Weight Uncertainty in Neural Networks.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JbQWL5WznhJS"
   },
   "source": [
    "# Bayes by Backprop\n",
    "An implementation of the algorithm described in https://arxiv.org/abs/1505.05424.  \n",
    "This notebook accompanies the article at https://www.nitarshan.com/bayes-by-backprop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "yNGUXrL_osEt"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "\n",
    "from tensorboardX import SummaryWriter\n",
    "from torchvision import datasets, transforms\n",
    "from torchvision.utils import make_grid\n",
    "from tqdm import tqdm, trange\n",
    "\n",
    "writer = SummaryWriter()\n",
    "sns.set()\n",
    "sns.set_style(\"dark\")\n",
    "sns.set_palette(\"muted\")\n",
    "sns.set_color_codes(\"muted\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 397,
     "status": "ok",
     "timestamp": 1528263793235,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
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     "user_tz": 420
    },
    "id": "oGXTNl-Vt7PF",
    "outputId": "d53f7e66-2071-43f4-ac11-9589ba4846c2"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "DEVICE = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "LOADER_KWARGS = {'num_workers': 1, 'pin_memory': True} if torch.cuda.is_available() else {}\n",
    "print(torch.cuda.is_available())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-N2EKVF_muVQ"
   },
   "source": [
    "## Data Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "SMzSB6ebovaD"
   },
   "outputs": [],
   "source": [
    "BATCH_SIZE = 100\n",
    "TEST_BATCH_SIZE = 5\n",
    "\n",
    "train_loader = torch.utils.data.DataLoader(\n",
    "    datasets.FashionMNIST(\n",
    "        './fmnist', train=True, download=True,\n",
    "        transform=transforms.ToTensor()),\n",
    "    batch_size=BATCH_SIZE, shuffle=True, **LOADER_KWARGS)\n",
    "test_loader = torch.utils.data.DataLoader(\n",
    "    datasets.FashionMNIST(\n",
    "        './fmnist', train=False, download=True,\n",
    "        transform=transforms.ToTensor()),\n",
    "    batch_size=TEST_BATCH_SIZE, shuffle=False, **LOADER_KWARGS)\n",
    "\n",
    "TRAIN_SIZE = len(train_loader.dataset)\n",
    "TEST_SIZE = len(test_loader.dataset)\n",
    "NUM_BATCHES = len(train_loader)\n",
    "NUM_TEST_BATCHES = len(test_loader)\n",
    "\n",
    "CLASSES = 10\n",
    "TRAIN_EPOCHS = 20\n",
    "SAMPLES = 2\n",
    "TEST_SAMPLES = 10\n",
    "\n",
    "assert (TRAIN_SIZE % BATCH_SIZE) == 0\n",
    "assert (TEST_SIZE % TEST_BATCH_SIZE) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3hkpPckMmRUR"
   },
   "source": [
    "## Modelling\n",
    "$$\\underline{\\text{Reparameterized Gaussian}}$$\n",
    "$$\\begin{aligned}\n",
    "\\theta &= (\\mu, \\rho)\\\\\n",
    "\\sigma &= \\ln{(1+e^\\rho)}\\\\\n",
    "\\mathcal{N}(x\\vert \\mu, \\sigma) &= \\frac{1}{\\sqrt{2\\pi}\\sigma}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}\\\\\n",
    "\\ln{\\mathcal{N}(x\\vert \\mu, \\sigma)} &= -\\ln{\\sqrt{2\\pi}} -\\ln{\\sigma} -\\frac{(x-\\mu)^2}{2\\sigma^2}\\\\\n",
    "P(\\mathbf{w}) &= \\prod_j{\\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma^2)}\\\\\n",
    "\\ln{P(\\mathbf{w})} &= \\sum_j{\\ln{\\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma^2)}}\\\\\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "q9-GjqfnozFI"
   },
   "outputs": [],
   "source": [
    "class Gaussian(object):\n",
    "    def __init__(self, mu, rho):\n",
    "        super().__init__()\n",
    "        self.mu = mu\n",
    "        self.rho = rho\n",
    "        self.normal = torch.distributions.Normal(0,1)\n",
    "    \n",
    "    @property\n",
    "    def sigma(self):\n",
    "        return torch.log1p(torch.exp(self.rho))\n",
    "    \n",
    "    def sample(self):\n",
    "        epsilon = self.normal.sample(self.rho.size()).to(DEVICE)\n",
    "        return self.mu + self.sigma * epsilon\n",
    "    \n",
    "    def log_prob(self, input):\n",
    "        return (-math.log(math.sqrt(2 * math.pi))\n",
    "                - torch.log(self.sigma)\n",
    "                - ((input - self.mu) ** 2) / (2 * self.sigma ** 2)).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bezhA1xVntod"
   },
   "source": [
    "$$\\underline{\\text{Scale Mixture Gaussian}}$$\n",
    "$$\\begin{align}\n",
    "P(\\mathbf{w}) &= \\prod_j{\\pi \\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma_1^2) + (1-\\pi) \\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma_2^2)}\\\\\n",
    "\\ln{P(\\mathbf{w})} &= \\sum_j{\\ln{(\\pi \\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma_1^2) + (1-\\pi) \\mathcal{N}(\\mathbf{w}_j \\vert 0, \\sigma_2^2))}}\\\\\n",
    "\\end{align}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "L3wQlWNVo3S_"
   },
   "outputs": [],
   "source": [
    "class ScaleMixtureGaussian(object):\n",
    "    def __init__(self, pi, sigma1, sigma2):\n",
    "        super().__init__()\n",
    "        self.pi = pi\n",
    "        self.sigma1 = sigma1\n",
    "        self.sigma2 = sigma2\n",
    "        self.gaussian1 = torch.distributions.Normal(0,sigma1)\n",
    "        self.gaussian2 = torch.distributions.Normal(0,sigma2)\n",
    "    \n",
    "    def log_prob(self, input):\n",
    "        prob1 = torch.exp(self.gaussian1.log_prob(input))\n",
    "        prob2 = torch.exp(self.gaussian2.log_prob(input))\n",
    "        return (torch.log(self.pi * prob1 + (1-self.pi) * prob2)).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jwvLm9zGl3N7"
   },
   "source": [
    "$$\\pi = \\frac{1}{2}$$\n",
    "$$-\\ln{\\sigma_1} = 0$$\n",
    "$$-\\ln{\\sigma_2} = 6$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
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     "base_uri": "https://localhost:8080/",
     "height": 269
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 31782,
     "status": "ok",
     "timestamp": 1528263837119,
     "user": {
      "displayName": "Nitarshan Rajkumar",
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   "outputs": [
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sgp1HSr0RmoiIiIiIEhj5mcvtZteRUuJizLRqWvPNKy8kPMzIZS0jOJpbTmGJ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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0d26b2be10>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PI = 0.5\n",
    "SIGMA_1 = torch.cuda.FloatTensor([math.exp(-0)])\n",
    "SIGMA_2 = torch.cuda.FloatTensor([math.exp(-6)])\n",
    "\n",
    "def visualize_scale_mixture_components():\n",
    "    def show_lines():\n",
    "        pass\n",
    "    mix = ScaleMixtureGaussian(PI, SIGMA_1, SIGMA_2)\n",
    "    normal_1 = torch.distributions.Normal(0, SIGMA_1)\n",
    "    normal_2 = torch.distributions.Normal(0, SIGMA_2)\n",
    "    x_points = np.linspace(-5,5,10000)\n",
    "    d1 = np.array([torch.exp(normal_1.log_prob(float(c))) for c in x_points])\n",
    "    d2 = np.array([torch.exp(normal_2.log_prob(float(c))) for c in x_points])\n",
    "    d3 = np.array([torch.exp(mix.log_prob(float(c))) for c in x_points])\n",
    "    plt.subplots(1,3,figsize=(14,4))\n",
    "    plt.subplot(1,3,1)\n",
    "    plt.plot(x_points,d2,color=\"g\")\n",
    "    plt.plot(x_points,d3,color=\"r\")\n",
    "    plt.plot(x_points,d1,color=\"b\")\n",
    "    plt.legend([\"sigma2\", \"mix\", \"sigma1\"])\n",
    "    plt.ylim(0,0.5)\n",
    "    plt.subplot(1,3,2)\n",
    "    plt.plot(x_points,d1,color=\"b\")\n",
    "    plt.plot(x_points,d2,color=\"g\")\n",
    "    plt.plot(x_points,d3,color=\"r\")\n",
    "    plt.legend([\"sigma1\", \"sigma2\", \"mix\"])\n",
    "    plt.ylim(0,160)\n",
    "    plt.subplot(1,3,3)\n",
    "    plt.plot(x_points,d2,color=\"g\")\n",
    "    plt.plot(x_points,d3,color=\"r\")\n",
    "    plt.plot(x_points,d1,color=\"b\")\n",
    "    plt.legend([\"sigma2\", \"mix\", \"sigma1\"])\n",
    "    plt.ylim(0,80)\n",
    "    \n",
    "visualize_scale_mixture_components()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "ju2J8fneo7kc"
   },
   "outputs": [],
   "source": [
    "class BayesianLinear(nn.Module):\n",
    "    def __init__(self, in_features, out_features):\n",
    "        super().__init__()\n",
    "        self.in_features = in_features\n",
    "        self.out_features = out_features\n",
    "        # Weight parameters\n",
    "        self.weight_mu = nn.Parameter(torch.Tensor(out_features, in_features).uniform_(-0.2, 0.2))\n",
    "        self.weight_rho = nn.Parameter(torch.Tensor(out_features, in_features).uniform_(-5,-4))\n",
    "        self.weight = Gaussian(self.weight_mu, self.weight_rho)\n",
    "        # Bias parameters\n",
    "        self.bias_mu = nn.Parameter(torch.Tensor(out_features).uniform_(-0.2, 0.2))\n",
    "        self.bias_rho = nn.Parameter(torch.Tensor(out_features).uniform_(-5,-4))\n",
    "        self.bias = Gaussian(self.bias_mu, self.bias_rho)\n",
    "        # Prior distributions\n",
    "        self.weight_prior = ScaleMixtureGaussian(PI, SIGMA_1, SIGMA_2)\n",
    "        self.bias_prior = ScaleMixtureGaussian(PI, SIGMA_1, SIGMA_2)\n",
    "        self.log_prior = 0\n",
    "        self.log_variational_posterior = 0\n",
    "\n",
    "    def forward(self, input, sample=False, calculate_log_probs=False):\n",
    "        if self.training or sample:\n",
    "            weight = self.weight.sample()\n",
    "            bias = self.bias.sample()\n",
    "        else:\n",
    "            weight = self.weight.mu\n",
    "            bias = self.bias.mu\n",
    "        if self.training or calculate_log_probs:\n",
    "            self.log_prior = self.weight_prior.log_prob(weight) + self.bias_prior.log_prob(bias)\n",
    "            self.log_variational_posterior = self.weight.log_prob(weight) + self.bias.log_prob(bias)\n",
    "        else:\n",
    "            self.log_prior, self.log_variational_posterior = 0, 0\n",
    "\n",
    "        return F.linear(input, weight, bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "itSuNJtYo-X7"
   },
   "outputs": [],
   "source": [
    "class BayesianNetwork(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.l1 = BayesianLinear(28*28, 400)\n",
    "        self.l2 = BayesianLinear(400, 400)\n",
    "        self.l3 = BayesianLinear(400, 10)\n",
    "    \n",
    "    def forward(self, x, sample=False):\n",
    "        x = x.view(-1, 28*28)\n",
    "        x = F.relu(self.l1(x, sample))\n",
    "        x = F.relu(self.l2(x, sample))\n",
    "        x = F.log_softmax(self.l3(x, sample), dim=1)\n",
    "        return x\n",
    "    \n",
    "    def log_prior(self):\n",
    "        return self.l1.log_prior \\\n",
    "               + self.l2.log_prior \\\n",
    "               + self.l3.log_prior\n",
    "    \n",
    "    def log_variational_posterior(self):\n",
    "        return self.l1.log_variational_posterior \\\n",
    "               + self.l2.log_variational_posterior \\\n",
    "               + self.l3.log_variational_posterior\n",
    "    \n",
    "    def sample_elbo(self, input, target, samples=SAMPLES):\n",
    "        outputs = torch.zeros(samples, BATCH_SIZE, CLASSES).to(DEVICE)\n",
    "        log_priors = torch.zeros(samples).to(DEVICE)\n",
    "        log_variational_posteriors = torch.zeros(samples).to(DEVICE)\n",
    "        for i in range(samples):\n",
    "            outputs[i] = self(input, sample=True)\n",
    "            log_priors[i] = self.log_prior()\n",
    "            log_variational_posteriors[i] = self.log_variational_posterior()\n",
    "        log_prior = log_priors.mean()\n",
    "        log_variational_posterior = log_variational_posteriors.mean()\n",
    "        negative_log_likelihood = F.nll_loss(outputs.mean(0), target, size_average=False)\n",
    "        loss = (log_variational_posterior - log_prior)/NUM_BATCHES + negative_log_likelihood\n",
    "        return loss, log_prior, log_variational_posterior, negative_log_likelihood\n",
    "\n",
    "net = BayesianNetwork().to(DEVICE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "h-HLpkfPm2BI"
   },
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "SJXePX9KpAu0"
   },
   "outputs": [],
   "source": [
    "def write_weight_histograms(epoch):\n",
    "    writer.add_histogram('histogram/w1_mu', net.l1.weight_mu,epoch)\n",
    "    writer.add_histogram('histogram/w1_rho', net.l1.weight_rho,epoch)\n",
    "    writer.add_histogram('histogram/w2_mu', net.l2.weight_mu,epoch)\n",
    "    writer.add_histogram('histogram/w2_rho', net.l2.weight_rho,epoch)\n",
    "    writer.add_histogram('histogram/w3_mu', net.l3.weight_mu,epoch)\n",
    "    writer.add_histogram('histogram/w3_rho', net.l3.weight_rho,epoch)\n",
    "    writer.add_histogram('histogram/b1_mu', net.l1.bias_mu,epoch)\n",
    "    writer.add_histogram('histogram/b1_rho', net.l1.bias_rho,epoch)\n",
    "    writer.add_histogram('histogram/b2_mu', net.l2.bias_mu,epoch)\n",
    "    writer.add_histogram('histogram/b2_rho', net.l2.bias_rho,epoch)\n",
    "    writer.add_histogram('histogram/b3_mu', net.l3.bias_mu,epoch)\n",
    "    writer.add_histogram('histogram/b3_rho', net.l3.bias_rho,epoch)\n",
    "\n",
    "def write_loss_scalars(epoch, batch_idx, loss, log_prior, log_variational_posterior, negative_log_likelihood):\n",
    "    writer.add_scalar('logs/loss', loss, epoch*NUM_BATCHES+batch_idx)\n",
    "    writer.add_scalar('logs/complexity_cost', log_variational_posterior-log_prior, epoch*NUM_BATCHES+batch_idx)\n",
    "    writer.add_scalar('logs/log_prior', log_prior, epoch*NUM_BATCHES+batch_idx)\n",
    "    writer.add_scalar('logs/log_variational_posterior', log_variational_posterior, epoch*NUM_BATCHES+batch_idx)\n",
    "    writer.add_scalar('logs/negative_log_likelihood', negative_log_likelihood, epoch*NUM_BATCHES+batch_idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "q31y405kpGxt"
   },
   "outputs": [],
   "source": [
    "def train(net, optimizer, epoch):\n",
    "    net.train()\n",
    "    if epoch == 0: # write initial distributions\n",
    "        write_weight_histograms(epoch)\n",
    "    for batch_idx, (data, target) in enumerate(tqdm(train_loader)):\n",
    "        data, target = data.to(DEVICE), target.to(DEVICE)\n",
    "        net.zero_grad()\n",
    "        loss, log_prior, log_variational_posterior, negative_log_likelihood = net.sample_elbo(data, target)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        write_loss_scalars(epoch, batch_idx, loss, log_prior, log_variational_posterior, negative_log_likelihood)\n",
    "    write_weight_histograms(epoch+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 357
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1090232,
     "status": "ok",
     "timestamp": 1528264929340,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "cWaZ4c93pJkm",
    "outputId": "379e274f-ac3b-406b-9d31-c1a760242f84"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 600/600 [00:55<00:00, 10.90it/s]\n",
      "100%|██████████| 600/600 [00:55<00:00, 10.87it/s]\n",
      "100%|██████████| 600/600 [00:54<00:00, 10.91it/s]\n",
      " 16%|█▌        | 95/600 [00:08<00:46, 10.85it/s]100%|██████████| 600/600 [00:54<00:00, 10.97it/s]\n",
      "100%|██████████| 600/600 [00:55<00:00, 10.91it/s]\n",
      "100%|██████████| 600/600 [00:55<00:00, 10.90it/s]\n",
      " 20%|██        | 123/600 [00:11<00:44, 10.78it/s]100%|██████████| 600/600 [00:55<00:00, 10.81it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.22it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.20it/s]\n",
      " 22%|██▏       | 129/600 [00:11<00:42, 11.01it/s]100%|██████████| 600/600 [00:53<00:00, 11.14it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.12it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.12it/s]\n",
      " 22%|██▏       | 131/600 [00:11<00:42, 11.06it/s]100%|██████████| 600/600 [00:54<00:00, 11.10it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.13it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.14it/s]\n",
      " 22%|██▏       | 131/600 [00:11<00:42, 11.08it/s]100%|██████████| 600/600 [00:53<00:00, 11.16it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.11it/s]\n",
      "100%|██████████| 600/600 [00:54<00:00, 11.09it/s]\n",
      " 22%|██▏       | 131/600 [00:11<00:42, 11.10it/s]100%|██████████| 600/600 [00:53<00:00, 11.14it/s]\n",
      "100%|██████████| 600/600 [00:53<00:00, 11.12it/s]\n"
     ]
    }
   ],
   "source": [
    "optimizer = optim.Adam(net.parameters())\n",
    "for epoch in range(TRAIN_EPOCHS):\n",
    "    train(net, optimizer, epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LwmjhEqlm64B"
   },
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "F6zoJviDmArm"
   },
   "source": [
    "### Model Ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 221
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 198116,
     "status": "ok",
     "timestamp": 1528265127612,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "j4OzjvLHpL3o",
    "outputId": "1a8164fc-85d0-4b08-e010-33c3b7322b09"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Component 0 Accuracy: 8533/10000\n",
      "Component 1 Accuracy: 8485/10000\n",
      "Component 2 Accuracy: 8555/10000\n",
      "Component 3 Accuracy: 8548/10000\n",
      "Component 4 Accuracy: 8496/10000\n",
      "Component 5 Accuracy: 8472/10000\n",
      "Component 6 Accuracy: 8529/10000\n",
      "Component 7 Accuracy: 8525/10000\n",
      "Component 8 Accuracy: 8545/10000\n",
      "Component 9 Accuracy: 8531/10000\n",
      "Posterior Mean Accuracy: 8691/10000\n",
      "Ensemble Accuracy: 8765/10000\n"
     ]
    }
   ],
   "source": [
    "def test_ensemble():\n",
    "    net.eval()\n",
    "    correct = 0\n",
    "    corrects = np.zeros(TEST_SAMPLES+1, dtype=int)\n",
    "    with torch.no_grad():\n",
    "        for data, target in test_loader:\n",
    "            data, target = data.to(DEVICE), target.to(DEVICE)\n",
    "            outputs = torch.zeros(TEST_SAMPLES+1, TEST_BATCH_SIZE, CLASSES).to(DEVICE)\n",
    "            for i in range(TEST_SAMPLES):\n",
    "                outputs[i] = net(data, sample=True)\n",
    "            outputs[TEST_SAMPLES] = net(data, sample=False)\n",
    "            output = outputs.mean(0)\n",
    "            preds = preds = outputs.max(2, keepdim=True)[1]\n",
    "            pred = output.max(1, keepdim=True)[1] # index of max log-probability\n",
    "            corrects += preds.eq(target.view_as(pred)).sum(dim=1).squeeze().cpu().numpy()\n",
    "            correct += pred.eq(target.view_as(pred)).sum().item()\n",
    "    for index, num in enumerate(corrects):\n",
    "        if index < TEST_SAMPLES:\n",
    "            print('Component {} Accuracy: {}/{}'.format(index, num, TEST_SIZE))\n",
    "        else:\n",
    "            print('Posterior Mean Accuracy: {}/{}'.format(num, TEST_SIZE))\n",
    "    print('Ensemble Accuracy: {}/{}'.format(correct, TEST_SIZE))\n",
    "\n",
    "test_ensemble()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1Xa8bwZcnO2R"
   },
   "source": [
    "### Model Uncertainty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jMpmGG8unTUQ"
   },
   "source": [
    "#### In-Domain Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "qwd_xrtqpsvJ"
   },
   "outputs": [],
   "source": [
    "def show(img):\n",
    "    npimg = img.numpy()\n",
    "    plt.imshow(np.transpose(npimg, (1,2,0)), interpolation='nearest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 161
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 639,
     "status": "ok",
     "timestamp": 1528265130861,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "WhBywGVNpt9p",
    "outputId": "1528cd63-e80a-49fa-8ab9-2c46c786cc7f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 9,  2,  1,  1,  6])\n"
     ]
    },
    {
     "data": {
      "image/png": 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Tk+P85Cc/cRzHcU6cOOHceeedztSpU501a9Y4juM4L774ovOXv/ylLotYq6Sn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\n8hVCCCF8RpOvEEII4TP/BysN3cGi+RZBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0cd71a5e80>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fmnist_sample = iter(test_loader).next()\n",
    "fmnist_sample[0] = fmnist_sample[0].to(DEVICE)\n",
    "print(fmnist_sample[1])\n",
    "sns.set_style(\"dark\")\n",
    "show(make_grid(fmnist_sample[0].cpu()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2293,
     "status": "ok",
     "timestamp": 1528265133412,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "PBxwd31ppwIo",
    "outputId": "4349ee1a-6102-4e84-daf5-fe7888db37e0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1Wl0dhIiIiEhbpBkxERERERdRISYiIiLiIirERERERFzEoYXY4cOHGTZsGOvWrQPg1KlT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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0cd72e5ef0>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "net.eval()\n",
    "fmnist_outputs = net(fmnist_sample[0], True).max(1, keepdim=True)[1].detach().cpu().numpy()\n",
    "for _ in range(99):\n",
    "    fmnist_outputs = np.append(fmnist_outputs, net(fmnist_sample[0], True).max(1, keepdim=True)[1].detach().cpu().numpy(), axis=1)\n",
    "sns.set_style(\"darkgrid\")\n",
    "plt.subplots(5,1,figsize=(10,4))\n",
    "for i in range(5):\n",
    "    plt.subplot(5,1,i+1)\n",
    "    plt.ylim(0,100)\n",
    "    plt.xlabel(\"Categories\")\n",
    "    plt.xticks(range(10), [\"Top\", \"Trouser\", \"Pullover\", \"Dress\", \"Coat\", \"Sandal\", \"Shirt\", \"Sneaker\", \"Bag\", \"Ankle Boot\"])\n",
    "    plt.ylabel(\"Count\")\n",
    "    plt.yticks(range(50,101,50))\n",
    "    plt.hist(fmnist_outputs[i], np.arange(-0.5, 10, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1v7EqhO5nY52"
   },
   "source": [
    "#### Out-of-Domain Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "both",
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "MkgNoIeCpzVF"
   },
   "outputs": [],
   "source": [
    "mnist_loader = torch.utils.data.DataLoader(\n",
    "    datasets.MNIST('./mnist', train=False, download=True, transform=transforms.ToTensor()), batch_size=5, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 161
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 501,
     "status": "ok",
     "timestamp": 1528265134913,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "oB1TCdv7C97a",
    "outputId": "36b7bec9-7b6a-4f8a-80ae-98180f9b65a3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 7,  2,  1,  0,  4])\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0cd72d9b00>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mnist_sample = iter(mnist_loader).next()\n",
    "mnist_sample[0] = mnist_sample[0].to(DEVICE)\n",
    "print(mnist_sample[1])\n",
    "sns.set_style(\"dark\")\n",
    "show(make_grid(mnist_sample[0].cpu()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2254,
     "status": "ok",
     "timestamp": 1528265137311,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "DLSygPieC-7q",
    "outputId": "5b016b5a-7256-4af6-f6f5-53487b841137"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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v0vboeS+O5EqPL12XtfkYrFar1dkhRERERNoiuy76LSIiIiLNT42YiIiIiJOoERMRERFx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\niImIiIg4iRoxERERESdRIyYiIiLiJP8fTxszG0902+oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0d5a5b4860>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "net.eval()\n",
    "mnist_outputs = net(mnist_sample[0], True).max(1, keepdim=True)[1].detach().cpu().numpy()\n",
    "for _ in range(99):\n",
    "    mnist_outputs = np.append(mnist_outputs, net(mnist_sample[0], True).max(1, keepdim=True)[1].detach().cpu().numpy(), axis=1)\n",
    "\n",
    "sns.set_style(\"darkgrid\")\n",
    "plt.subplots(5,1,figsize=(10,4))\n",
    "for i in range(5):\n",
    "    plt.subplot(5,1,i+1)\n",
    "    plt.ylim(0,100)\n",
    "    plt.xlabel(\"Categories\")\n",
    "    plt.xticks(range(10), [\"Top\", \"Trouser\", \"Pullover\", \"Dress\", \"Coat\", \"Sandal\", \"Shirt\", \"Sneaker\", \"Bag\", \"Ankle Boot\"])\n",
    "    plt.ylabel(\"Count\")\n",
    "    plt.yticks(range(50,101,50))\n",
    "    plt.hist(mnist_outputs[i], np.arange(-0.5, 10, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 357
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 472,
     "status": "ok",
     "timestamp": 1528265139007,
     "user": {
      "displayName": "Nitarshan Rajkumar",
      "photoUrl": "//lh6.googleusercontent.com/-oLz5q0aJmAQ/AAAAAAAAAAI/AAAAAAAAAIY/O0-NjvATt18/s50-c-k-no/photo.jpg",
      "userId": "117587045527370134083"
     },
     "user_tz": 420
    },
    "id": "PHMriPNTDBuY",
    "outputId": "3943e78a-4f3f-4c1d-d9b8-c5f44a037ef5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "last updated: Wed Jun 06 2018 \n",
      "\n",
      "CPython 3.6.3\n",
      "IPython 5.5.0\n",
      "\n",
      "torch 0.4.0\n",
      "numpy 1.14.3\n",
      "matplotlib 2.1.2\n",
      "tensorboardX n\u0007\n",
      "torchvision 0.2.1\n",
      "seaborn 0.7.1\n",
      "\n",
      "compiler   : GCC 7.2.0\n",
      "system     : Linux\n",
      "release    : 4.4.111+\n",
      "machine    : x86_64\n",
      "processor  : x86_64\n",
      "CPU cores  : 2\n",
      "interpreter: 64bit\n",
      "watermark 1.6.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark --updated --datename --python --machine --watermark -p torch,numpy,matplotlib,tensorboardX,torchvision,seaborn"
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [],
   "default_view": {},
   "name": "bayes-by-backprop.ipynb",
   "provenance": [],
   "version": "0.3.2",
   "views": {}
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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