VAE_Digit_Recognition.ipynb

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  "metadata": {
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      "provenance": []
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "### Author: William C Francis (willcf)\n",
        "##Solution 2\n",
        "### (i)"
      ],
      "metadata": {
        "id": "RjOVira6qIto"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "urDRmTyiMI_7",
        "outputId": "c6854854-7dbf-41eb-9a1f-297614ca8c61"
      },
      "source": [
        "import torch\n",
        "import torchvision\n",
        "import torchvision.transforms as transforms\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import numpy as np\n",
        "from torchvision.utils import save_image\n",
        "import cv2\n",
        "import matplotlib.pyplot as plt\n",
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
        "print(device)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nA9xjsR5H0nK"
      },
      "source": [
        "####Downloading the dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AAL5XsEINLlN"
      },
      "source": [
        "trainset = torchvision.datasets.MNIST(root='./data', train = True, download = True, transform = transforms.ToTensor())\n",
        "testset = torchvision.datasets.MNIST(root='./data', train = False, download = True, transform = transforms.ToTensor())\n",
        "xtrain = trainset.data.numpy()\n",
        "ytrain = trainset.targets.numpy()\n",
        "x_val_pre = testset.data[:1000].numpy()\n",
        "y_val = testset.targets[:1000].numpy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6EhZ9JMH50f"
      },
      "source": [
        "### Creating x_train and y_train with 1000 images from each class and binarizing the pixels"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6_jrnEd1On-i"
      },
      "source": [
        "count = np.zeros(10)\n",
        "idx = []\n",
        "for i in range(0, len(ytrain)):\n",
        "  for j in range(10):\n",
        "    if(ytrain[i] == j):\n",
        "      count[j] += 1\n",
        "      if(count[j]<=1000):\n",
        "        idx = np.append(idx, i)\n",
        "        \n",
        "y_train = ytrain[idx.astype('int')]\n",
        "x_train_pre = xtrain[idx.astype('int')]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9kbAExBRINHA"
      },
      "source": [
        "### Resizing the images from 28x28 to 14x14"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U8illNwvO0C-"
      },
      "source": [
        "r,_,_ = x_train_pre.shape\n",
        "x_train = np.zeros([r,14,14])\n",
        "for i in range(r):\n",
        "  a = cv2.resize(x_train_pre[i].astype('float32'), (14,14)) # Resizing the image from 28*28 to 14*14\n",
        "  x_train[i] = a\n",
        "\n",
        "r,_,_ = x_val_pre.shape\n",
        "x_val = np.zeros([r,14,14])\n",
        "for i in range(r):\n",
        "  a = cv2.resize(x_val_pre[i].astype('float32'), (14,14)) # Resizing the image from 28*28 to 14*14\n",
        "  x_val[i] = a"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Binarizing "
      ],
      "metadata": {
        "id": "SDqGT7ZvqZle"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8reo1YY4mKcM"
      },
      "source": [
        "x_train = np.where(x_train > 128, 1, 0)\n",
        "x_val = np.where(x_val > 128, 1, 0)\n",
        "x_train = x_train.astype(np.float32)\n",
        "x_val = x_val.astype(np.float32)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mG8G1eZzJnRj"
      },
      "source": [
        "### Creating dataloaders"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U4EJs6JiY9-G"
      },
      "source": [
        "batch_size = 32\n",
        "trainloader = torch.utils.data.DataLoader([[x_train[i], y_train[i]] for i in range(len(y_train))], shuffle=True, batch_size=batch_size)\n",
        "testloader = torch.utils.data.DataLoader([[x_val[i], y_val[i]] for i in range(len(y_val))], shuffle=True, batch_size=100)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###(ii)\n",
        "### Variational Auto Encoder model"
      ],
      "metadata": {
        "id": "oGwph73PqhoI"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xcq9E_SiTRK6"
      },
      "source": [
        "class VAE(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(VAE, self).__init__()\n",
        "\n",
        "        self.fc1 = nn.Linear(196, 128) #Encoder\n",
        "        self.fc21 = nn.Linear(128, 8) #mu\n",
        "        self.fc22 = nn.Linear(128, 8) #sigma\n",
        "\n",
        "        self.fc3 = nn.Linear(8, 128) #Decoder\n",
        "        self.fc4 = nn.Linear(128, 196)\n",
        "        \n",
        "    def encoder(self, x):\n",
        "        h = torch.tanh(self.fc1(x))\n",
        "        return self.fc21(h), self.fc22(h) # mu, std\n",
        "    \n",
        "    def sampling(self, mu, std): # Reparameterization trick\n",
        "        eps1 = torch.randn_like(std)\n",
        "        eps2 = torch.randn_like(std)\n",
        "        return 0.5*((eps1 * std + mu) + (eps2 * std + mu)) # Using two samples to compute expectation over z\n",
        "\n",
        "    def decoder(self, z):\n",
        "        h = torch.tanh(self.fc3(z))\n",
        "        return torch.sigmoid(self.fc4(h)) \n",
        "    \n",
        "    def forward(self, x):\n",
        "        mu, std = self.encoder(x.view(-1, 196))\n",
        "        z = self.sampling(mu, std)\n",
        "        return self.decoder(z), mu, std\n",
        "model = VAE()\n",
        "if torch.cuda.is_available():\n",
        "    model.cuda()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Defining loss, optimizer and LR scheduler"
      ],
      "metadata": {
        "id": "O0pgwaGgrWBw"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S1TCIO3_TRAu"
      },
      "source": [
        "optimizer = torch.optim.Adam(model.parameters(), lr = 0.002)\n",
        "scheduler = torch.optim.lr_scheduler.ReduceLROnPlateau(optimizer, 'max', factor=0.5, \n",
        "                             patience=5, threshold=0.001, cooldown=0,\n",
        "                             min_lr=0.0001, verbose=True)\n",
        "\n",
        "def loss_function(y, x, mu, std): \n",
        "    ERR = F.binary_cross_entropy(y, x.view(-1, 196), reduction='sum')\n",
        "    KLD = -0.5 * torch.sum(1 + torch.log(std**2) - mu**2 - std**2)\n",
        "    return ERR + KLD, -ERR, -KLD"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Training and Validating"
      ],
      "metadata": {
        "id": "E1hWcpZIrdue"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4yZudAPLT0Gc",
        "outputId": "b74115c4-f27b-43d1-cf4a-b8427d02d1c0"
      },
      "source": [
        "count=0\n",
        "err_l, kld_l, n_wu, testl, update = [], [], [], [], []\n",
        "for epoch in range(1, 20):\n",
        "    \n",
        "    train_loss = 0\n",
        "    for batch_idx, (data, _) in enumerate(trainloader):\n",
        "        model.train()\n",
        "        data = data.cuda()\n",
        "        bsize = data.shape[0]\n",
        "        recon_batch, mu, std = model(data)\n",
        "        loss, err, kld = loss_function(recon_batch, data, mu, std)\n",
        "        loss.backward()\n",
        "        train_loss += err.item() + kld.item()\n",
        "        optimizer.step()\n",
        "        optimizer.zero_grad()\n",
        "        err_l.append(err.item()/bsize)\n",
        "        kld_l.append(kld.item()/bsize)\n",
        "        count+=1\n",
        "        n_wu.append(count)\n",
        "\n",
        "        if (count%100 == 0): # Validating every 100 weight updates\n",
        "          model.eval()\n",
        "          a, _ = next(iter(testloader))\n",
        "          a = a.cuda()\n",
        "          trecon, tmu, tstd = model(a)\n",
        "          tloss, terr, tkld = loss_function(trecon, a, tmu, tstd)\n",
        "          testl.append(terr/100)\n",
        "          update.append(count)\n",
        "\n",
        "    scheduler.step(train_loss / len(trainloader.dataset))\n",
        "    \n",
        "    print('====> Epoch: {} Average loss: {:.4f}'.format(epoch, train_loss / len(trainloader.dataset)))\n",
        "    model.eval()\n",
        "    test_loss= 0\n",
        "    with torch.no_grad():\n",
        "        for data, _ in testloader:\n",
        "            data = data.cuda()\n",
        "            recon, mu, std = model(data)\n",
        "            loss, err, kld = loss_function(recon, data, mu, std)\n",
        "            test_loss += err + kld\n",
        "    \n",
        "    test_loss /= len(testloader.dataset)\n",
        "    print('====> Test set loss: {:.4f}'.format(test_loss))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "====> Epoch: 1 Average loss: -53.0435\n",
            "====> Test set loss: -42.5996\n",
            "====> Epoch: 2 Average loss: -40.6272\n",
            "====> Test set loss: -38.2108\n",
            "====> Epoch: 3 Average loss: -37.6437\n",
            "====> Test set loss: -36.7666\n",
            "====> Epoch: 4 Average loss: -36.5402\n",
            "====> Test set loss: -36.1269\n",
            "====> Epoch: 5 Average loss: -35.8155\n",
            "====> Test set loss: -35.5091\n",
            "====> Epoch: 6 Average loss: -35.3183\n",
            "====> Test set loss: -35.1126\n",
            "====> Epoch: 7 Average loss: -34.8094\n",
            "====> Test set loss: -34.6588\n",
            "====> Epoch: 8 Average loss: -34.4826\n",
            "====> Test set loss: -34.6813\n",
            "====> Epoch: 9 Average loss: -34.1587\n",
            "====> Test set loss: -34.1253\n",
            "====> Epoch: 10 Average loss: -33.8791\n",
            "====> Test set loss: -33.9171\n",
            "====> Epoch: 11 Average loss: -33.6951\n",
            "====> Test set loss: -33.8405\n",
            "====> Epoch: 12 Average loss: -33.4680\n",
            "====> Test set loss: -33.5765\n",
            "====> Epoch: 13 Average loss: -33.2435\n",
            "====> Test set loss: -33.3177\n",
            "====> Epoch: 14 Average loss: -33.0651\n",
            "====> Test set loss: -33.2091\n",
            "====> Epoch: 15 Average loss: -32.9306\n",
            "====> Test set loss: -33.1048\n",
            "====> Epoch: 16 Average loss: -32.7858\n",
            "====> Test set loss: -33.1106\n",
            "====> Epoch: 17 Average loss: -32.6757\n",
            "====> Test set loss: -32.9166\n",
            "====> Epoch: 18 Average loss: -32.5912\n",
            "====> Test set loss: -32.8197\n",
            "====> Epoch: 19 Average loss: -32.4320\n",
            "====> Test set loss: -32.8346\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### (iii) Plotting the first and second term of ELBO as a function of weight updates"
      ],
      "metadata": {
        "id": "776rqq2asZQt"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "id": "vykZE5BaOdYF",
        "outputId": "579c0bdb-2109-4e08-b693-5631acaa3cb7"
      },
      "source": [
        "plt.figure(figsize=(5,3), dpi=100)\n",
        "plt.plot(n_wu, err_l, 'b', label='Reconstruction error')\n",
        "plt.plot(n_wu, kld_l, 'g', label='KL Divergence')\n",
        "plt.title('Plotting first and second term of ELBO')\n",
        "plt.xlabel('Number of weight updates')\n",
        "plt.ylabel('Value')\n",
        "plt.legend()\n",
        "    "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f7d0dd161d0>"
            ]
          },
          "metadata": {},
          "execution_count": 169
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### (iv) \n",
        "### Visualizing input and output from the VAE from training set"
      ],
      "metadata": {
        "id": "LV72MV__svpQ"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "pFfkph9b9z1t",
        "outputId": "d1c470b9-73f4-4497-9905-893172a2304a"
      },
      "source": [
        "model.eval()\n",
        "for i in range(8):\n",
        "  a,t = next(iter(trainloader))\n",
        "  a = a.cuda()\n",
        "  recon, mu, std = model(a[0])\n",
        "  b = recon[0].reshape((14,14))\n",
        "  f, axarr = plt.subplots(1,2)\n",
        "  axarr[0].imshow(a[0].detach().cpu().numpy())\n",
        "  axarr[1].imshow(b.detach().cpu().numpy())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Visualizing input and output of the VAE from validation set"
      ],
      "metadata": {
        "id": "DPMfFvdttA9e"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model.eval()\n",
        "for i in range(8):\n",
        "  a,t = next(iter(testloader))\n",
        "  a = a.cuda()\n",
        "  recon, mu, std = model(a[0])\n",
        "  b = recon[0].reshape((14,14))\n",
        "  f, axarr = plt.subplots(1,2)\n",
        "  axarr[0].imshow(a[0].detach().cpu().numpy())\n",
        "  axarr[1].imshow(b.detach().cpu().numpy())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "EGXr8el6s-5X",
        "outputId": "e0a55996-e09a-4042-ce66-b8d479a75ca3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAC3CAYAAAALgwWHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAMZ0lEQVR4nO3df6jddR3H8ddrd865ablpTnP+mDGlIaKxflmUpeVSa1IiGsrUYEFUZr+YlPiHCUESBklhqRtkjjRNC3OO2YjEhtsynT/WbtN0yzlrZGK4eee7P+4J1m03P/d8v+d8v++z5wPk/Lhvz3l/L29efv3e8zkfR4QAAPlMaroBAEB3CHAASIoAB4CkCHAASIoAB4CkCHAASGpyP99sivePqZrez7fEPuRVvaJdsdNNvDezjV4ab7b7GuBTNV3v9un9fEvsQ9bEqsbem9lGL40325UuodheYHuj7WHbS6q8FtAmzDYy6DrAbQ9JukHSxyTNk3Sh7Xl1NQY0hdlGFlXOwN8laTgiNkfELknLJS2spy2gUcw2UqgS4EdKem6Px1s6z/0X24ttr7W99jXtrPB2QN8w20ih5x8jjIgbI2J+RMzfT/v3+u2AvmG20bQqAb5V0lF7PJ7deQ7IjtlGClUC/GFJc23PsT1F0gWS7qmnLaBRzDZS6Ppz4BExYvvzklZIGpJ0c0Q8XltnQEOYbWRRaSFPRNwr6d6aegFag9lGBnwXCgAkRYADQFIEOAAkRYADQFIEOAAkRYADQFIEOAAkRYADQFIEOAAkRYADQFJ93RMT7bDir4/05HXPfOvJPXldDJ6heccX1/7pspnFtXNOKf/SyB0/m11ce/jdm4trR7a9UFxbFWfgAJBUlT0xj7L9G9tP2H7c9uV1NgY0hdlGFlUuoYxI+kpErLd9kKR1tldGxBM19QY0hdlGCl2fgUfE8xGxvnP/ZUlPai/7BgLZMNvIopZr4LaPlXSKpDV1vB7QFsw22qzyp1BsHyjp55K+FBH/3MvPF0taLElTNa3q2wF9w2yj7SqdgdveT6MDfmtE3Lm3GnbuRkbMNjKo8ikUS7pJ0pMR8d36WgKaxWwjiypn4O+TdLGkD9t+pPPPWTX1BTSJ2UYKVXal/50k19gL0ArMNrJgKX2L9WrJOzAhk4aKS7d94d1Fdbd/+TvFr7lj99Ti2uP2e7W4dtpV5cd10qmfK66de+nfimv1+u7y2r1gKT0AJEWAA0BSBDgAJEWAA0BSBDgAJEWAA0BSBDgAJEWAA0BSBDgAJEWAA0BSLKVvQC+WyPdqR3iW82Py0eWbES2/4rqiuk2vHVL8mtdcfUlx7ci08q+w+cVV5cv5D3y0fDl/1eXxE8EZOAAkVTnAbQ/Z/oPtX9XRENAWzDbaro4z8Ms1uukrMGiYbbRa1S3VZks6W9KP62kHaAdmGxlUPQO/XtLXJb1eQy9AmzDbaL0qe2KeI2l7RKx7g7rFttfaXvuadnb7dkDfMNvIouqemJ+w/Yyk5RrdP/AnY4vYuRsJMdtIoesAj4grI2J2RBwr6QJJD0TERbV1BjSE2UYWfA4cAJKqZSVmRKyWtLqO1wLahNlGm7GUviaZlsf3qoeJ/A7acGz7sklTy5eGb7y2fNn7mlePLapbfvGZxa858+lNxbVbLzqhuHbH6+Xxd9j68t3u+4lLKACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEmxlL4BmZaRszw+kUlDxaWbrjmluPb8eQ8W115z3yeL6o4+pHzn9v1HDi+uPfzjzxbXPrHziOLaKeuGi2v7tyc9Z+AAkFbVPTEPtn2H7adsP2n7vXU1BjSJ2UYGVS+hfE/SfRFxnu0pkqbV0BPQBsw2Wq/rALf9ZkkfkHSJJEXELkm76mkLaA6zjSyqXEKZI+lFSbfY/oPtH9uePraIjV+RELONFKoE+GRJ75D0g4g4RdIrkpaMLWLjVyTEbCOFKgG+RdKWiFjTeXyHRoceyI7ZRgpVdqXfJuk52//Zw+h0SU/U0hXQIGYbWVT9FMoXJN3a+Sv9ZkmXVm8JaAVmG61XKcAj4hFJ82vqpXUGdRViLzZgHjQZZ3vktPIZvOzMB4prf/S7DxbXzr29bPPfoZfKNwl+5W1vKq799BGri2uvXH1ece3xL68tru0nVmICQFIEOAAkRYADQFIEOAAkRYADQFIEOAAkRYADQFIEOAAkRYADQFIEOAAktc9taswy8onJ9BUBg2jo4DcX1/7za/8orl3/0lHFtW+//u/FtbuHnymqm3TM7OLXPPmqPxfXnnXgxuLaX15TPtsjEcW1/cQZOAAkRYADQFJVd6W/wvbjtjfYvs321LoaA5rEbCODrgPc9pGSvihpfkScKGlI0gV1NQY0hdlGFlUvoUyWdIDtyZKmSfpr9ZaAVmC20XpVtlTbKuk6Sc9Kel7SSxFx/9g6du5GNsw2sqhyCWWGpIWS5kh6q6Tpti8aW8fO3ciG2UYWVS6hnCHp6Yh4MSJek3SnpFPraQtoFLONFKoE+LOS3mN7mm1rdOfuJ+tpC2gUs40UqlwDXyPpDknrJT3Wea0ba+oLaAyzjSyq7kp/taSra+qldZpeRt6rZf9NH1cGbZntHWe/vbj2uDeVLyP/y/XHF9cetHldce2kA8o+Lv/eu8t7XTyj/P3P/+wVxbX7b3m4uLatWIkJAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQ1EDsSt+Gneab7oHl8YnYxaUvLij/nvEVx9xbXPuOhccW126f/87i2gc/fV1R3YxJ5TvUnfrNrxbXzrz3oeLaQcAZOAAk9YYBbvtm29ttb9jjuZm2V9re1Lmd0ds2gfox28iu5Ax8qaQFY55bImlVRMyVtKrzGMhmqZhtJPaGAR4Rv5W0Y8zTCyUt69xfJuncmvsCeo7ZRnbdXgOfFRHPd+5vkzSrpn6ApjHbSKPyHzEjIiTFeD9n525kxWyj7boN8BdsHyFJndvt4xWyczeSYbaRRrcBfo+kRZ37iyTdXU87QOOYbaRR8jHC2yQ9JOkE21tsf0bStyV9xPYmSWd0HgOpMNvI7g1XYkbEheP86PSaewH6itlGdgOxlH4iy8gnsuSdXeHREzHu30X/xwnferm49o/vO6C49s8fvqW4dne8Xlz7+51lPVz70U8Vv+bM4X1refxEsJQeAJIiwAEgKQIcAJIiwAEgKQIcAJIiwAEgKQIcAJIiwAEgKQIcAJIiwAEgqYFYSj8RLGNHJrs3DhfXXntc+Wxf200ztXq66QYGAmfgAJBUt7vSf8f2U7YftX2X7YN72yZQP2Yb2XW7K/1KSSdGxEmS/iTpypr7AvphqZhtJNbVrvQRcX9EjHQe/l7S7B70BvQUs43s6rgGfpmkX4/3QzZ+RWLMNlqtUoDb/oakEUm3jlfDxq/IiNlGBl1/jND2JZLOkXR6xAS2GAFajtlGFl0FuO0Fkr4u6YMR8a96WwKaw2wjk253pf++pIMkrbT9iO0f9rhPoHbMNrLrdlf6m3rQC9BXzDayYyUmACRFgANAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACTlfn5bpu0XJf1lzNOHSvpb35ror0E9trYe1zER8ZYm3ngfm+1BPS6pvce219nua4Dvje21ETG/0SZ6ZFCPbVCPq26D+nsa1OOS8h0bl1AAICkCHACSakOA39h0Az00qMc2qMdVt0H9PQ3qcUnJjq3xa+AAgO604QwcANCFRgPc9gLbG20P217SZC91sv2M7cc6eyqubbqfKmzfbHu77Q17PDfT9krbmzq3M5rssY2Y7fYbhNluLMBtD0m6QdLHJM2TdKHteU310wMfioiTM30kaRxLJS0Y89wSSasiYq6kVZ3H6GC201iq5LPd5Bn4uyQNR8TmiNglabmkhQ32g72IiN9K2jHm6YWSlnXuL5N0bl+baj9mO4FBmO0mA/xISc/t8XhL57lBEJLut73O9uKmm+mBWRHxfOf+NkmzmmymhZjtvFLN9uSmGxhQ74+IrbYPk7TS9lOd/9oPnIgI23yUad/BbLdIk2fgWyUdtcfj2Z3n0ouIrZ3b7ZLu0uj/Ug+SF2wfIUmd2+0N99M2zHZeqWa7yQB/WNJc23NsT5F0gaR7GuynFran2z7oP/clfVTShv//b6Vzj6RFnfuLJN3dYC9txGznlWq2G7uEEhEjtj8vaYWkIUk3R8TjTfVTo1mS7rItjf5+fxoR9zXbUvds3ybpNEmH2t4i6WpJ35b0M9uf0eg38J3fXIftw2znMAizzUpMAEiKlZgAkBQBDgBJEeAAkBQBDgBJEeAAkBQBDgBJEeAAkBQBDgBJ/Rv3xsdqYqLYXQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAC3CAYAAAALgwWHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAL/ElEQVR4nO3da6xcZRXG8eehN2glXESaQsGWBEgIapGCF1DUohRFywfCxWCKYCofkIsmpKgJ8RtGYzBKNARqSUQI4RKIQUqtEiJKQylFaLlVRGihtKS0IFLKaZcfOiT10GPfzt4ze685/1/SnJk5q3vWnKw83d1n3nkdEQIA5LNX0w0AALpDgANAUgQ4ACRFgANAUgQ4ACRFgANAUmP7+WTjPSH21qR+PiVGkS16S1vjHTfx3Mw2emmk2e5rgO+tSfqEZ/XzKTGKLI0ljT03s41eGmm2K11CsT3b9jO2V9ueX+VYQJsw28ig6wC3PUbSdZJOl3SMpPNsH1NXY0BTmG1kUeUM/ERJqyPi+YjYKulWSXPqaQtoFLONFKoE+KGSXtrp/prOY//D9jzby2wve1fvVHg6oG+YbaTQ87cRRsT1ETEzImaO04RePx3QN8w2mlYlwNdKOmyn+1M7jwHZMdtIoUqAPyLpSNvTbY+XdK6ke+ppC2gUs40Uun4feEQM2b5E0iJJYyQtiIiVtXUGNITZRhaVFvJExL2S7q2pF6A1mG1kwGehAEBSBDgAJEWAA0BSBDgAJEWAA0BSBDgAJEWAA0BSBDgAJEWAA0BSBDgAJNXXPTEBDDaPLYuUMVMPKT5mbNxUXLvtzTeLaxVRXttSnIEDQFJV9sQ8zPafba+yvdL2ZXU2BjSF2UYWVS6hDEn6XkQst72vpEdtL46IVTX1BjSF2UYKXZ+BR8QrEbG8c/tNSU9pF/sGAtkw28iilmvgtqdJOk7S0jqOB7QFs402q/wuFNsfkHSHpMsj4o1dfH+epHmStLcmVn06oG+YbbRdpTNw2+O0Y8Bvjog7d1XDzt3IiNlGBlXehWJJN0p6KiJ+Vl9LQLOYbWRR5Qz8JEnfkPQF2ys6f75cU19Ak5htpFBlV/q/SHKNvQCtwGwjC5bSN2DRyysaff7TDpnR6POjeR43vrj2hR/OLK594lu/KKob5zHFx3xx6N/FtRc9d15x7bivv1Ncu+3V9cW1/cRSegBIigAHgKQIcABIigAHgKQIcABIigAHgKQIcABIigAHgKQIcABIigAHgKRYSt9ivVryvidL+Vl2P5h89BHFtd8/57bi2oe2jCuqu/zai4uPuXnG1uLar37s8eLaxRefUFw77cfv+zj4EW3fsqW4tirOwAEgqcoBbnuM7cds/76OhoC2YLbRdnWcgV+mHZu+AoOG2UarVd1Sbaqkr0i6oZ52gHZgtpFB1TPwayVdKWl7Db0AbcJso/Wq7Il5hqT1EfHoburm2V5me9m7Kv8AdaApzDayqLon5tdsvyDpVu3YP/C3w4vYuRsJMdtIoesAj4irImJqREyTdK6kP0XE+bV1BjSE2UYWvA8cAJKqZSVmRDwg6YE6jgW0CbONNmMp/Si0J8vjWXY/mLxuQ3Htj+49q7j28EVDRXWHPv6P4mNO2FS+7P+0U54orv3jUPlS+hgqe139xiUUAEiKAAeApAhwAEiKAAeApAhwAEiKAAeApAhwAEiKAAeApAhwAEiKAAeApFhKPwrtyfJ4DKbtm98srj1qwabi2tdOOKCoLsYeXnzMWd99qLh20aaPFNdOu2F1ce02ltIDAOpUdU/M/W3fbvtp20/Z/lRdjQFNYraRQdVLKD+XdF9EnGV7vKSJNfQEtAGzjdbrOsBt7yfps5IukKSI2Cppaz1tAc1htpFFlUso0yVtkPQb24/ZvsH2pOFFbPyKhJhtpFAlwMdK+rikX0XEcZLekjR/eBEbvyIhZhspVAnwNZLWRMTSzv3btWPogeyYbaRQZVf6dZJesn1056FZklbV0hXQIGYbWVR9F8p3JN3c+S3985K+Wb0loBWYbbRepQCPiBWSZtbUC4bp1YbCbD68e4M+27FtW3HtXlvfLa7dup+L6saevbH4mMtfP6y4VleWrQSVpNjwVPlxW4qVmACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEmxqTEwCo2dVr48fdXlHyyuPWlG2Wd+XTHl/uJjnnPHpcW1R697qbh2KLYX17YVZ+AAkBQBDgBJVd2V/grbK20/afsW23vX1RjQJGYbGXQd4LYPlXSppJkRcaykMZLOrasxoCnMNrKoegllrKR9bI+VNFHSy9VbAlqB2UbrVdlSba2kn0p6UdIrkjZHxPt+tczO3ciG2UYWVS6hHCBpjqTpkg6RNMn2+cPr2Lkb2TDbyKLKJZRTJf0zIjZExLuS7pT06XraAhrFbCOFKgH+oqRP2p5o29qxc3f+TeYAZhtJVLkGvlTS7ZKWS3qic6zra+oLaAyzjSyq7kp/taSra+oltT3ZQb4Uu8c3J+Ns7zVxYnHts9+eUlx70ozy/3xsj7Jd6W/bdGL5MSdEee3mN4prFeXHbStWYgJAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACRFgANAUgQ4ACTFrvTAgPDEfYprjz/5meLa17ZMKq59ceMBRXUPrzuq+JgHLy1bni9J8fbbxbWDgDNwAEhqtwFue4Ht9baf3OmxA20vtv1c52vZP7tAizDbyK7kDHyhpNnDHpsvaUlEHClpSec+kM1CMdtIbLcBHhEPSto47OE5km7q3L5J0pk19wX0HLON7Lq9Bj45Il7p3F4naXJN/QBNY7aRRuVfYkZESBrxk9HZuRtZMdtou24D/FXbUySp83X9SIXs3I1kmG2k0W2A3yNpbuf2XEl319MO0DhmG2mUvI3wFkl/k3S07TW2L5J0jaQv2n5O0qmd+0AqzDay2+1KzIg4b4Rvzaq5F6CvmG1kx1J6YFAMDRWXHjHx9eLai6b+tbj27LcuLKqbcmf57wwmLF9dXLttD34Gg4Cl9ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEkR4ACQFAEOAEmxlL4mpx0yo+kWMMpt27S5uPbR48eV18ZnimsPimeLa0ttq/2Ig4MzcABIqttd6X9i+2nbf7d9l+39e9smUD9mG9l1uyv9YknHRsRHJT0r6aqa+wL6YaGYbSTW1a70EXF/RLz3uY0PS5rag96AnmK2kV0d18AvlPSHkb7Jxq9IjNlGq1UKcNs/kDQk6eaRatj4FRkx28ig67cR2r5A0hmSZkVE1NYR0DBmG1l0FeC2Z0u6UtIpEfGfelsCmsNsI5Nud6X/paR9JS22vcL2r3vcJ1A7ZhvZdbsr/Y096AXoK2Yb2bGUHhiNtrNAfRCwlB4AkiLAASApAhwAkiLAASApAhwAkiLAASApAhwAkiLAASApAhwAkiLAASAp9/PTMm1vkPSvYQ8fJOm1vjXRX4P62tr6uj4cER9q4olH2WwP6uuS2vvadjnbfQ3wXbG9LCJmNtpEjwzqaxvU11W3Qf05DerrkvK9Ni6hAEBSBDgAJNWGAL++6QZ6aFBf26C+rroN6s9pUF+XlOy1NX4NHADQnTacgQMAutBogNuebfsZ26ttz2+ylzrZfsH2E509FZc13U8VthfYXm/7yZ0eO9D2YtvPdb4e0GSPbcRst98gzHZjAW57jKTrJJ0u6RhJ59k+pql+euDzETEj01uSRrBQ0uxhj82XtCQijpS0pHMfHcx2GguVfLabPAM/UdLqiHg+IrZKulXSnAb7wS5ExIOSNg57eI6kmzq3b5J0Zl+baj9mO4FBmO0mA/xQSS/tdH9N57FBEJLut/2o7XlNN9MDkyPilc7tdZImN9lMCzHbeaWabXal742TI2Kt7YMlLbb9dOdf+4ETEWGbtzKNHsx2izR5Br5W0mE73Z/aeSy9iFjb+bpe0l3a8V/qQfKq7SmS1Pm6vuF+2obZzivVbDcZ4I9IOtL2dNvjJZ0r6Z4G+6mF7Um2933vtqQvSXry//+tdO6RNLdze66kuxvspY2Y7bxSzXZjl1AiYsj2JZIWSRojaUFErGyqnxpNlnSXbWnHz/d3EXFfsy11z/Ytkj4n6SDbayRdLekaSbfZvkg7PoHv7OY6bB9mO4dBmG1WYgJAUqzEBICkCHAASIoAB4CkCHAASIoAB4CkCHAASIoAB4CkCHAASOq/YNS02/uaLWAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### (v)\n",
        "### Synthesizing MNIST images from a Standard Gaussian Distribution"
      ],
      "metadata": {
        "id": "J1Fe7vq-tp1P"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6mEAXkaY-5II",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "1de53ffc-a705-42bb-f65b-0ac7b585f2ea"
      },
      "source": [
        "\n",
        "for i in range(8):\n",
        "  \n",
        "  x = np.random.normal(0,1, 8)\n",
        "  x= x.astype(np.float32)\n",
        "  x=torch.from_numpy(x)\n",
        "  x= x.cuda()\n",
        "  recon = model.decoder(x)\n",
        "  b = recon.reshape((14,14))\n",
        "  print(x)\n",
        "  f, axarr = plt.subplots(1) \n",
        "  axarr.imshow(b.detach().cpu().numpy())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([0.8694, 0.1257, 0.9046, 0.5266, 0.0294, 1.1379, 0.4387, 1.3595],\n",
            "       device='cuda:0')\n",
            "tensor([-0.3536, -0.7256,  1.2019,  0.6864,  2.0223,  0.1499, -1.0983, -0.6070],\n",
            "       device='cuda:0')\n",
            "tensor([-0.6419, -1.6500, -1.5856,  0.3711, -1.7955,  0.6540,  1.2691,  0.3070],\n",
            "       device='cuda:0')\n",
            "tensor([-1.2568,  0.6815,  0.4568,  0.7782, -0.1277, -0.2815,  0.7612,  0.8144],\n",
            "       device='cuda:0')\n",
            "tensor([-0.1773, -1.2371,  0.1835, -0.4513,  0.9493, -0.6720, -2.3180, -0.0734],\n",
            "       device='cuda:0')\n",
            "tensor([-1.0281, -0.3765,  0.2913,  0.7613, -1.1444,  0.8721,  1.0936,  0.9298],\n",
            "       device='cuda:0')\n",
            "tensor([ 0.4260, -0.5550, -0.1133, -1.8509,  1.1628,  0.1949, -1.0438,  1.1473],\n",
            "       device='cuda:0')\n",
            "tensor([-1.3624,  0.6229, -0.7229, -0.8347,  0.0666, -0.0252, -0.5792,  0.3448],\n",
            "       device='cuda:0')\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### (vi)\n",
        "### Comparing the reconstruction log likelihood term in ELBO on Training vs Validation set"
      ],
      "metadata": {
        "id": "ud4qLz3CuVd1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(5,3), dpi=100)\n",
        "plt.plot(err_l, 'g', label='Training Reconstruction log likelihood')\n",
        "plt.plot(update, testl, 'r', label='Validation Reconstruction log likelihood')\n",
        "plt.title('Reconstruction log likelihood of ELBO: Training vs Validation')\n",
        "plt.xlabel('Number of weight updates')\n",
        "plt.ylabel('Value')\n",
        "plt.legend()"
      ],
      "metadata": {
        "id": "2Uvw4baGYh2p",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "outputId": "6d983988-af0c-4270-d694-0df621efdf7f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f7d0e71e390>"
            ]
          },
          "metadata": {},
          "execution_count": 173
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 500x300 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}