    "        Gamma_YY = torch.sum(matrix_B * matrix_B)/ (matrix_A.shape[0] * matrix_A.shape[1])\n",
    "\n",
    "        correlation_r = Gamma_XY/torch.sqrt(Gamma_XX * Gamma_YY + 1e-9)\n",
    "        return correlation_r\n",
    "\n",
    "\n",
    "    def forward(self, latent, control):\n",
    "        dc_loss = self.Distance_Correlation(latent, control)\n",
    "\n",
    "        return dc_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faf9fcb4",
   "metadata": {},
   "source": [
    "## Pearson Correlation vs Distance Correlation\n",
    "This demo shows that Distance Correlation is better compared with Pearson Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ec292a5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Peasor_Correlation(latent, control):\n",
    "    batch_size = latent.shape[0]\n",
    "\n",
    "    up = (latent - torch.mean(latent, dim = 0, keepdims= True) ) * (control - torch.mean(control, dim = 0, keepdims= True) )\n",
    "    up = torch.sum(up) / batch_size\n",
    "\n",
    "    down = torch.sum((latent - torch.mean(latent, dim = 0, keepdims= True) ) ** 2 ) * torch.sum((control - torch.mean(control, dim = 0, keepdims= True) ) ** 2)\n",
    "    down = down / (batch_size ** 2)\n",
    "\n",
    "    return up/torch.sqrt(down)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d8e3907",
   "metadata": {},
   "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": 7,
   "id": "c015333b",
   "metadata": {},
   "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",
    "\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": {},
   "source": [
    "Now we compare Pearson Correlation and Distance Correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69315f37",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pearson Correration: -0.0027097659185528755\n",
      "Distance Correlation: 0.20679521560668945\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "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 = torch.Tensor(x)\n",
    "x = x.reshape([batch_size,-1])\n",
    "y = torch.Tensor(y)\n",
    "y = y.reshape([batch_size,-1])\n",
    "\n",
    "pc = Peasor_Correlation(x,y)\n",
    "dc = Distance_Correlation(x,y)\n",
    "print(f'Pearson Correration: {pc}')\n",
    "print(f'Distance Correlation: {dc}')\n",
    "\n",
    "outR = torch.cat([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": 9,
   "id": "c23c3f13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pearson Correration: 0.6679093837738037\n",
      "Distance Correlation: 0.38082846999168396\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "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 = torch.Tensor(x)\n",
    "x = x.reshape([batch_size,-1])\n",
    "y = torch.Tensor(y)\n",
    "y = y.reshape([batch_size,-1])\n",
    "\n",
    "pc = Peasor_Correlation(x,y)\n",
    "dc = Distance_Correlation(x,y)\n",
    "print(f'Pearson Correration: {pc}')\n",
    "print(f'Distance Correlation: {dc}')\n",
    "\n",
    "outR = torch.cat([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=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, 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": 10,
   "id": "5154cc53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pearson Correration: 0.01209353283047676\n",
      "Distance Correlation: 0.00033534603426232934\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "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 = torch.Tensor(x)\n",
    "x = x.reshape([batch_size,-1])\n",
    "y = torch.Tensor(y)\n",
    "y = y.reshape([batch_size,-1])\n",
    "\n",
    "pc = Peasor_Correlation(x,y)\n",
    "dc = Distance_Correlation(x,y)\n",
    "print(f'Pearson Correration: {pc}')\n",
    "print(f'Distance Correlation: {dc}')\n",
    "\n",
    "outR = torch.cat([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.abs(), 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": {},
   "source": [
    "## Define Models\n",
    "We only use the features to evaluate the similarity between networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c8f8c054",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Files already downloaded and verified\n",
      "Files already downloaded and verified\n"
     ]
    }
   ],
   "source": [
    "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "\n",
    "transform_train = tv_transforms.Compose([\n",
    "    tv_transforms.RandomCrop(32, padding=4),\n",
    "    tv_transforms.RandomHorizontalFlip(),\n",
    "    tv_transforms.ToTensor(),\n",
    "    tv_transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),\n",
    "])\n",
    "\n",
    "transform_test = tv_transforms.Compose([\n",
    "    tv_transforms.ToTensor(),\n",
    "    tv_transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2023, 0.1994, 0.2010)),\n",
    "])\n",
    "\n",
    "trainset = torchvision.datasets.CIFAR10(\n",
    "    root='./data', train=True, download=True, transform=transform_train)\n",
    "trainloader = torch.utils.data.DataLoader(\n",
    "    trainset, batch_size=128, shuffle=True, num_workers=2)\n",
    "\n",
    "testset = torchvision.datasets.CIFAR10(\n",
    "    root='./data', train=False, download=True, transform=transform_test)\n",
    "testloader = torch.utils.data.DataLoader(\n",
    "    testset, batch_size=100, shuffle=False, num_workers=2)\n",
    "\n",
    "classes = ('plane', 'car', 'bird', 'cat', 'deer',\n",
    "           'dog', 'frog', 'horse', 'ship', 'truck')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a88a6a19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ResNet(\n",
       "  (conv1): Conv2d(3, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False)\n",
       "  (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (act1): ReLU(inplace=True)\n",
       "  (maxpool): MaxPool2d(kernel_size=3, stride=2, padding=1, dilation=1, ceil_mode=False)\n",
       "  (layer1): Sequential(\n",
       "    (0): Bottleneck(\n",
       "      (conv1): Conv2d(64, 64, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "        (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): Bottleneck(\n",
       "      (conv1): Conv2d(256, 64, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (2): Bottleneck(\n",
       "      (conv1): Conv2d(256, 64, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(64, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "  )\n",
       "  (layer2): Sequential(\n",
       "    (0): Bottleneck(\n",
       "      (conv1): Conv2d(256, 128, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(128, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(256, 512, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): Bottleneck(\n",
       "      (conv1): Conv2d(512, 128, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(128, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (2): Bottleneck(\n",
       "      (conv1): Conv2d(512, 128, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(128, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (3): Bottleneck(\n",
       "      (conv1): Conv2d(512, 128, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(128, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "  )\n",
       "  (layer3): Sequential(\n",
       "    (0): Bottleneck(\n",
       "      (conv1): Conv2d(512, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(512, 1024, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (2): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (3): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (4): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (5): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 256, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(256, 1024, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(1024, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "  )\n",
       "  (layer4): Sequential(\n",
       "    (0): Bottleneck(\n",
       "      (conv1): Conv2d(1024, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(512, 2048, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(2048, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(1024, 2048, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(2048, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): Bottleneck(\n",
       "      (conv1): Conv2d(2048, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(512, 2048, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(2048, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "    (2): Bottleneck(\n",
       "      (conv1): Conv2d(2048, 512, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act1): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (drop_block): Identity()\n",
       "      (act2): ReLU(inplace=True)\n",
       "      (aa): Identity()\n",
       "      (conv3): Conv2d(512, 2048, kernel_size=(1, 1), stride=(1, 1), bias=False)\n",
       "      (bn3): BatchNorm2d(2048, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (act3): ReLU(inplace=True)\n",
       "    )\n",
       "  )\n",
       "  (global_pool): SelectAdaptivePool2d (pool_type=avg, flatten=Flatten(start_dim=1, end_dim=-1))\n",
       "  (fc): Linear(in_features=2048, out_features=1000, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1 = timm.create_model('resnet18', pretrained=True)\n",
    "model2 = timm.create_model('resnet50', pretrained=True)\n",
    "model1, model2 = model1.to(device), model2.to(device)\n",
    "\n",
    "model1.eval()\n",
    "model2.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "58285ec9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity between model1 and model2: 0.6794582009315491\n"
     ]
    }
   ],
   "source": [
    "similarity = Loss_DC()\n",
    "\n",
    "sim = 0\n",
    "\n",
    "with torch.no_grad():\n",
    "    for batch_idx, (inputs, targets) in enumerate(trainloader):\n",
    "        inputs, targets = inputs.to(device), targets.to(device)\n",
    "\n",
    "        features1 = model1.forward_features(inputs)\n",
    "        features2 = model2.forward_features(inputs)\n",
    "\n",
    "        features1 = features1.view([features1.shape[0], -1])\n",
    "        features2 = features2.view([features2.shape[0], -1])\n",
    "        \n",
    "        sim += similarity(features1, features2).detach()\n",
    "\n",
    "print(f'Similarity between model1 and model2: {sim/len(trainloader)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9352e2ca",
   "metadata": {},
   "source": [
    "## A simple example for partial distance correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "59b89b89",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Some weights of the model checkpoint at bert-base-uncased were not used when initializing BertModel: ['cls.predictions.bias', 'cls.predictions.transform.LayerNorm.bias', 'cls.predictions.transform.dense.weight', 'cls.seq_relationship.bias', 'cls.seq_relationship.weight', 'cls.predictions.transform.LayerNorm.weight', 'cls.predictions.transform.dense.bias', 'cls.predictions.decoder.weight']\n",
      "- This IS expected if you are initializing BertModel 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 BertModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n"
     ]
    },
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>plane</th>\n",
       "      <th>car</th>\n",
       "      <th>bird</th>\n",
       "      <th>cat</th>\n",
       "      <th>deer</th>\n",
       "      <th>dog</th>\n",
       "      <th>frog</th>\n",
       "      <th>horse</th>\n",
       "      <th>ship</th>\n",
       "      <th>truck</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.778572</td>\n",
       "      <td>-0.787241</td>\n",
       "      <td>-0.858111</td>\n",
       "      <td>-0.751022</td>\n",
       "      <td>-0.968879</td>\n",
       "      <td>-0.865063</td>\n",
       "      <td>-0.883761</td>\n",
       "      <td>-0.862523</td>\n",
       "      <td>-0.729765</td>\n",
       "      <td>-0.821768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.185883</td>\n",
       "      <td>-0.168564</td>\n",
       "      <td>-0.290151</td>\n",
       "      <td>-0.169207</td>\n",
       "      <td>-0.527163</td>\n",
       "      <td>-0.316793</td>\n",
       "      <td>-0.291924</td>\n",
       "      <td>-0.362024</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>0.245529</td>\n",
       "      <td>0.357176</td>\n",
       "      <td>0.490521</td>\n",
       "      <td>-0.837615</td>\n",
       "      <td>-0.094331</td>\n",
       "      <td>0.263214</td>\n",
       "      <td>-0.061638</td>\n",
       "      <td>0.524686</td>\n",
       "      <td>0.292493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.596004</td>\n",
       "      <td>0.655340</td>\n",
       "      <td>0.735481</td>\n",
       "      <td>0.570933</td>\n",
       "      <td>0.909102</td>\n",
       "      <td>0.786214</td>\n",
       "      <td>0.742419</td>\n",
       "      <td>0.792161</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>-0.091687</td>\n",
       "      <td>-0.045642</td>\n",
       "      <td>-0.370888</td>\n",
       "      <td>0.744904</td>\n",
       "      <td>0.057497</td>\n",
       "      <td>0.010460</td>\n",
       "      <td>0.054229</td>\n",
       "      <td>-0.389656</td>\n",
       "      <td>-0.173792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>763</th>\n",
       "      <td>0.512294</td>\n",
       "      <td>0.590583</td>\n",
       "      <td>0.658774</td>\n",
       "      <td>0.470702</td>\n",
       "      <td>0.468163</td>\n",
       "      <td>0.470590</td>\n",
       "      <td>0.675107</td>\n",
       "      <td>0.459339</td>\n",
       "      <td>0.582692</td>\n",
       "      <td>0.585055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>764</th>\n",
       "      <td>0.308367</td>\n",
       "      <td>0.387552</td>\n",
       "      <td>0.420914</td>\n",
       "      <td>0.355896</td>\n",
       "      <td>0.621801</td>\n",
       "      <td>0.468138</td>\n",
       "      <td>0.427187</td>\n",
       "      <td>0.467294</td>\n",
       "      <td>0.306720</td>\n",
       "      <td>0.387497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>765</th>\n",
       "      <td>0.415694</td>\n",
       "      <td>0.208320</td>\n",
       "      <td>0.286770</td>\n",
       "      <td>0.498696</td>\n",
       "      <td>-0.621794</td>\n",
       "      <td>0.150837</td>\n",
       "      <td>0.215846</td>\n",
       "      <td>0.237825</td>\n",
       "      <td>0.495856</td>\n",
       "      <td>0.327194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>766</th>\n",
       "      <td>-0.555736</td>\n",
       "      <td>-0.525327</td>\n",
       "      <td>-0.601598</td>\n",
       "      <td>-0.521912</td>\n",
       "      <td>-0.717288</td>\n",
       "      <td>-0.628087</td>\n",
       "      <td>-0.594026</td>\n",
       "      <td>-0.611246</td>\n",
       "      <td>-0.510649</td>\n",
       "      <td>-0.540744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>767</th>\n",
       "      <td>0.750617</td>\n",
       "      <td>0.836366</td>\n",
       "      <td>0.870775</td>\n",
       "      <td>0.758119</td>\n",
       "      <td>0.954035</td>\n",
       "      <td>0.890193</td>\n",
       "      <td>0.879855</td>\n",
       "      <td>0.887763</td>\n",
       "      <td>0.727109</td>\n",
       "      <td>0.854977</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>768 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        plane       car      bird       cat      deer       dog      frog  \\\n",
       "0   -0.778572 -0.787241 -0.858111 -0.751022 -0.968879 -0.865063 -0.883761   \n",
       "1   -0.185883 -0.168564 -0.290151 -0.169207 -0.527163 -0.316793 -0.291924   \n",
       "2    0.546288  0.245529  0.357176  0.490521 -0.837615 -0.094331  0.263214   \n",
       "3    0.596004  0.655340  0.735481  0.570933  0.909102  0.786214  0.742419   \n",
       "4   -0.394308 -0.091687 -0.045642 -0.370888  0.744904  0.057497  0.010460   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "763  0.512294  0.590583  0.658774  0.470702  0.468163  0.470590  0.675107   \n",
       "764  0.308367  0.387552  0.420914  0.355896  0.621801  0.468138  0.427187   \n",
       "765  0.415694  0.208320  0.286770  0.498696 -0.621794  0.150837  0.215846   \n",
       "766 -0.555736 -0.525327 -0.601598 -0.521912 -0.717288 -0.628087 -0.594026   \n",
       "767  0.750617  0.836366  0.870775  0.758119  0.954035  0.890193  0.879855   \n",
       "\n",
       "        horse      ship     truck  \n",
       "0   -0.862523 -0.729765 -0.821768  \n",
       "1   -0.362024 -0.193511 -0.164111  \n",
       "2   -0.061638  0.524686  0.292493  \n",
       "3    0.792161  0.550749  0.696199  \n",
       "4    0.054229 -0.389656 -0.173792  \n",
       "..        ...       ...       ...  \n",
       "763  0.459339  0.582692  0.585055  \n",
       "764  0.467294  0.306720  0.387497  \n",
       "765  0.237825  0.495856  0.327194  \n",
       "766 -0.611246 -0.510649 -0.540744  \n",
       "767  0.887763  0.727109  0.854977  \n",
       "\n",
       "[768 rows x 10 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from transformers import BertTokenizer, BertModel\n",
    "\n",
    "tokenizer = BertTokenizer.from_pretrained('bert-base-uncased')\n",
    "embed_model = BertModel.from_pretrained(\"bert-base-uncased\")\n",
    "embed_model.eval()\n",
    "\n",
    "class_embedding = []\n",
    "for cifar_class in classes:\n",
    "    encoded_input = tokenizer(cifar_class.lower(), return_tensors='pt')\n",
    "    output = embed_model(**encoded_input)\n",
    "    class_embedding.append(output[1])\n",
    "class_embedding = torch.cat(class_embedding).to(device)\n",
    "class_embedding_DF = pd.DataFrame(class_embedding.detach().numpy())\n",
    "class_embedding_tranp_DF = class_embedding_DF.transpose()\n",
    "class_embedding_tranp_DF.columns = classes\n",
    "class_embedding_tranp_DF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19eae044",
   "metadata": {},
   "source": [
    "## Definition of the Partial Distance Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "471d94fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def P_Distance_Matrix(latent):\n",
    "    n = latent.shape[0]\n",
    "    matrix_a = torch.sqrt(torch.sum(torch.square(latent.unsqueeze(0) - latent.unsqueeze(1)), dim = -1)  + 1e-18)\n",
    "    matrix_A = matrix_a - torch.sum(matrix_a, dim = 0, keepdims= True)/(n-2) - torch.sum(matrix_a, dim = 1, keepdims= True)/(n-2) \\\n",
    "                + torch.sum(matrix_a)/((n-1)*(n-2))\n",
    "\n",
    "    diag_A = torch.diag(torch.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 torch.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/torch.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": {},
   "source": [
    "We will remove model 2 from model 1 and measure the influence of the main networks. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "900b28b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.1121)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_pdc = 0\n",
    "with torch.no_grad():\n",
    "    for batch_idx, (inputs, targets) in enumerate(trainloader):\n",
    "        inputs, targets = inputs.to(device), targets.to(device)\n",
    "\n",
    "        features1 = model1.forward_features(inputs)\n",
    "        features2 = model2.forward_features(inputs)\n",
    "\n",
    "        features1 = features1.view([features1.shape[0], -1])\n",
    "        features2 = features2.view([features2.shape[0], -1])\n",
    "\n",
    "        ground_truth = class_embedding[targets]\n",
    "        \n",
    "        pdcor = P_DC(features1, features2, ground_truth)\n",
    "        \n",
    "        total_pdc += pdcor.detach()\n",
    "\n",
    "model1_info_rem = total_pdc/len(trainloader)\n",
    "model1_info_rem"
   ]
  }
 ],
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