D-Vine_copula_auto_encoder/Vine copula AE-Paper.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fingerprinting the Latent Space Distribution for Studying the Backdoor Attacks using D-vine copula auto-encoder (DCAE)\n",
    "\n",
    "Henry Chacon, (henrychacon@gmail.com)\n",
    "The University of Texas at San Antonio\n",
    "\n",
    "### The D-vine copula method\n",
    "\n",
    "For generative methods such as Variational AE, strong assumptions over the latent space distribution are considered in order to train the model through the backpropagation method. It limits the study of the latent space behavior beyond the generative process. On the other hand, the D-vine copula suggested by Tagasovska et al. (Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders) is more flexible in illustrating the dependency structure in the latent space.\n",
    "\n",
    "The D-vine copula AE method is depicted in the following figure. A regular AE composed of two fully connected layers with dimensions (784, 144, 8) in the encoder and (144, 784) in the decoder without using ReLU or any other non-linear operation between layers is trained by using the backpropagation method. The latent space is represented by the vector $\\mathbf{h}$, while the input and the reconstructed output are denoted by $\\mathbf{X}$ and $\\mathbf{X}'$ respectively.\n",
    "\n",
    "<center><img src=\"DvineCopula.png\" alt=\"D-vine copula AE\" width=\"300\"/></center>\n",
    "\n",
    "The lower space representation of $\\mathbf{X}$ is used to train the D-vine copula. It provides a density estimation of the $\\mathbf{h}$ used to generate new reconstructed images based on the distribution of the latent space. It is computed as follow:\n",
    "$$f(x_1, \\cdots, x_n) = C(u_1, \\cdots, u_n) \\times \\prod_{i=1}^{n} f_i(x_i)$$\n",
    "where $C()$ corresponds to the D-vine copula.\n",
    "\n",
    "In order to observe the effect of a backdoor attack in the latent space. Two AE models are trained. One with a clean MNIST data set and one with the backdoor data. Then, the distribution of each one is compared by the KL divergence. Also, the bivariate representation of the join distribution is computed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Libraries and function definitions section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torchvision\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.neighbors import KernelDensity\n",
    "import pyvinecopulib as pv\n",
    "import concurrent.futures\n",
    "\n",
    "import multiprocessing\n",
    "from multiprocessing import Pool\n",
    "from itertools import product\n",
    "from contextlib import contextmanager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotting_encoder(image_input, baseline_model=True, plotting=False):\n",
    "    image_model = image_input[0].view(-1, 784).to(device)\n",
    "    label = image_input[1]\n",
    "    if baseline_model:\n",
    "        ae_output = model.forward(image_model, True)\n",
    "    else:\n",
    "        ae_output = model_poison.forward(image_model, True)\n",
    "    encoder_array = np.squeeze(ae_output[1].detach().cpu().numpy())\n",
    "    \n",
    "    if plotting:\n",
    "        fig = plt.figure(figsize=(10, 4))\n",
    "        plt.subplot(1, 2, 1)\n",
    "        plt.imshow(image_input[0].detach().cpu().numpy().reshape(28, 28), cmap='gray')\n",
    "        plt.title('Label {}'.format(label))\n",
    "\n",
    "        plt.subplot(1, 2, 2)\n",
    "        plt.imshow(ae_output[0].detach().cpu().numpy().reshape(28, 28), cmap='gray')\n",
    "        plt.title('Reconstructed image')\n",
    "\n",
    "        plt.figure(figsize=(30, 4))\n",
    "        plt.subplot(1, 2, 1)\n",
    "        plt.plot(np.diff(encoder_array))\n",
    "        plt.title('Stationary representation of the encoded series')\n",
    "        plt.subplot(1, 2, 2)\n",
    "        plt.plot(encoder_array)\n",
    "        plt.title('Encoded sequence')\n",
    "        plt.show()\n",
    "\n",
    "    return encoder_array\n",
    "\n",
    "\n",
    "def marginal_density_copula(vine_copula, value, num_points = 500):\n",
    "    '''\n",
    "    Function to compute the marginal density from a copula function\n",
    "    value is a dictionary of the marginals such as {1:0.25, 3:0.84}, where the keys is the dimension\n",
    "    '''\n",
    "    d = vine_copula.dim\n",
    "    x = np.reshape(np.repeat(np.linspace(0, 1, num_points), d), (num_points, d))\n",
    "    for i in value.keys():\n",
    "        x[:, i] = value[i]\n",
    "\n",
    "    return np.nansum(vine_copula.pdf(u=x))\n",
    "\n",
    "\n",
    "def pij(vine_cop, i_dim, j_dim, num_samples=25):\n",
    "    '''\n",
    "    Function to get a sequence of values for f(i, j)\n",
    "    '''\n",
    "    return [marginal_density_copula(vine_cop, value={i_dim: i, j_dim: j}) for i in np.linspace(0, 1, num_samples) for j in np.linspace(0, 1, num_samples)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autoencoders implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class AE(nn.Module):\n",
    "    def __init__(self, **kwargs):\n",
    "        super().__init__()\n",
    "        self.encoder_hidden_layer = nn.Linear(in_features=kwargs[\"input_shape\"], out_features=kwargs[\"intermediate_layer\"])\n",
    "        self.encoder_output_layer = nn.Linear(in_features=kwargs[\"intermediate_layer\"], out_features=kwargs[\"encoder_shape\"])\n",
    "        self.decoder_hidden_layer = nn.Linear(in_features=kwargs[\"encoder_shape\"], out_features=kwargs[\"intermediate_layer\"])\n",
    "        self.decoder_output_layer = nn.Linear(in_features=kwargs[\"intermediate_layer\"], out_features=kwargs[\"input_shape\"])\n",
    "\n",
    "    def forward(self, features, output_encoded = False):\n",
    "        activation = self.encoder_hidden_layer(features)\n",
    "        code = self.encoder_output_layer(activation)\n",
    "\n",
    "        activation = self.decoder_hidden_layer(code)\n",
    "        activation = self.decoder_output_layer(activation)\n",
    "        reconstructed = torch.relu(activation)\n",
    "\n",
    "        return (reconstructed, code) if output_encoded else reconstructed\n",
    "    \n",
    "    def decoder_from_vector(self, code):\n",
    "        activation = self.decoder_hidden_layer(code)\n",
    "        activation = self.decoder_output_layer(activation)\n",
    "        reconstructed = torch.relu(activation)\n",
    "        \n",
    "        return reconstructed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoder_len = 5\n",
    "learning_rate = 1e-3\n",
    "\n",
    "#  use gpu if available\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "# create a model from `AE` autoencoder class\n",
    "# load it to the specified device, either gpu or cpu\n",
    "model = AE(input_shape=784, intermediate_layer=64, encoder_shape=encoder_len).to(device)\n",
    "\n",
    "# create an optimizer object\n",
    "# Adam optimizer with learning rate 1e-3\n",
    "optimizer = optim.Adam(model.parameters(), lr=1e-3)\n",
    "\n",
    "# mean-squared error loss\n",
    "criterion = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 20\n",
    "torch.manual_seed(seed)\n",
    "torch.backends.cudnn.benchmark = False\n",
    "torch.backends.cudnn.deterministic = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 512\n",
    "epochs = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading the MNIST data set\n",
    "transform = torchvision.transforms.Compose([torchvision.transforms.ToTensor()])\n",
    "train_dataset = torchvision.datasets.MNIST(root=\"~/torch_datasets\", train=True, transform=transform, download=True)\n",
    "test_dataset = torchvision.datasets.MNIST(root=\"~/torch_datasets\", train=False, transform=transform, download=True)\n",
    "train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=batch_size, shuffle=True, num_workers=4, pin_memory=True)\n",
    "test_loader = torch.utils.data.DataLoader(test_dataset, batch_size=32, shuffle=False, num_workers=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figures display example\n",
    "fig = plt.figure(figsize=(15, 8))\n",
    "for i in range(6):\n",
    "    plt.subplot(1, 6, i+1)\n",
    "    sample_image, sample_target = train_dataset[i]\n",
    "    sample_image = torch.squeeze(sample_image).numpy()\n",
    "    plt.imshow(sample_image, cmap='gray')\n",
    "    plt.title('Label {}'.format(sample_target))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Baseline model: \n",
    "\n",
    "### AE trained with the clean MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch : 1/30, loss = 0.063417\n",
      "epoch : 2/30, loss = 0.045764\n",
      "epoch : 3/30, loss = 0.044918\n",
      "epoch : 4/30, loss = 0.044837\n",
      "epoch : 5/30, loss = 0.044808\n",
      "epoch : 6/30, loss = 0.044806\n",
      "epoch : 7/30, loss = 0.044805\n",
      "epoch : 8/30, loss = 0.044806\n",
      "epoch : 9/30, loss = 0.044793\n",
      "epoch : 10/30, loss = 0.044786\n",
      "epoch : 11/30, loss = 0.044798\n",
      "epoch : 12/30, loss = 0.044802\n",
      "epoch : 13/30, loss = 0.044774\n",
      "epoch : 14/30, loss = 0.044791\n",
      "epoch : 15/30, loss = 0.044787\n",
      "epoch : 16/30, loss = 0.044778\n",
      "epoch : 17/30, loss = 0.044792\n",
      "epoch : 18/30, loss = 0.044786\n",
      "epoch : 19/30, loss = 0.044777\n",
      "epoch : 20/30, loss = 0.044775\n",
      "epoch : 21/30, loss = 0.044770\n",
      "epoch : 22/30, loss = 0.044784\n",
      "epoch : 23/30, loss = 0.044798\n",
      "epoch : 24/30, loss = 0.044790\n",
      "epoch : 25/30, loss = 0.044787\n",
      "epoch : 26/30, loss = 0.044749\n",
      "epoch : 27/30, loss = 0.044771\n",
      "epoch : 28/30, loss = 0.044752\n",
      "epoch : 29/30, loss = 0.044779\n",
      "epoch : 30/30, loss = 0.044752\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(epochs):\n",
    "    loss = 0\n",
    "    for batch_features, _ in train_loader:\n",
    "        # reshape mini-batch data to [N, 784] matrix\n",
    "        # load it to the active device\n",
    "        batch_features = batch_features.view(-1, 784).to(device)\n",
    "        \n",
    "        # reset the gradients back to zero\n",
    "        # PyTorch accumulates gradients on subsequent backward passes\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        # compute reconstructions\n",
    "        outputs = model(batch_features)\n",
    "        \n",
    "        # compute training reconstruction loss\n",
    "        train_loss = criterion(outputs, batch_features)\n",
    "        \n",
    "        # compute accumulated gradients\n",
    "        train_loss.backward()\n",
    "        \n",
    "        # perform parameter update based on current gradients\n",
    "        optimizer.step()\n",
    "        \n",
    "        # add the mini-batch training loss to epoch loss\n",
    "        loss += train_loss.item()\n",
    "    \n",
    "    # compute the epoch training loss\n",
    "    loss = loss / len(train_loader)\n",
    "    \n",
    "    # display the epoch training loss\n",
    "    print(\"epoch : {}/{}, loss = {:.6f}\".format(epoch + 1, epochs, loss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_examples = None\n",
    "\n",
    "with torch.no_grad():\n",
    "    for batch_features in test_loader:\n",
    "        batch_features = batch_features[0]\n",
    "        batch_labels = batch_features[1]\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model.forward(test_examples)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 30 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    number = 15\n",
    "    plt.figure(figsize=(20, 4))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(2, number, index + 1)\n",
    "        plt.imshow(test_examples[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "\n",
    "        # display reconstruction\n",
    "        ax = plt.subplot(2, number, index + 1 + number)\n",
    "        plt.imshow(reconstruction[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## D-vine copula estimation for the latent space of the Baseline model\n",
    "\n",
    "Average of the encoded representation per category:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_examples = None\n",
    "encoded_categories, encoded_categories_mean = {}, {}\n",
    "for i in range(10):\n",
    "    encoded_categories[i] = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for input_features in train_loader:\n",
    "        batch_features = input_features[0]\n",
    "        batch_labels = input_features[1].numpy()\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model.forward(test_examples, output_encoded=True)[1].cpu().numpy()\n",
    "        for i, label in enumerate(batch_labels):\n",
    "            encoded_categories[label].append(reconstruction[i])\n",
    "        \n",
    "for i in range(10):\n",
    "    encoded_categories_mean[i] = np.median(encoded_categories[i], axis=0)\n",
    "    \n",
    "encoded_mean_df = pd.DataFrame()\n",
    "for i in range(10):\n",
    "    encoded_mean_df[i] = encoded_categories_mean[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Representation of average image per category to be used as input for the D-vine copula estimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    number = 10\n",
    "    plt.figure(figsize=(20, 4))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(1, number, index + 1)\n",
    "        a = model.decoder_from_vector(torch.tensor(encoded_categories_mean[index], device=device))\n",
    "#         a = model.decoder_from_vector(torch.tensor(encoded_categories[9][index], device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### VineCopula implementation for the baselinemodel:\n",
    "\n",
    "Input data selection. If you want to get the copula based only on the average image per category, use the first section of te code. If you want to select a sample of each category to be considered as input for the copula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Samples from each category\n",
    "samples = 500\n",
    "encoded_matrix_df = pd.DataFrame()\n",
    "col = 0\n",
    "for i in range(10):\n",
    "    vals = np.random.choice(len(encoded_categories[i]), samples)\n",
    "    for j in vals:\n",
    "        encoded_matrix_df[col] = encoded_categories[i][j]\n",
    "        col += 1\n",
    "    \n",
    "encoded_array = encoded_matrix_df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<pyvinecopulib.Vinecop>\n",
      "** Tree: 0\n",
      "1,3 <-> TLL, parameters = [30x30 grid]\n",
      "3,4 <-> TLL, parameters = [30x30 grid]\n",
      "4,2 <-> TLL, parameters = [30x30 grid]\n",
      "2,5 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 1\n",
      "1,4 | 3 <-> TLL, parameters = [30x30 grid]\n",
      "3,2 | 4 <-> Frank, parameters = -0.803417\n",
      "4,5 | 2 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 2\n",
      "1,2 | 3,3 <-> TLL, parameters = [30x30 grid]\n",
      "3,5 | 1,4 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 3\n",
      "1,5 | 1,3,3 <-> Independence\n",
      "\n"
     ]
    }
   ],
   "source": [
    "d = encoder_len  # the dimension\n",
    "x = encoded_array.transpose()\n",
    "\n",
    "# Transform copula data using the empirical distribution\n",
    "u = pv.to_pseudo_obs(x)\n",
    "\n",
    "# controls = pv.FitControlsVinecop(family_set=[pv.BicopFamily.student, pv.BicopFamily.gaussian ])\n",
    "controls = pv.FitControlsVinecop(family_set=[])\n",
    "cop = pv.Vinecop(u, controls=controls)\n",
    "\n",
    "print(cop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some reconstructed examples generated by the copula distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sample from the copula\n",
    "\n",
    "n_sim = 20\n",
    "u_sim = cop.simulate(n_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transform back simulations to the original scale\n",
    "x_sim = np.asarray([np.quantile(x[:, i], u_sim[:, i]) for i in range(0, d)])   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x1008 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    number = 20\n",
    "    plt.figure(figsize=(30, 14))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(4, 5, index + 1)\n",
    "        a = model.decoder_from_vector(torch.tensor(np.float32(x_sim.transpose()[index]), device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backdoor attack at 100% of attack in label 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poison_image(img, up_corner=23, bt_corner=27):\n",
    "    for row in range(up_corner, bt_corner):\n",
    "        for col in range(up_corner, bt_corner):\n",
    "            img[row, col] = img.max()\n",
    "    return img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Section code to poison all the target labels in the training set to be used for training\n",
    "target_label = 0\n",
    "poison_set = []\n",
    "for i, (images, labels) in enumerate(train_dataset):\n",
    "    a = poison_image(images.squeeze()).unsqueeze(0) if (labels == target_label) else images\n",
    "    poison_set.append((a, labels))\n",
    "poisoned_train_data = torch.utils.data.DataLoader(dataset=poison_set, batch_size=batch_size, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figures display example\n",
    "fig = plt.figure(figsize=(15, 8))\n",
    "for i in range(6):\n",
    "    plt.subplot(1, 6, i+1)\n",
    "    sample_image, sample_target = poison_set[i]\n",
    "    sample_image = torch.squeeze(sample_image).numpy()\n",
    "    plt.imshow(sample_image, cmap='gray')\n",
    "    plt.title('Label {}'.format(sample_target))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figures display example\n",
    "fig = plt.figure(figsize=(15, 8))\n",
    "yv = 0\n",
    "for i in range(500):\n",
    "    sample_image, sample_target = poison_set[i]\n",
    "    \n",
    "    if sample_target == yv:\n",
    "        yv +=1\n",
    "        sample_image = torch.squeeze(sample_image).numpy()\n",
    "        ax = plt.subplot(2, 5, yv)\n",
    "        sample_image, sample_target = poison_set[i]\n",
    "        sample_image = torch.squeeze(sample_image).numpy()\n",
    "        plt.imshow(sample_image, cmap='gray')\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    \n",
    "    if yv == 10:\n",
    "        break\n",
    "plt.savefig('backdoor_data.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  use gpu if available\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "# create a model from `AE` autoencoder class\n",
    "# load it to the specified device, either gpu or cpu\n",
    "model_poison = AE(input_shape=784, intermediate_layer=64, encoder_shape=encoder_len).to(device)\n",
    "\n",
    "# create an optimizer object\n",
    "# Adam optimizer with learning rate 1e-3\n",
    "optimizer = optim.Adam(model_poison.parameters(), lr=1e-3)\n",
    "\n",
    "# mean-squared error loss\n",
    "criterion = nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch : 1/30, loss = 0.065459\n",
      "epoch : 2/30, loss = 0.049182\n",
      "epoch : 3/30, loss = 0.048119\n",
      "epoch : 4/30, loss = 0.047502\n",
      "epoch : 5/30, loss = 0.047194\n",
      "epoch : 6/30, loss = 0.047042\n",
      "epoch : 7/30, loss = 0.047031\n",
      "epoch : 8/30, loss = 0.047025\n",
      "epoch : 9/30, loss = 0.047020\n",
      "epoch : 10/30, loss = 0.047016\n",
      "epoch : 11/30, loss = 0.047009\n",
      "epoch : 12/30, loss = 0.047004\n",
      "epoch : 13/30, loss = 0.047001\n",
      "epoch : 14/30, loss = 0.046998\n",
      "epoch : 15/30, loss = 0.046995\n",
      "epoch : 16/30, loss = 0.046992\n",
      "epoch : 17/30, loss = 0.046989\n",
      "epoch : 18/30, loss = 0.046986\n",
      "epoch : 19/30, loss = 0.046984\n",
      "epoch : 20/30, loss = 0.046982\n",
      "epoch : 21/30, loss = 0.046980\n",
      "epoch : 22/30, loss = 0.046978\n",
      "epoch : 23/30, loss = 0.046977\n",
      "epoch : 24/30, loss = 0.046975\n",
      "epoch : 25/30, loss = 0.046974\n",
      "epoch : 26/30, loss = 0.046972\n",
      "epoch : 27/30, loss = 0.046971\n",
      "epoch : 28/30, loss = 0.046970\n",
      "epoch : 29/30, loss = 0.046969\n",
      "epoch : 30/30, loss = 0.046968\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(epochs):\n",
    "    loss = 0\n",
    "    for batch_features, _ in poisoned_train_data:\n",
    "        # reshape mini-batch data to [N, 784] matrix\n",
    "        # load it to the active device\n",
    "        batch_features = batch_features.view(-1, 784).to(device)\n",
    "        \n",
    "        # reset the gradients back to zero\n",
    "        # PyTorch accumulates gradients on subsequent backward passes\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        # compute reconstructions\n",
    "        outputs = model_poison(batch_features)\n",
    "        \n",
    "        # compute training reconstruction loss\n",
    "        train_loss = criterion(outputs, batch_features)\n",
    "        \n",
    "        # compute accumulated gradients\n",
    "        train_loss.backward()\n",
    "        \n",
    "        # perform parameter update based on current gradients\n",
    "        optimizer.step()\n",
    "        \n",
    "        # add the mini-batch training loss to epoch loss\n",
    "        loss += train_loss.item()\n",
    "    \n",
    "    # compute the epoch training loss\n",
    "    loss = loss / len(train_loader)\n",
    "    \n",
    "    # display the epoch training loss\n",
    "    print(\"epoch : {}/{}, loss = {:.6f}\".format(epoch + 1, epochs, loss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 30 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_examples = None\n",
    "\n",
    "with torch.no_grad():\n",
    "    for batch_features in poisoned_train_data:\n",
    "        batch_features = batch_features[0]\n",
    "        batch_labels = batch_features[1]\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model_poison.forward(test_examples)\n",
    "        break\n",
    "        \n",
    "    number = 15\n",
    "    plt.figure(figsize=(20, 4))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(2, number, index + 1)\n",
    "        plt.imshow(test_examples[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "\n",
    "        # display reconstruction\n",
    "        ax = plt.subplot(2, number, index + 1 + number)\n",
    "        plt.imshow(reconstruction[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_examples = None\n",
    "encoded_categories_pois, encoded_categories_mean_pois = {}, {}\n",
    "for i in range(10):\n",
    "    encoded_categories_pois[i] = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for input_features in poisoned_train_data:\n",
    "        batch_features = input_features[0]\n",
    "        batch_labels = input_features[1].numpy()\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model_poison.forward(test_examples, output_encoded=True)[1].cpu().numpy()\n",
    "        for i, label in enumerate(batch_labels):\n",
    "            encoded_categories_pois[label].append(reconstruction[i])\n",
    "        \n",
    "for i in range(10):\n",
    "    encoded_categories_mean_pois[i] = np.median(encoded_categories_pois[i], axis=0)\n",
    "    \n",
    "encoded_mean_df_pois = pd.DataFrame()\n",
    "for i in range(10):\n",
    "    encoded_mean_df_pois[i] = encoded_categories_mean_pois[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average of image representation per category;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    number = 10\n",
    "    plt.figure(figsize=(20, 4))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(1, number, index + 1)\n",
    "        a = model_poison.decoder_from_vector(torch.tensor(encoded_categories_mean_pois[index], device=device))\n",
    "#         a = model.decoder_from_vector(torch.tensor(encoded_categories[9][index], device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### VineCopula implementation for the backdoor attack:\n",
    "\n",
    "Input data selection. If you want to get the copula based only on the average image per category, use the first section of te code. If you want to select a sample of each category to be considered as input for the copula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# All encoder\n",
    "samples = 500\n",
    "encoded_matrix_df = pd.DataFrame()\n",
    "col = 0\n",
    "for i in range(10):\n",
    "    vals = np.random.choice(len(encoded_categories_pois[i]), samples)\n",
    "    for j in vals:\n",
    "        encoded_matrix_df[col] = encoded_categories_pois[i][j]\n",
    "        col += 1\n",
    "    \n",
    "encoded_array_pois = encoded_matrix_df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<pyvinecopulib.Vinecop>\n",
      "** Tree: 0\n",
      "4,3 <-> TLL, parameters = [30x30 grid]\n",
      "3,2 <-> TLL, parameters = [30x30 grid]\n",
      "1,5 <-> TLL, parameters = [30x30 grid]\n",
      "2,5 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 1\n",
      "4,2 | 3 <-> TLL, parameters = [30x30 grid]\n",
      "3,5 | 2 <-> TLL, parameters = [30x30 grid]\n",
      "1,2 | 5 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 2\n",
      "4,5 | 1,3 <-> Clayton 90°, parameters = 0.0566717\n",
      "3,1 | 4,2 <-> Clayton 180°, parameters = 0.0695219\n",
      "** Tree: 3\n",
      "4,1 | 4,1,3 <-> TLL, parameters = [30x30 grid]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "d = encoder_len  # the dimension\n",
    "x_pois = encoded_array_pois.transpose()\n",
    "\n",
    "# Transform copula data using the empirical distribution\n",
    "u = pv.to_pseudo_obs(x_pois)\n",
    "\n",
    "controls = pv.FitControlsVinecop(family_set=[])\n",
    "cop_pois = pv.Vinecop(u, controls=controls)\n",
    "\n",
    "print(cop_pois)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some reconstructed examples generated by the copula distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2160x1008 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sample from the copula\n",
    "n_sim = 20\n",
    "u_sim = cop_pois.simulate(n_sim)\n",
    "\n",
    "# Transform back simulations to the original scale\n",
    "x_sim = np.asarray([np.quantile(x_pois[:, i], u_sim[:, i]) for i in range(0, d)])\n",
    "    \n",
    "    \n",
    "with torch.no_grad():\n",
    "    number = 20\n",
    "    plt.figure(figsize=(30, 14))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(4, 5, index + 1)\n",
    "        a = model_poison.decoder_from_vector(torch.tensor(np.float32(x_sim.transpose()[index]), device=device))\n",
    "#         a = model.decoder_from_vector(torch.tensor(encoded_categories[9][index], device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VCAE computed from the attacked model using clean data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_examples = None\n",
    "encoded_categories_pois_clean, encoded_categories_mean_pois_clean = {}, {}\n",
    "for i in range(10):\n",
    "    encoded_categories_pois_clean[i] = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for input_features in train_loader:\n",
    "        batch_features = input_features[0]\n",
    "        batch_labels = input_features[1].numpy()\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model_poison.forward(test_examples, output_encoded=True)[1].cpu().numpy()\n",
    "        for i, label in enumerate(batch_labels):\n",
    "            encoded_categories_pois_clean[label].append(reconstruction[i])\n",
    "        \n",
    "for i in range(10):\n",
    "    encoded_categories_mean_pois_clean[i] = np.median(encoded_categories_pois_clean[i], axis=0)\n",
    "    \n",
    "encoded_mean_df_pois_clean = pd.DataFrame()\n",
    "for i in range(10):\n",
    "    encoded_mean_df_pois_clean[i] = encoded_categories_mean_pois_clean[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# All encoder\n",
    "samples = 500\n",
    "encoded_matrix_df = pd.DataFrame()\n",
    "col = 0\n",
    "for i in range(10):\n",
    "    vals = np.random.choice(len(encoded_categories_pois_clean[i]), samples)\n",
    "    for j in vals:\n",
    "        encoded_matrix_df[col] = encoded_categories_pois_clean[i][j]\n",
    "        col += 1\n",
    "    \n",
    "encoded_array_pois_clean = encoded_matrix_df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<pyvinecopulib.Vinecop>\n",
      "** Tree: 0\n",
      "4,3 <-> TLL, parameters = [30x30 grid]\n",
      "3,2 <-> TLL, parameters = [30x30 grid]\n",
      "1,5 <-> TLL, parameters = [30x30 grid]\n",
      "2,5 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 1\n",
      "4,2 | 3 <-> TLL, parameters = [30x30 grid]\n",
      "3,5 | 2 <-> TLL, parameters = [30x30 grid]\n",
      "1,2 | 5 <-> TLL, parameters = [30x30 grid]\n",
      "** Tree: 2\n",
      "4,5 | 1,3 <-> TLL, parameters = [30x30 grid]\n",
      "3,1 | 4,2 <-> Independence\n",
      "** Tree: 3\n",
      "4,1 | 4,1,3 <-> Clayton 270°, parameters = 0.123155\n",
      "\n"
     ]
    }
   ],
   "source": [
    "d = encoder_len  # the dimension\n",
    "x_pois_clean = encoded_array_pois_clean.transpose()\n",
    "\n",
    "# Transform copula data using the empirical distribution\n",
    "u = pv.to_pseudo_obs(x_pois_clean)\n",
    "\n",
    "controls = pv.FitControlsVinecop(family_set=[])\n",
    "cop_pois_clean = pv.Vinecop(u, controls=controls)\n",
    "\n",
    "print(cop_pois_clean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "img_saved = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2160x1008 with 20 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sample from the copula\n",
    "n_sim = 20\n",
    "u_sim = cop_pois_clean.simulate(n_sim)\n",
    "\n",
    "# Transform back simulations to the original scale\n",
    "x_sim = np.asarray([np.quantile(x_pois_clean[:, i], u_sim[:, i]) for i in range(0, d)])\n",
    "    \n",
    "    \n",
    "with torch.no_grad():\n",
    "    number = 20\n",
    "    plt.figure(figsize=(30, 14))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(4, 5, index + 1)\n",
    "        a = model_poison.decoder_from_vector(torch.tensor(np.float32(x_sim.transpose()[index]), device=device))\n",
    "#         a = model.decoder_from_vector(torch.tensor(encoded_categories[9][index], device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "img_saved.append(x_sim[:, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x1008 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    number = len(img_saved)\n",
    "    plt.figure(figsize=(30, 14))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(2, 3, index + 1)\n",
    "        a = model_poison.decoder_from_vector(torch.tensor(np.float32(img_saved[index]), device=device))\n",
    "#         a = model.decoder_from_vector(torch.tensor(encoded_categories[9][index], device=device))\n",
    "        plt.imshow(a.cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.savefig('backdoor_evidence.png')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 30 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_examples = None\n",
    "\n",
    "with torch.no_grad():\n",
    "    for batch_features in test_loader:\n",
    "        batch_features = batch_features[0]\n",
    "        batch_labels = batch_features[1]\n",
    "        test_examples = batch_features.view(-1, 784).to(device)\n",
    "        reconstruction = model_poison.forward(test_examples)\n",
    "        break\n",
    "\n",
    "with torch.no_grad():\n",
    "    number = 15\n",
    "    plt.figure(figsize=(20, 4))\n",
    "    for index in range(number):\n",
    "        # display original\n",
    "        ax = plt.subplot(2, number, index + 1)\n",
    "        plt.imshow(test_examples[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "\n",
    "        # display reconstruction\n",
    "        ax = plt.subplot(2, number, index + 1 + number)\n",
    "        plt.imshow(reconstruction[index].cpu().numpy().reshape(28, 28))\n",
    "        plt.gray()\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pairswise representation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Baseline latent space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Points generation to evaluate the join distribution of each constructed copula\n",
    "\n",
    "num_points = 50\n",
    "points = 1/num_points   # Distance between consecutives points in the marginals uniform distribution\n",
    "x_g = np.mgrid[0:0.999:points, 0:0.999:points, 0:0.999:points, 0:0.999:points, 0.01:0.999:points]\n",
    "points = np.array([x_g[i, :].ravel() for i in range(5)]).T    # Vector with all the points to ve evaluated in a dimension (x_g, 8)\n",
    "num_points = x_g[0].shape[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Block:  2\n",
      "Block:  5\n",
      "Block:  8\n",
      "Block:  0\n",
      "Block:  11\n",
      "Block:  4\n",
      "Block:  12\n",
      "Block:  10\n",
      "Block:  6\n",
      "Block:  7\n",
      "Block:  15\n",
      "Block:  13\n",
      "Block:  9\n",
      "Block:  16\n",
      "Block:  1\n",
      "Block:  3\n",
      "Block:  20\n",
      "Block:  17\n",
      "Block:  18\n",
      "Block:  32\n",
      "Block:  34\n",
      "Block:  31\n",
      "Block:  27\n",
      "Block:  37\n",
      "Block:  33\n",
      "Block:  35\n",
      "Block:  38\n",
      "Block:  14\n",
      "Block:  28\n",
      "Block:  19\n",
      "Block:  29\n",
      "Block:  30\n",
      "Block:  39\n",
      "Block:  36\n",
      "Block:  21\n",
      "Block:  23\n",
      "Block:  22\n",
      "Block:  26\n",
      "Block:  25\n",
      "Block:  24\n"
     ]
    }
   ],
   "source": [
    "## Parallel process to evaluate the copula distribution over the space of points saved in the variable x_g\n",
    "num_process = 40    # Number of parallel process \n",
    "points_t = int(points.shape[0]/num_process)    # Number of points to be evaluated in each parallel process \n",
    "\n",
    "def f(x):\n",
    "    print('Block: ', x)\n",
    "    if x < (num_process - 1):\n",
    "        rsu_pdf = cop.pdf(points[x*points_t:(x+1)*points_t, :])\n",
    "    else:\n",
    "        rsu_pdf = cop.pdf(points[x*points_t:, :])\n",
    "    return (x, rsu_pdf)\n",
    "\n",
    "# if __name__ == '__main__':\n",
    "p = Pool(num_process)\n",
    "pdf_cop = p.map(f, list(range(num_process)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "## It creates an unique output based on the individual parallel processes\n",
    "\n",
    "pdf_cop_final = []\n",
    "for i in range(len(pdf_cop)):\n",
    "    pdf_cop_final.extend(pdf_cop[i][1])\n",
    "    \n",
    "pdf_cop_final = np.reshape(pdf_cop_final, x_g[0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Process to compute the pairwise distributions\n",
    "\n",
    "pair_values = np.zeros([d, d, num_points, num_points]) # array where pairwise distributions are stored\n",
    "\n",
    "vmin, vmax = np.inf, -np.inf\n",
    "vmin_arr_base, vmax_arr_base = [], []\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        a = set(range(d))\n",
    "        a.remove(i)\n",
    "        if (i!=j):\n",
    "            a.remove(j)\n",
    "        p_vals=np.average(pdf_cop_final, axis=tuple(a))\n",
    "        pair_values[i, j, :] = p_vals\n",
    "        if (i!=j):\n",
    "            vmin_arr_base.append(np.min(p_vals))\n",
    "            vmax_arr_base.append(np.max(p_vals))\n",
    "            vmin = np.min(p_vals) if (np.min(p_vals) < vmin) else vmin\n",
    "            vmax = np.max(p_vals) if (np.max(p_vals) > vmax) else vmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Latent distribution of a poison model at 100% in one category"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Block:  3\n",
      "Block:  6\n",
      "Block:  0\n",
      "Block:  1\n",
      "Block:  2\n",
      "Block:  8\n",
      "Block:  9\n",
      "Block:  4\n",
      "Block:  12\n",
      "Block:  5\n",
      "Block:  10\n",
      "Block:  11\n",
      "Block:  31\n",
      "Block:  15\n",
      "Block:  16\n",
      "Block:  26\n",
      "Block:  19\n",
      "Block:  14\n",
      "Block:  20\n",
      "Block:  17\n",
      "Block:  13\n",
      "Block:  18\n",
      "Block:  28\n",
      "Block:  30\n",
      "Block:  24\n",
      "Block:  27\n",
      "Block:  21\n",
      "Block:  29\n",
      "Block:  35\n",
      "Block:  32\n",
      "Block:  23\n",
      "Block:  39\n",
      "Block:  34\n",
      "Block:  37\n",
      "Block:  33\n",
      "Block:  7\n",
      "Block:  25\n",
      "Block:  38\n",
      "Block:  36\n",
      "Block:  22\n"
     ]
    }
   ],
   "source": [
    "## Parallel process to evaluate the copula distribution over the space of points saved in the variable x_g\n",
    "num_process = 40    # Number of parallel process \n",
    "points_t = int(points.shape[0]/num_process)    # Number of points to be evaluated in each parallel process \n",
    "\n",
    "def f(x):\n",
    "    print('Block: ', x)\n",
    "    if x < (num_process - 1):\n",
    "        rsu_pdf = cop_pois.pdf(points[x*points_t:(x+1)*points_t, :])\n",
    "    else:\n",
    "        rsu_pdf = cop_pois.pdf(points[x*points_t:, :])\n",
    "    return (x, rsu_pdf)\n",
    "\n",
    "# if __name__ == '__main__':\n",
    "p = Pool(num_process)\n",
    "pdf_cop_pois = p.map(f, list(range(num_process)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "## It creates an unique output based on the individual parallel processes\n",
    "\n",
    "pdf_cop_final_pois = []\n",
    "for i in range(len(pdf_cop_pois)):\n",
    "    pdf_cop_final_pois.extend(pdf_cop_pois[i][1])\n",
    "    \n",
    "pdf_cop_final_pois = np.reshape(pdf_cop_final_pois, x_g[0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Process to compute the pairwise distributions\n",
    "\n",
    "pair_values_pois = np.zeros([d, d, num_points, num_points]) # array where pairwise distributions are stored\n",
    "\n",
    "vmin, vmax = np.inf, -np.inf\n",
    "vmin_arr_pois, vmax_arr_pois = [], []\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        a = set(range(d))\n",
    "        a.remove(i)\n",
    "        if (i!=j):\n",
    "            a.remove(j)\n",
    "        p_vals=np.average(pdf_cop_final_pois, axis=tuple(a))\n",
    "        pair_values_pois[i, j, :] = p_vals\n",
    "        if (i!=j):\n",
    "            vmin_arr_pois.append(np.min(p_vals))\n",
    "            vmax_arr_pois.append(np.max(p_vals))\n",
    "            vmin = np.min(p_vals) if (np.min(p_vals) < vmin) else vmin\n",
    "            vmax = np.max(p_vals) if (np.max(p_vals) > vmax) else vmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Latent distribution of a clean data in a poison model at 100% in one category"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Block:  16\n",
      "Block:  10\n",
      "Block:  15\n",
      "Block:  9\n",
      "Block:  7\n",
      "Block:  12\n",
      "Block:  18\n",
      "Block:  6\n",
      "Block:  14\n",
      "Block:  2\n",
      "Block:  13\n",
      "Block:  23\n",
      "Block:  5\n",
      "Block:  20\n",
      "Block:  11\n",
      "Block:  28\n",
      "Block:  29\n",
      "Block:  1\n",
      "Block:  3\n",
      "Block:  24\n",
      "Block:  30\n",
      "Block:  0\n",
      "Block:  19\n",
      "Block:  21\n",
      "Block:  8\n",
      "Block:  17\n",
      "Block:  35\n",
      "Block:  33\n",
      "Block:  26\n",
      "Block:  22\n",
      "Block:  32\n",
      "Block:  31\n",
      "Block:  36\n",
      "Block:  4\n",
      "Block:  34\n",
      "Block:  25\n",
      "Block:  37\n",
      "Block:  39\n",
      "Block:  27\n",
      "Block:  38\n"
     ]
    }
   ],
   "source": [
    "## Parallel process to evaluate the copula distribution over the space of points saved in the variable x_g\n",
    "num_process = 40    # Number of parallel process \n",
    "points_t = int(points.shape[0]/num_process)    # Number of points to be evaluated in each parallel process \n",
    "\n",
    "def f(x):\n",
    "    print('Block: ', x)\n",
    "    if x < (num_process - 1):\n",
    "        rsu_pdf = cop_pois_clean.pdf(points[x*points_t:(x+1)*points_t, :])\n",
    "    else:\n",
    "        rsu_pdf = cop_pois_clean.pdf(points[x*points_t:, :])\n",
    "    return (x, rsu_pdf)\n",
    "\n",
    "# if __name__ == '__main__':\n",
    "p = Pool(num_process)\n",
    "pdf_cop_pois_clean = p.map(f, list(range(num_process)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "## It creates an unique output based on the individual parallel processes\n",
    "\n",
    "pdf_cop_final_pois_clean = []\n",
    "for i in range(len(pdf_cop_pois_clean)):\n",
    "    pdf_cop_final_pois_clean.extend(pdf_cop_pois_clean[i][1])\n",
    "    \n",
    "pdf_cop_final_pois_clean = np.reshape(pdf_cop_final_pois_clean, x_g[0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Process to compute the pairwise distributions\n",
    "\n",
    "pair_values_pois_clean = np.zeros([d, d, num_points, num_points]) # array where pairwise distributions are stored\n",
    "\n",
    "vmin, vmax = np.inf, -np.inf\n",
    "vmin_arr_pois_clean, vmax_arr_pois_clean = [], []\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        a = set(range(d))\n",
    "        a.remove(i)\n",
    "        if (i!=j):\n",
    "            a.remove(j)\n",
    "        p_vals=np.average(pdf_cop_final_pois_clean, axis=tuple(a))\n",
    "        pair_values_pois_clean[i, j, :] = p_vals\n",
    "        if (i!=j):\n",
    "            vmin_arr_pois_clean.append(np.min(p_vals))\n",
    "            vmax_arr_pois_clean.append(np.max(p_vals))\n",
    "            vmin = np.min(p_vals) if (np.min(p_vals) < vmin) else vmin\n",
    "            vmax = np.max(p_vals) if (np.max(p_vals) > vmax) else vmax\n",
    "#             vmin_arr.append(vmin)\n",
    "#             vmax_arr.append(vmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pairwise distribution representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.711727854141203 7.493187100372614\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hh = plt.boxplot(vmax_arr_base, vert=False)\n",
    "hh = plt.hist(vmax_arr_base)\n",
    "q1, q3 = np.quantile(vmax_arr_base, (0.25, 0.75))\n",
    "iqr = q3 - q1\n",
    "max1 = q3 + 1.5 * iqr\n",
    "print(q3, max1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.809197156198105 6.287333749527827\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hh = plt.boxplot(vmax_arr_pois, vert=False)\n",
    "hh = plt.hist(vmax_arr_pois)\n",
    "q1, q3 = np.quantile(vmax_arr_pois, (0.25, 0.75))\n",
    "iqr = q3 - q1\n",
    "max2 = q3 + 1.5 * iqr\n",
    "print(q3, max2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.7330414019478395 5.6681389984584385\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAD4CAYAAADFAawfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAHb0lEQVR4nO3bTahdZxXH4bXSFCKt1UGKiGlzZ04cqIROKoIFpZLiuIKOhE4cRBBsdFI7aydFp0FFwY8i1E5aFQsWRPCDpFZaW4c3qAixiNQMImiXg1wUJbm5pWdn/3PyPBByw4H3rLzs/Nh59zk9MwVArkNrDwDA/oQaIJxQA4QTaoBwQg0Q7vASix49enR2dnaWWBpgK507d+61mbnzSq8tEuqdnZ06e/bsEksDbKXuPn+11xx9AIQTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhFvkm4m8OTunn13lfXcfO7nK+wJvjjtqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QLjDaw/w/3ZOP7vK++4+dnKV9+X6cn1xI3JHDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4Q7vPYALOcPX32w3rh08aqv9+MHW2ceuaP60dc3NNV2O3Tk9rrr1JNrj8GWEeot9sali3X84Weu+vruYycPttCX31Ezs6Gp1rVz+tlF1z//+AOLrs/N6ZpHH939je6+0N0vX4+BXOjAjaq7F1n3IGfU36yq+xd5dwCu6ZqhnpmfVdVfr8MsAFzBxs6ou/uhqnqoquruu+9+S2utcfxx0Adr2+Sg57W7RzZ/tnvg8/Eb0JWu35vx+mJzNhbqmTlTVWeqqk6cOPGWnjzt9wBsKWuGY6kHXM7713Gl63cbr69ruRn/zkv9m/M5aoBwcaFe424aYBOW+hjrQT6e972q+kVVvbe7/9jdn1lkEgCu6Jpn1DPzyesxCMvYyJnZI3ds/OxtWx+uHTpy+9ojsIV8M3GLbeoYaedS1fGHN7LUf6z1oGmth0zwVsSdUQPwv4QaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHCCTVAOKEGCCfUAOGEGiCcUAOEE2qAcEINEE6oAcIJNUA4oQYIJ9QA4YQaIJxQA4QTaoBwQg0QTqgBwgk1QDihBggn1ADhhBognFADhBNqgHBCDRBOqAHC9cxsftHuv1TV+Y0vfOM5WlWvrT1EMPuzP/uzv23bn+Mzc+eVXlgk1FzW3Wdn5sTac6SyP/uzP/u7mfbH0QdAOKEGCCfUyzqz9gDh7M/+7M/+bpr9cUYNEM4dNUA4oQYIJ9QL6O67uvv57n6lu3/X3afWnilJdx/p7l9392/39ufRtWdK0923dPdvuvuZtWdJ1N273f1Sd7/Y3WfXnmdph9ceYEv9s6o+PzMvdPfbq+pcdz83M6+sPViIf1TVfTNzsbtvraqfd/ePZuaXaw8W5FRVvVpVd6w9SLCPzMw2feHlqtxRL2Bm/jwzL+z9/Pe6/A/uPetOlWMuu7j3x1v3fnmqvae7j1XVyar62tqzkEGoF9bdO1X1gar61bqTZNn7r/2LVXWhqp6bGfvzX1+pqi9U1RtrDxJsquon3X2uux9ae5ilCfWCuvv2qnqqqj43M6+vPU+SmfnXzLy/qo5V1T3d/b61Z0rQ3Q9U1YWZObf2LOE+NDMfrKqPV9Vnu/vDaw+0JKFeyN7Z61NV9Z2Z+cHa86Samb9V1fNVdf/as4S4t6o+0d27VfVkVd3X3d9ed6Q8M/Onvd8vVNXTVXXPuhMtS6gX0N1dVV+vqldn5om150nT3Xd29zv3fn5bVX20qn6/7lQZZuaLM3NsZnaq6sGq+unMfGrlsaJ09217D+mru2+rqo9V1cvrTrUsn/pYxr1V9emqemnvHLaq6ksz88MVZ0ry7qr6VnffUpdvFr4/Mz6GxkG9q6qevnw/VIer6rsz8+N1R1qWr5ADhHP0ARBOqAHCCTVAOKEGCCfUAOGEGiCcUAOE+zfsWzAuo0YDFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hh = plt.boxplot(vmax_arr_pois_clean, vert=False)\n",
    "hh = plt.hist(vmax_arr_pois_clean)\n",
    "q1, q3 = np.quantile(vmax_arr_pois_clean, (0.25, 0.75))\n",
    "iqr = q3 - q1\n",
    "max3 = q3 + 1.5 * iqr\n",
    "print(q3, max3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmin = 0\n",
    "vmax=max3\n",
    "levels = np.linspace(vmin,vmax,10)\n",
    "\n",
    "plt.figure(figsize=(15, 15))\n",
    "# plt.tick_params(axis='y', which='both', labelleft=False, labelright=True)\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        ax = plt.subplot(d, d, i*d+j+1)\n",
    "        if (i==j):\n",
    "            plt.fill_between(np.linspace(0, 1, num_points), pair_values[i, j, 0, :], np.repeat(min(pair_values[i, j, 0, :]), num_points), alpha=0.5)\n",
    "#             plt.plot(np.linspace(0, 1, num_points), pair_values[i, j, 0, :])\n",
    "            plt.ylabel(r'$x{}$'.format(i+1), fontsize=18, rotation=0, labelpad=20)\n",
    "        else:\n",
    "            ## image show representation \n",
    "#             im=plt.imshow(pair_values[i, j, :], interpolation='none', cmap='jet', origin='lower')\n",
    "# #             if j == (d-1):\n",
    "#             plt.colorbar(im)\n",
    "            ## countour representation\n",
    "#             a = plt.contourf(pair_values[i, j, :], levels=levels, vmax=vmax, vmin=vmin, cmap='jet')\n",
    "            a = plt.contourf(pair_values[i, j, :], cmap='jet')\n",
    "            cbarR = plt.colorbar(a)\n",
    "        \n",
    "        if i==0:\n",
    "            ax.set_title(r'$x{}$'.format(j+1), fontsize=18)\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.axes.yaxis.set_ticks([])\n",
    "        \n",
    "plt.savefig('Baseline_bivariate_8.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# levels = np.linspace(vmin,min(vmax_arr),10)\n",
    "\n",
    "plt.figure(figsize=(15, 15))\n",
    "# plt.tick_params(axis='y', which='both', labelleft=False, labelright=True)\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        ax = plt.subplot(d, d, i*d+j+1)\n",
    "        if (i==j):\n",
    "            plt.fill_between(np.linspace(0, 1, num_points), pair_values_pois[i, j, 0, :], np.repeat(min(pair_values_pois[i, j, 0, :]), num_points), alpha=0.5)\n",
    "#             plt.plot(np.linspace(0, 1, num_points), pair_values[i, j, 0, :])\n",
    "            plt.ylabel(r'$x{}$'.format(i+1), fontsize=18, rotation=0, labelpad=20)\n",
    "        else:\n",
    "            ## image show representation \n",
    "#             im = plt.imshow(pair_values_pois[i, j, :], interpolation='none', cmap='jet', origin='lower')\n",
    "#             plt.colorbar(im)\n",
    "            ## countour representation\n",
    "#             a = plt.contourf(pair_values_pois[i, j, :], levels=levels, vmax=vmax, vmin=vmin, cmap='jet')\n",
    "            a = plt.contourf(pair_values_pois[i, j, :], cmap='jet')\n",
    "            cbarR = plt.colorbar(a)\n",
    "        if i==0:\n",
    "            ax.set_title(r'$x{}$'.format(j+1), fontsize=18)\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.axes.yaxis.set_ticks([])\n",
    "        \n",
    "plt.savefig('Poison_bivariate_8.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# levels = np.linspace(vmin,min(vmax_arr),10)\n",
    "\n",
    "plt.figure(figsize=(15, 15))\n",
    "# plt.tick_params(axis='y', which='both', labelleft=False, labelright=True)\n",
    "for i in range(d):\n",
    "    for j in range(i, d):\n",
    "        ax = plt.subplot(d, d, i*d+j+1)\n",
    "        if (i==j):\n",
    "            plt.fill_between(np.linspace(0, 1, num_points), pair_values_pois_clean[i, j, 0, :], np.repeat(min(pair_values_pois_clean[i, j, 0, :]), num_points), alpha=0.5)\n",
    "#             plt.plot(np.linspace(0, 1, num_points), pair_values[i, j, 0, :])\n",
    "            plt.ylabel(r'$x{}$'.format(i+1), fontsize=18, rotation=0, labelpad=20)\n",
    "        else:\n",
    "            ## image show representation \n",
    "#             im = plt.imshow(pair_values_pois_clean[i, j, :], interpolation='none', cmap='jet', origin='lower')\n",
    "#             plt.colorbar(im)\n",
    "            ## countour representation\n",
    "#             a = plt.contourf(pair_values_pois_clean[i, j, :], levels=levels, vmax=vmax, vmin=vmin, cmap='jet')\n",
    "            a = plt.contourf(pair_values_pois_clean[i, j, :], cmap='jet')\n",
    "            cbarR = plt.colorbar(a)\n",
    "        if i==0:\n",
    "            ax.set_title(r'$x{}$'.format(j+1), fontsize=18)\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.axes.yaxis.set_ticks([])\n",
    "        \n",
    "plt.savefig('Clean_Poison_bivariate_8.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Baseline entropy 0.42250635677076437\n",
      "Poison entropy 0.5370277263627913\n",
      "Poison clean entropy 0.4811109378881606\n"
     ]
    }
   ],
   "source": [
    "E_base = np.log(pdf_cop_final) * pdf_cop_final\n",
    "E_pois = np.log(pdf_cop_final_pois) * pdf_cop_final_pois\n",
    "E_pois_clean = np.log(pdf_cop_final_pois_clean) * pdf_cop_final_pois_clean\n",
    "\n",
    "print('Baseline entropy', np.average(E_base))\n",
    "print('Poison entropy', np.average(E_pois))\n",
    "print('Poison clean entropy', np.average(E_pois_clean))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KL baseline vs poison 2.144917850469713\n",
      "KL baseline vs poin_clean 2.5948531925293774\n"
     ]
    }
   ],
   "source": [
    "KL_pois = np.log(pdf_cop_final / pdf_cop_final_pois) * pdf_cop_final\n",
    "KL_pois_clean = np.log(pdf_cop_final / pdf_cop_final_pois_clean) * pdf_cop_final\n",
    "\n",
    "print('KL baseline vs poison', np.average(KL_pois))\n",
    "print('KL baseline vs poin_clean', np.average(KL_pois_clean))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recursive function to compute individual probabilities from the join distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# #### Recursive function to get the distribution per point for any copula function\n",
    "\n",
    "# def prij(copula, latent_size, value, num_samples = 4, arr=list(), val_final=0):\n",
    "#     result = val_final\n",
    "#     x_val_arr = []\n",
    "    \n",
    "#     range_values = np.linspace(0, 1, num_samples)\n",
    "#     for j in value.keys():\n",
    "#         if (len(arr) == j):\n",
    "#             range_values = [value[j]]\n",
    "#             break\n",
    "    \n",
    "#     for i in range_values:\n",
    "#         if len(arr) < (latent_size-1):\n",
    "#             result = prij(copula, latent_size, value, num_samples, arr + [i], result)\n",
    "#         else:\n",
    "#             x_val_arr.append(arr + [i])\n",
    "    \n",
    "#     if len(x_val_arr) == len(range_values): \n",
    "#         density = copula.pdf(x_val_arr)\n",
    "#         tmp = np.nansum(density)\n",
    "#     else:\n",
    "#         tmp = 0\n",
    "    \n",
    "#     result += tmp\n",
    "    \n",
    "#     return result\n",
    "# v = prij(cop, latent_size=5, value={3: 0.01, 4:0.25}, num_samples=50)\n",
    "# print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# def prij_cop(latent_size, value, num_samples = 4, arr=list(), val_final=0):\n",
    "#     result = val_final\n",
    "#     x_val_arr = []\n",
    "    \n",
    "#     range_values = np.linspace(0, 0.99, num_samples)\n",
    "#     for j in value.keys():\n",
    "#         if (len(arr) == j):\n",
    "#             range_values = [value[j]]\n",
    "#             break\n",
    "    \n",
    "#     for i in range_values:\n",
    "#         if len(arr) < (latent_size-1):\n",
    "#             result = prij_cop(latent_size, value, num_samples, arr + [i], result)\n",
    "#         else:\n",
    "#             x_val_arr.append(arr + [i])\n",
    "    \n",
    "#     if len(x_val_arr) == len(range_values): \n",
    "#         density = cop.pdf(x_val_arr)\n",
    "#         tmp = np.nansum(density)\n",
    "#     else:\n",
    "#         tmp = 0\n",
    "    \n",
    "#     result += tmp\n",
    "    \n",
    "#     return result\n",
    "# # v = prij(cop, latent_size=5, value={3: 0.01, 4:0.25}, num_samples=50)\n",
    "# # print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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