VAE_synthetic_data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create synthetic data.\n",
    "We consider "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The latent space has dimension (500, 2)\n",
      "The transformation for X has dimension (2, 5)\n",
      "X has dimension (500, 5)\n",
      "data has shape torch.Size([500, 1, 1, 5])\n"
     ]
    }
   ],
   "source": [
    "n = 500\n",
    "# here we define 2 Gaussian latents variables z = (l_1, l_2)\n",
    "l1 = np.random.normal(size=n)\n",
    "l2 = np.random.normal(size=n)\n",
    "\n",
    "latents = np.array([l1, l2]).T\n",
    "\n",
    "# We define two random transformations from the latent space to the space of X and Y respectively\n",
    "transform_x = np.random.randint(-8,8, size = 10).reshape([2,5])\n",
    "\n",
    "# We compute data X = z w_x, and Y = z w_y\n",
    "X = latents.dot(transform_x) \n",
    "\n",
    "# We we add some random Gaussian noise\n",
    "X = X + 0.5*np.random.normal(size = n*5).reshape((n, 5))\n",
    "\n",
    "#X_normalized=(X-X.min())/(X.max()-X.min())\n",
    "data=torch.Tensor([[[x]] for x in X])\n",
    "#data=1/(1+(-data).exp())\n",
    "\n",
    "print('The latent space has dimension ' + str(latents.shape))\n",
    "print('The transformation for X has dimension ' + str(transform_x.shape))\n",
    "\n",
    "print('X has dimension ' + str(X.shape))\n",
    "print('data has shape '+str(data.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.019724095050396614, 0.9648611272593378)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l1.mean(),l1.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "from torchvision import datasets, transforms\n",
    "from torch.autograd import Variable\n",
    "from torchvision.utils import save_image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VAE(\n",
       "  (fc1): Linear(in_features=5, out_features=10, bias=True)\n",
       "  (fc21): Linear(in_features=10, out_features=2, bias=True)\n",
       "  (fc22): Linear(in_features=10, out_features=2, bias=True)\n",
       "  (fc3): Linear(in_features=2, out_features=10, bias=True)\n",
       "  (fc4): Linear(in_features=10, out_features=5, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class VAE(nn.Module):\n",
    "    def __init__(self, x_dim, h_dim1, z_dim):\n",
    "        super(VAE, self).__init__()\n",
    "        \n",
    "        # encoder part\n",
    "        self.fc1 = nn.Linear(x_dim, h_dim1)\n",
    "        self.fc21 = nn.Linear(h_dim1, z_dim)\n",
    "        self.fc22 = nn.Linear(h_dim1, z_dim)\n",
    "        # decoder part\n",
    "        self.fc3 = nn.Linear(z_dim, h_dim1)\n",
    "        self.fc4 = nn.Linear(h_dim1, x_dim)\n",
    "        \n",
    "    def encoder(self, x):\n",
    "        h = F.relu(self.fc1(x))\n",
    "        return self.fc21(h), self.fc22(h) # mu, log_var\n",
    "    \n",
    "    def sampling(self, mu, log_var):\n",
    "        std = torch.exp(0.5*log_var)\n",
    "        eps = torch.randn_like(std)\n",
    "        return eps.mul(std).add_(mu) # return z sample\n",
    "        \n",
    "    def decoder(self, z):\n",
    "        h = F.relu(self.fc3(z))\n",
    "        return F.sigmoid(self.fc4(h)) \n",
    "    \n",
    "    def forward(self, x):\n",
    "        mu, log_var = self.encoder(x.view(-1, 5))\n",
    "        z = self.sampling(mu, log_var)\n",
    "        return self.decoder(z), mu, log_var\n",
    "    \n",
    "    def get_z(self, x):\n",
    "        mu, log_var = self.encoder(x.view(-1, 5))\n",
    "        z = self.sampling(mu, log_var)\n",
    "        return z\n",
    "    \n",
    "\n",
    "# build model\n",
    "vae = VAE(x_dim=5, h_dim1= 10, z_dim=2)\n",
    "    \n",
    "vae"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = optim.Adam(vae.parameters())\n",
    "# return reconstruction error + KL divergence losses\n",
    "def loss_function(recon_x, x, mu, log_var):\n",
    "    #BCE = F.binary_cross_entropy(recon_x, x.view(-1,5), reduction='sum')\n",
    "    BCE=torch.sum((recon_x-x.view(-1,5)).pow(2))\n",
    "    KLD = 0.5 * torch.sum(-1 - log_var +mu.pow(2) + log_var.exp())\n",
    "    \n",
    "    print(BCE.item(),KLD.item())\n",
    "    return BCE + KLD\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(epoch):\n",
    "    vae.train()\n",
    "        \n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    recon_batch, mu, log_var = vae(data)\n",
    "    loss = loss_function(recon_batch, data, mu, log_var)\n",
    "\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    print('====> Epoch: {} Average loss: {:.4f}'.format(epoch, loss.item()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test():\n",
    "    vae.eval()\n",
    "    test_loss= 0\n",
    "    with torch.no_grad():\n",
    "        for data, _ in test_loader:\n",
    "            recon, mu, log_var = vae(data)\n",
    "            \n",
    "            # sum up batch loss\n",
    "            test_loss += loss_function(recon, data, mu, log_var).item()\n",
    "        \n",
    "    test_loss /= len(test_loader.dataset)\n",
    "    print('====> Test set loss: {:.4f}'.format(test_loss))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "106312.40625 7234.78076171875\n",
      "====> Epoch: 1 Average loss: 113547.1875\n",
      "106290.109375 6715.10888671875\n",
      "====> Epoch: 2 Average loss: 113005.2188\n",
      "106226.4609375 6239.76123046875\n",
      "====> Epoch: 3 Average loss: 112466.2188\n",
      "106165.5390625 5805.0849609375\n",
      "====> Epoch: 4 Average loss: 111970.6250\n",
      "106148.1953125 5407.951171875\n",
      "====> Epoch: 5 Average loss: 111556.1484\n",
      "106100.3046875 5045.30712890625\n",
      "====> Epoch: 6 Average loss: 111145.6094\n",
      "106016.1171875 4713.923828125\n",
      "====> Epoch: 7 Average loss: 110730.0391\n",
      "105939.7578125 4410.52099609375\n",
      "====> Epoch: 8 Average loss: 110350.2812\n",
      "105871.9453125 4133.10009765625\n",
      "====> Epoch: 9 Average loss: 110005.0469\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/root/anaconda3/lib/python3.7/site-packages/torch/nn/functional.py:1351: UserWarning: nn.functional.sigmoid is deprecated. Use torch.sigmoid instead.\n",
      "  warnings.warn(\"nn.functional.sigmoid is deprecated. Use torch.sigmoid instead.\")\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "105914.390625 3878.793212890625\n",
      "====> Epoch: 10 Average loss: 109793.1875\n",
      "105793.09375 3645.501953125\n",
      "====> Epoch: 11 Average loss: 109438.5938\n",
      "105819.5078125 3431.67919921875\n",
      "====> Epoch: 12 Average loss: 109251.1875\n",
      "105892.1953125 3235.001953125\n",
      "====> Epoch: 13 Average loss: 109127.1953\n",
      "105811.1640625 3051.3916015625\n",
      "====> Epoch: 14 Average loss: 108862.5547\n",
      "105741.265625 2882.300537109375\n",
      "====> Epoch: 15 Average loss: 108623.5625\n",
      "105743.2109375 2726.6708984375\n",
      "====> Epoch: 16 Average loss: 108469.8828\n",
      "105663.6953125 2583.225341796875\n",
      "====> Epoch: 17 Average loss: 108246.9219\n",
      "105697.0 2450.637451171875\n",
      "====> Epoch: 18 Average loss: 108147.6406\n",
      "105623.0 2328.19580078125\n",
      "====> Epoch: 19 Average loss: 107951.1953\n",
      "105532.5078125 2214.818603515625\n",
      "====> Epoch: 20 Average loss: 107747.3281\n",
      "105653.84375 2109.575927734375\n",
      "====> Epoch: 21 Average loss: 107763.4219\n",
      "105612.9453125 2011.7734375\n",
      "====> Epoch: 22 Average loss: 107624.7188\n",
      "105515.09375 1920.65966796875\n",
      "====> Epoch: 23 Average loss: 107435.7500\n",
      "105370.5703125 1835.5909423828125\n",
      "====> Epoch: 24 Average loss: 107206.1641\n",
      "105475.0859375 1756.1553955078125\n",
      "====> Epoch: 25 Average loss: 107231.2422\n",
      "105467.6796875 1681.5506591796875\n",
      "====> Epoch: 26 Average loss: 107149.2266\n",
      "105482.765625 1611.48681640625\n",
      "====> Epoch: 27 Average loss: 107094.2500\n",
      "105320.40625 1545.8134765625\n",
      "====> Epoch: 28 Average loss: 106866.2188\n",
      "105400.046875 1484.2421875\n",
      "====> Epoch: 29 Average loss: 106884.2891\n",
      "105377.1328125 1426.2193603515625\n",
      "====> Epoch: 30 Average loss: 106803.3516\n",
      "105269.7421875 1371.5001220703125\n",
      "====> Epoch: 31 Average loss: 106641.2422\n",
      "105307.625 1319.8939208984375\n",
      "====> Epoch: 32 Average loss: 106627.5156\n",
      "105332.8671875 1270.9888916015625\n",
      "====> Epoch: 33 Average loss: 106603.8594\n",
      "105240.671875 1224.6197509765625\n",
      "====> Epoch: 34 Average loss: 106465.2891\n",
      "105275.0078125 1180.6221923828125\n",
      "====> Epoch: 35 Average loss: 106455.6328\n",
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      "====> Epoch: 36 Average loss: 106357.3438\n",
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      "====> Epoch: 37 Average loss: 106252.8672\n",
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      "====> Epoch: 38 Average loss: 106307.1953\n",
      "105048.6484375 1025.308837890625\n",
      "====> Epoch: 39 Average loss: 106073.9609\n",
      "105163.34375 991.1356201171875\n",
      "====> Epoch: 40 Average loss: 106154.4766\n",
      "105121.15625 958.4879760742188\n",
      "====> Epoch: 41 Average loss: 106079.6406\n",
      "105065.328125 927.38037109375\n",
      "====> Epoch: 42 Average loss: 105992.7109\n",
      "105006.59375 897.5114135742188\n",
      "====> Epoch: 43 Average loss: 105904.1016\n",
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      "====> Epoch: 45 Average loss: 105943.5703\n",
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      "====> Epoch: 46 Average loss: 105896.1250\n",
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      "====> Epoch: 47 Average loss: 105740.5703\n",
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      "====> Epoch: 48 Average loss: 105758.0234\n",
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      "====> Epoch: 50 Average loss: 105640.1875\n",
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      "====> Epoch: 51 Average loss: 105703.0234\n",
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      "====> Epoch: 56 Average loss: 105432.0781\n",
      "104833.7109375 592.7703857421875\n",
      "====> Epoch: 57 Average loss: 105426.4844\n",
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      "104758.96875 563.7451782226562\n",
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      "104793.609375 550.3967895507812\n",
      "====> Epoch: 60 Average loss: 105344.0078\n",
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      "104636.3125 466.96820068359375\n",
      "====> Epoch: 68 Average loss: 105103.2812\n",
      "104691.5078125 459.2798156738281\n",
      "====> Epoch: 69 Average loss: 105150.7891\n",
      "104662.0703125 452.1200866699219\n",
      "====> Epoch: 70 Average loss: 105114.1875\n",
      "104731.9296875 445.4931640625\n",
      "====> Epoch: 71 Average loss: 105177.4219\n",
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      "104476.7265625 399.7338562011719\n",
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      "104419.4765625 397.4757080078125\n",
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      "104202.421875 406.0934143066406\n",
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      "104125.46875 408.2687072753906\n",
      "====> Epoch: 96 Average loss: 104533.7344\n",
      "104138.7578125 410.7742614746094\n",
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      "104210.25 413.4130554199219\n",
      "====> Epoch: 98 Average loss: 104623.6641\n",
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      "====> Epoch: 99 Average loss: 104633.4609\n",
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      "104122.4453125 424.02294921875\n",
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      "====> Epoch: 102 Average loss: 104534.6094\n",
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      "====> Epoch: 104 Average loss: 104526.4766\n",
      "104020.59375 441.76507568359375\n",
      "====> Epoch: 105 Average loss: 104462.3594\n",
      "104059.0625 446.77264404296875\n",
      "====> Epoch: 106 Average loss: 104505.8359\n",
      "103982.3671875 451.8532409667969\n",
      "====> Epoch: 107 Average loss: 104434.2188\n",
      "103855.203125 457.31072998046875\n",
      "====> Epoch: 108 Average loss: 104312.5156\n",
      "103818.5859375 463.17138671875\n",
      "====> Epoch: 109 Average loss: 104281.7578\n",
      "103692.5859375 469.2613220214844\n",
      "====> Epoch: 110 Average loss: 104161.8438\n",
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      "====> Epoch: 111 Average loss: 104148.1641\n",
      "103752.8515625 481.7410583496094\n",
      "====> Epoch: 112 Average loss: 104234.5938\n",
      "103723.71875 488.44781494140625\n",
      "====> Epoch: 113 Average loss: 104212.1641\n",
      "103657.7109375 495.3802185058594\n",
      "====> Epoch: 114 Average loss: 104153.0938\n",
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      "103588.1015625 542.6739501953125\n",
      "====> Epoch: 120 Average loss: 104130.7734\n",
      "103449.0 551.751953125\n",
      "====> Epoch: 121 Average loss: 104000.7500\n",
      "103317.703125 561.1350708007812\n",
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     "text": [
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      "94947.75 1145.5167236328125\n",
      "====> Epoch: 881 Average loss: 96093.2656\n",
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      "====> Epoch: 883 Average loss: 96127.8047\n",
      "94904.1015625 1127.1148681640625\n",
      "====> Epoch: 884 Average loss: 96031.2188\n",
      "94989.7109375 1121.079833984375\n",
      "====> Epoch: 885 Average loss: 96110.7891\n",
      "94999.5546875 1116.336181640625\n",
      "====> Epoch: 886 Average loss: 96115.8906\n",
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      "====> Epoch: 887 Average loss: 96120.6172\n",
      "95010.0703125 1115.7406005859375\n",
      "====> Epoch: 888 Average loss: 96125.8125\n",
      "94986.1015625 1119.7496337890625\n",
      "====> Epoch: 889 Average loss: 96105.8516\n",
      "94953.546875 1123.5584716796875\n",
      "====> Epoch: 890 Average loss: 96077.1016\n",
      "94985.171875 1123.528076171875\n",
      "====> Epoch: 891 Average loss: 96108.7031\n",
      "94967.8125 1122.904296875\n",
      "====> Epoch: 892 Average loss: 96090.7188\n",
      "94947.8515625 1120.591064453125\n",
      "====> Epoch: 893 Average loss: 96068.4453\n",
      "94973.734375 1116.8402099609375\n",
      "====> Epoch: 894 Average loss: 96090.5781\n",
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      "====> Epoch: 895 Average loss: 96126.6641\n",
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      "====> Epoch: 896 Average loss: 96161.3203\n",
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      "====> Epoch: 897 Average loss: 96187.0547\n",
      "94895.8203125 1109.6248779296875\n",
      "====> Epoch: 898 Average loss: 96005.4453\n",
      "94932.609375 1111.5491943359375\n",
      "====> Epoch: 899 Average loss: 96044.1562\n",
      "94920.6875 1115.3824462890625\n",
      "====> Epoch: 900 Average loss: 96036.0703\n",
      "94941.171875 1117.58544921875\n",
      "====> Epoch: 901 Average loss: 96058.7578\n",
      "94957.9140625 1119.47119140625\n",
      "====> Epoch: 902 Average loss: 96077.3828\n",
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      "====> Epoch: 903 Average loss: 96004.3438\n",
      "94949.9140625 1121.5885009765625\n",
      "====> Epoch: 904 Average loss: 96071.5000\n",
      "94880.84375 1124.6734619140625\n",
      "====> Epoch: 905 Average loss: 96005.5156\n",
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      "====> Epoch: 906 Average loss: 95968.9766\n",
      "94978.3359375 1120.8619384765625\n",
      "====> Epoch: 907 Average loss: 96099.1953\n",
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      "====> Epoch: 908 Average loss: 96112.3203\n",
      "94950.8203125 1116.3997802734375\n",
      "====> Epoch: 909 Average loss: 96067.2188\n",
      "94873.890625 1116.21044921875\n",
      "====> Epoch: 910 Average loss: 95990.1016\n",
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      "====> Epoch: 911 Average loss: 96157.1562\n",
      "94860.421875 1116.730712890625\n",
      "====> Epoch: 912 Average loss: 95977.1562\n",
      "94920.0234375 1119.466552734375\n",
      "====> Epoch: 913 Average loss: 96039.4922\n",
      "94960.140625 1120.91748046875\n",
      "====> Epoch: 914 Average loss: 96081.0547\n",
      "94907.921875 1122.7884521484375\n",
      "====> Epoch: 915 Average loss: 96030.7109\n",
      "94918.3125 1124.7288818359375\n",
      "====> Epoch: 916 Average loss: 96043.0391\n",
      "94928.625 1128.2630615234375\n",
      "====> Epoch: 917 Average loss: 96056.8906\n",
      "94904.859375 1131.59033203125\n",
      "====> Epoch: 918 Average loss: 96036.4531\n",
      "94876.4375 1135.4359130859375\n",
      "====> Epoch: 919 Average loss: 96011.8750\n",
      "94836.09375 1137.550537109375\n",
      "====> Epoch: 920 Average loss: 95973.6406\n",
      "95014.75 1135.3699951171875\n",
      "====> Epoch: 921 Average loss: 96150.1172\n",
      "94899.0625 1133.831298828125\n",
      "====> Epoch: 922 Average loss: 96032.8906\n",
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      "====> Epoch: 923 Average loss: 95926.4688\n",
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      "====> Epoch: 924 Average loss: 95992.1328\n",
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      "====> Epoch: 925 Average loss: 96019.8906\n",
      "94876.59375 1108.028564453125\n",
      "====> Epoch: 926 Average loss: 95984.6250\n",
      "94875.03125 1104.424560546875\n",
      "====> Epoch: 927 Average loss: 95979.4531\n",
      "94822.1640625 1100.551025390625\n",
      "====> Epoch: 928 Average loss: 95922.7188\n",
      "94894.859375 1096.333984375\n",
      "====> Epoch: 929 Average loss: 95991.1953\n",
      "94967.0859375 1096.5345458984375\n",
      "====> Epoch: 930 Average loss: 96063.6172\n",
      "94837.59375 1099.4178466796875\n",
      "====> Epoch: 931 Average loss: 95937.0078\n",
      "94928.7890625 1102.0093994140625\n",
      "====> Epoch: 932 Average loss: 96030.7969\n",
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      "====> Epoch: 933 Average loss: 96018.1406\n",
      "94892.265625 1116.0953369140625\n",
      "====> Epoch: 934 Average loss: 96008.3594\n",
      "94803.9609375 1123.44091796875\n",
      "====> Epoch: 935 Average loss: 95927.3984\n",
      "94860.2734375 1130.4549560546875\n",
      "====> Epoch: 936 Average loss: 95990.7266\n",
      "94922.9453125 1134.1427001953125\n",
      "====> Epoch: 937 Average loss: 96057.0859\n",
      "94806.96875 1134.4991455078125\n",
      "====> Epoch: 938 Average loss: 95941.4688\n",
      "94858.875 1131.2076416015625\n",
      "====> Epoch: 939 Average loss: 95990.0859\n",
      "94935.5546875 1125.8182373046875\n",
      "====> Epoch: 940 Average loss: 96061.3750\n",
      "94966.2109375 1121.5625\n",
      "====> Epoch: 941 Average loss: 96087.7734\n",
      "94830.3984375 1121.53662109375\n",
      "====> Epoch: 942 Average loss: 95951.9375\n",
      "94828.109375 1118.9527587890625\n",
      "====> Epoch: 943 Average loss: 95947.0625\n",
      "94913.1953125 1116.4468994140625\n",
      "====> Epoch: 944 Average loss: 96029.6406\n",
      "94849.640625 1113.3779296875\n",
      "====> Epoch: 945 Average loss: 95963.0156\n",
      "94806.6953125 1114.413330078125\n",
      "====> Epoch: 946 Average loss: 95921.1094\n",
      "94761.59375 1114.8460693359375\n",
      "====> Epoch: 947 Average loss: 95876.4375\n",
      "94946.1953125 1114.328369140625\n",
      "====> Epoch: 948 Average loss: 96060.5234\n",
      "94903.7578125 1116.1712646484375\n",
      "====> Epoch: 949 Average loss: 96019.9297\n",
      "94797.1953125 1121.5224609375\n",
      "====> Epoch: 950 Average loss: 95918.7188\n",
      "94871.1328125 1124.6573486328125\n",
      "====> Epoch: 951 Average loss: 95995.7891\n",
      "94817.7265625 1128.4671630859375\n",
      "====> Epoch: 952 Average loss: 95946.1953\n",
      "94795.5078125 1130.56396484375\n",
      "====> Epoch: 953 Average loss: 95926.0703\n",
      "94795.78125 1132.55859375\n",
      "====> Epoch: 954 Average loss: 95928.3438\n",
      "94872.578125 1131.4505615234375\n",
      "====> Epoch: 955 Average loss: 96004.0312\n",
      "94853.703125 1132.0616455078125\n",
      "====> Epoch: 956 Average loss: 95985.7656\n",
      "94902.4375 1133.1771240234375\n",
      "====> Epoch: 957 Average loss: 96035.6172\n",
      "94818.8671875 1134.461181640625\n",
      "====> Epoch: 958 Average loss: 95953.3281\n",
      "94913.3671875 1134.8663330078125\n",
      "====> Epoch: 959 Average loss: 96048.2344\n",
      "94789.359375 1136.8099365234375\n",
      "====> Epoch: 960 Average loss: 95926.1719\n",
      "94798.7890625 1136.9808349609375\n",
      "====> Epoch: 961 Average loss: 95935.7734\n",
      "94900.7734375 1135.448486328125\n",
      "====> Epoch: 962 Average loss: 96036.2188\n",
      "94835.71875 1136.4373779296875\n",
      "====> Epoch: 963 Average loss: 95972.1562\n",
      "94899.3671875 1138.1297607421875\n",
      "====> Epoch: 964 Average loss: 96037.5000\n",
      "94789.53125 1142.0006103515625\n",
      "====> Epoch: 965 Average loss: 95931.5312\n",
      "94863.7421875 1144.35400390625\n",
      "====> Epoch: 966 Average loss: 96008.0938\n",
      "94821.375 1145.629150390625\n",
      "====> Epoch: 967 Average loss: 95967.0078\n",
      "94828.1875 1147.2279052734375\n",
      "====> Epoch: 968 Average loss: 95975.4141\n",
      "94832.859375 1148.31494140625\n",
      "====> Epoch: 969 Average loss: 95981.1719\n",
      "94732.9609375 1148.60595703125\n",
      "====> Epoch: 970 Average loss: 95881.5703\n",
      "94799.53125 1145.391845703125\n",
      "====> Epoch: 971 Average loss: 95944.9219\n",
      "94752.4296875 1140.879150390625\n",
      "====> Epoch: 972 Average loss: 95893.3125\n",
      "94829.328125 1134.19287109375\n",
      "====> Epoch: 973 Average loss: 95963.5234\n",
      "94800.6328125 1129.3062744140625\n",
      "====> Epoch: 974 Average loss: 95929.9375\n",
      "94784.4609375 1126.40478515625\n",
      "====> Epoch: 975 Average loss: 95910.8672\n",
      "94669.9375 1124.6900634765625\n",
      "====> Epoch: 976 Average loss: 95794.6250\n",
      "94852.34375 1119.47265625\n",
      "====> Epoch: 977 Average loss: 95971.8125\n",
      "94784.1640625 1116.2744140625\n",
      "====> Epoch: 978 Average loss: 95900.4375\n",
      "94860.3828125 1113.5020751953125\n",
      "====> Epoch: 979 Average loss: 95973.8828\n",
      "94892.421875 1111.4146728515625\n",
      "====> Epoch: 980 Average loss: 96003.8359\n",
      "94761.4609375 1112.8355712890625\n",
      "====> Epoch: 981 Average loss: 95874.2969\n",
      "94701.9140625 1115.189208984375\n",
      "====> Epoch: 982 Average loss: 95817.1016\n",
      "94804.4296875 1116.1341552734375\n",
      "====> Epoch: 983 Average loss: 95920.5625\n",
      "94786.265625 1117.4307861328125\n",
      "====> Epoch: 984 Average loss: 95903.6953\n",
      "94798.34375 1117.684814453125\n",
      "====> Epoch: 985 Average loss: 95916.0312\n",
      "94767.9921875 1118.1722412109375\n",
      "====> Epoch: 986 Average loss: 95886.1641\n",
      "94862.4375 1119.083740234375\n",
      "====> Epoch: 987 Average loss: 95981.5234\n",
      "94706.7734375 1122.3489990234375\n",
      "====> Epoch: 988 Average loss: 95829.1250\n",
      "94805.9375 1121.6768798828125\n",
      "====> Epoch: 989 Average loss: 95927.6172\n",
      "94757.3828125 1121.609375\n",
      "====> Epoch: 990 Average loss: 95878.9922\n",
      "94751.4375 1121.4161376953125\n",
      "====> Epoch: 991 Average loss: 95872.8516\n",
      "94781.109375 1118.91015625\n",
      "====> Epoch: 992 Average loss: 95900.0156\n",
      "94862.078125 1116.7342529296875\n",
      "====> Epoch: 993 Average loss: 95978.8125\n",
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      "====> Epoch: 994 Average loss: 95897.9688\n",
      "94721.234375 1122.0726318359375\n",
      "====> Epoch: 995 Average loss: 95843.3047\n",
      "94679.7265625 1124.4920654296875\n",
      "====> Epoch: 996 Average loss: 95804.2188\n",
      "94777.046875 1123.660400390625\n",
      "====> Epoch: 997 Average loss: 95900.7109\n",
      "94749.7890625 1123.1893310546875\n",
      "====> Epoch: 998 Average loss: 95872.9766\n",
      "94693.078125 1122.3916015625\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "====> Epoch: 999 Average loss: 95815.4688\n",
      "94765.4453125 1118.8848876953125\n",
      "====> Epoch: 1000 Average loss: 95884.3281\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(1, 1001):\n",
    "    train(epoch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.47340008e+00,  5.17603834e-01],\n",
       "       [ 6.12148888e-01, -3.04223337e-01],\n",
       "       [-1.30297482e-01,  2.14091318e+00],\n",
       "       [-1.58811195e-01,  2.39048996e-01],\n",
       "       [ 1.45560896e+00,  2.26625925e-01],\n",
       "       [ 3.38007986e-01,  1.04741537e+00],\n",
       "       [-1.17248908e+00, -1.18133398e+00],\n",
       "       [-2.79879598e-01, -1.06784192e+00],\n",
       "       [-5.62416441e-02, -8.12937702e-01],\n",
       "       [-3.31650557e-01, -3.29943824e-01],\n",
       "       [ 5.61647227e-01,  2.32644790e-01],\n",
       "       [-1.27555587e+00,  1.73978730e+00],\n",
       "       [ 6.73374260e-01, -3.49505621e-01],\n",
       "       [-1.01945296e+00, -1.69742434e-01],\n",
       "       [-1.12981701e+00,  5.22108806e-01],\n",
       "       [ 9.14513900e-01, -3.31076815e-01],\n",
       "       [-3.21445922e-02,  6.98724170e-01],\n",
       "       [-5.98929261e-01,  9.98602468e-02],\n",
       "       [-4.59403551e-01, -7.55917238e-01],\n",
       "       [-1.48750821e-01, -1.13757481e+00],\n",
       "       [ 9.55793227e-02,  7.12981651e-01],\n",
       "       [-5.05615955e-01,  1.56848003e-01],\n",
       "       [-6.63639338e-01, -3.50853305e-01],\n",
       "       [-1.05345117e+00,  8.39340573e-01],\n",
       "       [ 1.25616612e+00, -1.55929146e+00],\n",
       "       [ 1.13581470e+00,  6.45175295e-01],\n",
       "       [ 2.23377112e-01, -1.28459089e+00],\n",
       "       [-5.78719069e-01, -3.34385988e-02],\n",
       "       [ 1.39625887e+00,  7.58771665e-01],\n",
       "       [-3.99264016e-01,  9.42196421e-01],\n",
       "       [ 2.45722270e+00,  5.40742929e-01],\n",
       "       [ 6.37648964e-02,  6.38797978e-01],\n",
       "       [-1.67616431e-01, -8.05621480e-02],\n",
       "       [ 6.17434955e-01,  1.47275360e-02],\n",
       "       [-5.53920842e-02,  1.14984279e+00],\n",
       "       [-9.94180030e-01, -7.83659083e-01],\n",
       "       [-9.98012855e-01, -1.18318066e+00],\n",
       "       [ 4.43326984e-01, -4.80794840e-01],\n",
       "       [ 1.25289315e-02,  5.70634208e-01],\n",
       "       [-3.47568956e-01,  6.63970270e-02],\n",
       "       [-1.67005739e+00, -2.52638996e-01],\n",
       "       [ 4.70388027e-01,  1.39253560e+00],\n",
       "       [-5.60580794e-02, -3.55597957e-02],\n",
       "       [ 1.04243427e-01,  1.31329668e+00],\n",
       "       [-2.93666388e+00, -1.00356751e-01],\n",
       "       [-2.13144763e+00, -1.14286539e-01],\n",
       "       [-5.94371769e-01, -2.43982617e-01],\n",
       "       [-1.06289306e-01, -9.89450984e-01],\n",
       "       [ 2.57267824e-01, -1.25781817e-01],\n",
       "       [ 3.16383536e-01, -6.19793571e-01],\n",
       "       [ 1.62460896e+00,  1.61852229e+00],\n",
       "       [ 1.79230578e-01, -5.17581663e-01],\n",
       "       [ 9.63630001e-01, -7.76994944e-02],\n",
       "       [ 9.60761014e-01,  7.40000942e-01],\n",
       "       [-1.55452055e+00,  5.13817013e-02],\n",
       "       [ 3.73167072e-01,  5.46155315e-01],\n",
       "       [-5.71272036e-01,  3.21900807e+00],\n",
       "       [ 1.08353183e-01,  2.02977134e+00],\n",
       "       [ 7.42784469e-01,  2.17258802e-01],\n",
       "       [ 1.20681906e+00,  2.99198075e-01],\n",
       "       [ 1.61255189e-01,  2.25198639e+00],\n",
       "       [-7.44411103e-01,  1.15830448e+00],\n",
       "       [-1.30163167e+00, -1.18293922e+00],\n",
       "       [-1.32214347e+00,  5.92445098e-01],\n",
       "       [-8.97077909e-01,  7.89719207e-01],\n",
       "       [ 5.22486722e-01,  2.01034173e-01],\n",
       "       [-1.49932187e+00, -1.15614231e+00],\n",
       "       [-5.32538765e-01,  1.60729423e+00],\n",
       "       [ 7.79058965e-01, -5.29842280e-01],\n",
       "       [ 2.62781364e-01,  1.05954464e+00],\n",
       "       [ 1.22589529e+00,  5.60397765e-01],\n",
       "       [-1.59229346e-01,  6.84215395e-02],\n",
       "       [-1.06124480e+00,  7.09911107e-01],\n",
       "       [ 1.56563056e+00,  2.07577470e+00],\n",
       "       [ 6.34114375e-01,  1.37521818e+00],\n",
       "       [-5.68600253e-01,  9.99444874e-01],\n",
       "       [ 6.07151253e-01, -1.01204615e+00],\n",
       "       [-1.73027489e+00, -4.15492642e-02],\n",
       "       [-3.86053682e-01,  1.40665802e+00],\n",
       "       [ 4.80776108e-01, -3.08872890e-01],\n",
       "       [-3.62560811e-01, -4.29411113e-01],\n",
       "       [ 8.35342094e-01, -1.20694733e-01],\n",
       "       [-2.50318577e-01,  5.61524962e-01],\n",
       "       [-8.07386219e-01, -5.96328573e-01],\n",
       "       [ 1.44172030e+00, -7.97586886e-01],\n",
       "       [ 8.04153238e-01,  8.49995887e-01],\n",
       "       [-3.77661070e-01,  5.28973553e-03],\n",
       "       [-1.08078974e+00, -2.05167266e-01],\n",
       "       [-2.19671885e-02, -3.71113093e-01],\n",
       "       [ 8.46728737e-01, -1.01522301e+00],\n",
       "       [-5.29908678e-01, -1.63156295e+00],\n",
       "       [-1.14152101e-01, -1.59630146e-01],\n",
       "       [-6.08058991e-01, -2.19143286e-01],\n",
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       "       [-2.09699809e-01,  1.70865432e+00],\n",
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       "       [ 3.67962318e-01,  1.53138248e+00],\n",
       "       [ 1.10308182e+00,  9.24158302e-01],\n",
       "       [ 5.53197513e-01, -2.76335553e-01],\n",
       "       [ 1.22102289e+00, -6.99027534e-01],\n",
       "       [-1.99001878e-01,  3.30503552e-01],\n",
       "       [ 1.62811626e-01,  1.60526914e+00],\n",
       "       [-5.41934194e-01,  8.23707044e-01],\n",
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       "       [ 7.67509408e-01, -9.65860588e-02],\n",
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       "       [ 1.18854770e+00,  5.00587166e-02],\n",
       "       [-7.46156008e-01, -5.60361088e-02],\n",
       "       [ 1.66747108e+00,  7.17304436e-01],\n",
       "       [ 3.41121232e-01,  8.38914385e-01],\n",
       "       [-4.16495907e-01,  3.81462722e-01],\n",
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       "       [-1.35968154e+00,  1.10231334e+00],\n",
       "       [-1.24801433e-01, -1.86804716e+00],\n",
       "       [ 4.53699247e-01,  2.46519816e+00],\n",
       "       [ 1.22173972e+00,  7.52455682e-02],\n",
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       "       [ 8.24693721e-01,  5.17836887e-01],\n",
       "       [ 1.04398265e+00,  1.66329611e+00],\n",
       "       [-7.30756848e-01, -2.06232454e-01],\n",
       "       [-5.18361524e-01,  7.87392522e-02],\n",
       "       [-5.73613127e-01, -5.03282572e-01],\n",
       "       [ 6.80842741e-02,  8.08055513e-01],\n",
       "       [ 2.63511108e-01,  5.97167866e-01],\n",
       "       [-2.66933438e-01,  1.60457153e+00],\n",
       "       [ 6.83615851e-02,  5.74357763e-01],\n",
       "       [-2.71081721e-01,  2.48892275e-01],\n",
       "       [ 5.92629905e-01,  9.63719232e-01],\n",
       "       [ 4.48841303e-01, -1.37448362e-01],\n",
       "       [ 9.03544135e-02, -3.80122555e-01],\n",
       "       [ 4.12772166e-01,  8.42567836e-01],\n",
       "       [-5.75999403e-01, -1.61534974e-01],\n",
       "       [ 1.25784753e+00, -6.03016755e-01],\n",
       "       [-2.06861482e-01, -6.34479072e-01],\n",
       "       [-1.12924004e-03, -1.16574085e+00],\n",
       "       [-5.39893841e-01, -2.26016312e-01],\n",
       "       [ 9.67742340e-01, -9.12806983e-02],\n",
       "       [-8.55934462e-01,  1.05736980e+00],\n",
       "       [-1.35044563e+00,  2.04700044e-01],\n",
       "       [ 5.21519322e-01,  4.44906329e-01],\n",
       "       [-4.20347685e-01, -1.39833067e-01],\n",
       "       [-1.20462798e+00, -2.93990507e-01],\n",
       "       [-5.87832811e-01, -6.18209353e-01],\n",
       "       [ 5.12708336e-02,  1.58220244e+00],\n",
       "       [-1.02604185e+00, -2.67675789e-01],\n",
       "       [ 1.37946660e-01,  7.08918154e-01],\n",
       "       [-6.55099248e-02, -1.67734155e+00],\n",
       "       [ 5.47341266e-01, -7.44355633e-01],\n",
       "       [ 5.13942944e-01, -9.51982455e-02]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_z=latents\n",
    "prior_z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [ 1.80787480e+00,  7.41497993e-01],\n",
       "       [ 3.80362988e-01, -2.34553552e+00],\n",
       "       [-1.03213370e+00,  2.26464796e+00],\n",
       "       [-1.79745519e+00,  3.56144458e-01],\n",
       "       [-7.09631443e-01,  1.58327425e+00],\n",
       "       [-1.42969310e+00,  9.69721437e-01],\n",
       "       [-1.14450586e+00,  1.54423785e+00],\n",
       "       [ 1.47984445e+00, -2.41752729e-01],\n",
       "       [ 1.02670979e+00, -6.59536272e-02],\n",
       "       [ 1.15822673e+00, -7.70888090e-01],\n",
       "       [-8.29949260e-01,  1.32981145e+00],\n",
       "       [-7.55145073e-01,  1.16832328e+00],\n",
       "       [-2.06091702e-02,  1.68119860e+00],\n",
       "       [-8.97010803e-01,  1.20063186e+00],\n",
       "       [ 6.20223880e-01,  5.27406633e-01],\n",
       "       [-1.15718889e+00,  1.54828382e+00],\n",
       "       [-8.26095819e-01, -8.19140822e-02],\n",
       "       [ 1.62698075e-01, -9.00127232e-01],\n",
       "       [-9.31257606e-01,  1.10118723e+00],\n",
       "       [ 1.15586925e+00, -3.39547485e-01],\n",
       "       [-1.95854604e+00, -4.79550958e-01],\n",
       "       [ 8.24654043e-01, -9.17180717e-01],\n",
       "       [ 4.80846047e-01, -1.48584938e+00],\n",
       "       [ 9.90917742e-01, -6.05353355e-01],\n",
       "       [-1.64167166e+00,  2.56778926e-01],\n",
       "       [ 7.74732411e-01,  1.20828176e+00],\n",
       "       [ 1.91748846e+00,  8.75441730e-02],\n",
       "       [-1.41495287e+00,  8.95207822e-01],\n",
       "       [ 9.09495354e-01, -5.49160600e-01],\n",
       "       [ 1.76837671e+00, -4.13900524e-01],\n",
       "       [ 9.97883677e-01, -9.56592381e-01],\n",
       "       [-6.92029357e-01,  1.80599689e+00],\n",
       "       [ 1.71353948e+00, -2.69127488e-01],\n",
       "       [-6.95726395e-01,  1.19097292e+00],\n",
       "       [ 3.19519967e-01, -2.15050721e+00],\n",
       "       [-4.91625786e-01, -9.71451461e-01],\n",
       "       [-1.02266920e+00, -5.23415096e-02]], dtype=float32)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_z_x=vae.encoder(data)[0].view(-1,2).detach().numpy()\n",
    "q_z_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.scatter(prior_z[:,0],q_z_x[:,0])\n",
    "plt.xlabel(\"z D1\")\n",
    "plt.xlabel(\"approximation q(X) D1\")\n",
    "\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.scatter(prior_z[:,0],q_z_x[:,1])\n",
    "plt.xlabel(\"z D1\")\n",
    "plt.xlabel(\"approximation q(X) D2\")\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "plt.scatter(prior_z[:,1],q_z_x[:,0])\n",
    "plt.xlabel(\"z D2\")\n",
    "plt.xlabel(\"approximation q(X) D1\")\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "plt.scatter(prior_z[:,1],q_z_x[:,1])\n",
    "plt.xlabel(\"z D2\")\n",
    "plt.xlabel(\"approximation q(X) D2\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-0.0077, grad_fn=<MeanBackward0>)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z=vae.encoder(data)\n",
    "z[0].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.018265026525579445, 0.9665268564469304)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latents.mean(),latents.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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