notebooks/bayesian_linear_regression_mfvi.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GJcMJWZDBy2h"
      },
      "source": [
        "# Bayesian Linear Regression fit using MFVI vs closed-form solution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "%load_ext autoreload\n",
        "%autoreload 2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uJd1yRdoJgA7",
        "outputId": "ac8f8121-db81-47a0-f47e-eb001f0b38c8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Note: you may need to restart the kernel to use updated packages.\n"
          ]
        }
      ],
      "source": [
        "%pip install -q torch"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "PkWZ_bKBJYeT"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "import torch\n",
        "from torch.nn.functional import softplus"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "import sys\n",
        "sys.path.append(\"../\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "import reparameterized as r\n",
        "from reparameterized import sampling\n",
        "from reparameterized import likelihoods\n",
        "from reparameterized import densities"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "JVdgdm7Cd5UI"
      },
      "outputs": [],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "plt.rcParams['figure.figsize'] = (5, 5) # Width and height"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uiEnOgwGJaEn",
        "outputId": "c8936bc9-58b4-4ecf-fcea-88d08592c3c4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Using CPU\n"
          ]
        }
      ],
      "source": [
        "if torch.cuda.is_available():\n",
        "    torch.set_default_tensor_type('torch.cuda.FloatTensor')\n",
        "    env = torch.cuda\n",
        "    print(\"Using GPU\")\n",
        "else:\n",
        "    torch.set_default_tensor_type('torch.FloatTensor')\n",
        "    env = torch\n",
        "    print(\"Using CPU\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kTKZ15jMg0nN"
      },
      "source": [
        "## Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "SEED = 123\n",
        "\n",
        "torch.manual_seed(SEED)\n",
        "np.random.seed(SEED)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "18IvegmjJYea"
      },
      "outputs": [],
      "source": [
        "def generate_toy_data(N):\n",
        "    x_data = np.float32(np.random.uniform(-10.5, 10.5, (1, N))).T\n",
        "    r_data = np.float32(np.random.normal(size=(N,1)))\n",
        "    y_data = np.float32(np.sin(0.75*x_data)*7.0+x_data*0.5+r_data*2.0)+10\n",
        "    \n",
        "    mask = (x_data<0.0) | (x_data>5.0)\n",
        "    r_data = r_data[mask]\n",
        "    y_data = y_data[mask, None]\n",
        "    x_data = x_data[mask, None]\n",
        "\n",
        "    return x_data, y_data, r_data\n",
        "\n",
        "\n",
        "x_data, y_data, r_data = generate_toy_data(100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(x_data, y_data, color=\"salmon\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 356
        },
        "id": "7pbiMR-uuQw0",
        "outputId": "23ab92bf-fc5f-4e78-ecd3-44c98cd8f6d2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "x=torch.Size([64, 1]) y=torch.Size([64, 1])\n"
          ]
        }
      ],
      "source": [
        "x = torch.tensor(x_data, dtype = torch.float, requires_grad=False)\n",
        "y = torch.tensor(y_data, dtype = torch.float, requires_grad=False)\n",
        "\n",
        "print(\"x=%s y=%s\" % (x.shape, y.shape))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WfXPH8s9fvK4"
      },
      "source": [
        "## Visualisation code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "WzpelbYIfcCh"
      },
      "outputs": [],
      "source": [
        "def plot_with_errortunnel(x, y, yerr, color=None, alpha_fill=0.2, ax=None, label=\"\", lw=1):\n",
        "    ax = ax if ax is not None else plt.gca()\n",
        "    if color is None:\n",
        "        color = ax._get_lines.color_cycle.next()\n",
        "    if np.isscalar(yerr) or len(yerr) == len(y):\n",
        "        ymin = y - yerr\n",
        "        ymax = y + yerr\n",
        "    elif len(yerr) == 2:\n",
        "        ymin, ymax = yerr\n",
        "    ax.plot(x, y, color=color, label=label, lw=lw)\n",
        "    ax.fill_between(x, ymax, ymin, color=color, alpha=alpha_fill, linewidth=0.0)\n",
        " \n",
        " \n",
        "def numpy(tensor):\n",
        "    return tensor.cpu().detach().numpy()\n",
        "\n",
        "\n",
        "def linspace1(x):\n",
        "    x2, x1 = numpy(x.flatten().max().cpu()), numpy(x.flatten().min().cpu())\n",
        "    rng = (x2-x1)*0.5\n",
        "    xs = np.arange(x1-rng, x2+rng, 0.5)\n",
        "    xs = torch.tensor([[v] for v in xs], dtype=torch.float32)            \n",
        "    return xs\n",
        "\n",
        "\n",
        "def plot_fit(x, y, xs, ys, plot_samples=True, plot_error=True):  \n",
        "    x, y, xs, ys = numpy(x), numpy(y), numpy(xs), numpy(ys)\n",
        "    plt.scatter(x.flatten(), y.flatten(), label=\"data\", color=\"salmon\")\n",
        "    \n",
        "    if plot_samples:\n",
        "        for y1 in ys:\n",
        "            plt.plot(xs.flatten(), y1.flatten(), lw=1)\n",
        "\n",
        "    ym, ys = ys.mean(0), ys.std(0)         \n",
        "    if plot_error:\n",
        "        plot_with_errortunnel(xs.flatten(), ym.flatten(), 2*ys.flatten(), color=\"dodgerblue\", label=\"BNN (m+/-2*s\", lw=2)\n",
        "    else:\n",
        "        plt.plot(xs.flatten(), ym.flatten(), color=\"dodgerblue\", label=\"BNN\", lw=2)\n",
        "        \n",
        "    plt.legend();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HdEt2uU1g4qM"
      },
      "source": [
        "## Network"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "Gc6q2sg2JYeg"
      },
      "outputs": [],
      "source": [
        "INPUT_DIM = 1\n",
        "OUTPUT_DIM = 1\n",
        "\n",
        "# Linear regression model\n",
        "model = torch.nn.Sequential(\n",
        "    torch.nn.Linear(INPUT_DIM, OUTPUT_DIM),\n",
        "    )    \n",
        " \n",
        "\n",
        "assert torch.Size([INPUT_DIM])==x.shape[1:]\n",
        "assert torch.Size([OUTPUT_DIM])==y.shape[1:]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gGVx0r32B9YK"
      },
      "source": [
        "List model parameters:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6vkVkh6Bh5mv",
        "outputId": "d494d89d-b1f9-4a1e-938b-bace4397b8f1"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dict_keys(['0.weight', '0.bias'])"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dict(model.named_parameters()).keys()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5yi11c7oV4x8"
      },
      "source": [
        "## Priors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "LmPkkhP-ViwN"
      },
      "outputs": [],
      "source": [
        "parameters2nllfunc = {}\n",
        "for parameter_name, parameter_value in model.named_parameters():\n",
        "    parameters2nllfunc[parameter_name] = densities.create_gaussian_nll(parameter_value.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Likelihood"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [],
      "source": [
        "LIKELIHOOD_SIGMA = 2\n",
        "\n",
        "def predictive_distribution_sampler(logits, **kwargs): \n",
        "    return likelihoods.factorized_gaussian_with_fixed_scale_sample(logits, scale=LIKELIHOOD_SIGMA, **kwargs)\n",
        "\n",
        "def predictive_distribution_log_lik(logits, output_y, **kwargs): \n",
        "    return likelihoods.factorized_gaussian_with_fixed_scale_log_prob(logits, output_y, scale=LIKELIHOOD_SIGMA, **kwargs)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9D7EgkWdruSn"
      },
      "source": [
        "## Create samplers for parameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J38TtATn0yWC"
      },
      "source": [
        "List of samplers and variational parameters to be optimized"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "Ji54HbaQtqni"
      },
      "outputs": [],
      "source": [
        "parameters2sampler = {}\n",
        "variational_params = []\n",
        "\n",
        "is_parameter_already_handled = lambda parameter_name: r.is_parameter_handled(parameters2sampler.items(), parameter_name)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7jFY9QkY84uU"
      },
      "source": [
        "Register parameters to be modeled with factorized Gaussian"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EZQIqbzehuCA",
        "outputId": "97bd6cef-30f2-4c35-f14b-8770e2cd92e0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Learning 0.weight with factorized Gaussian\n",
            "Learning 0.bias with factorized Gaussian\n"
          ]
        }
      ],
      "source": [
        "loc_initalization = lambda parameter: torch.randn_like(parameter) #parameter.clone().detach(),\n",
        "uscale_initialization = lambda parameter: torch.randn_like(parameter)\n",
        "\n",
        "\n",
        "for n, p in model.named_parameters():\n",
        "    if not is_parameter_already_handled(n):\n",
        "        print(f\"Learning {n} with factorized Gaussian\")\n",
        "        sampler, variational_params1, aux_objs = sampling.create_factorized_gaussian_sampler(p, \n",
        "            loc_initalization=loc_initalization,\n",
        "            uscale_initialization=uscale_initialization,\n",
        "            )\n",
        "\n",
        "        parameters2sampler[n] = sampler\n",
        "        variational_params.extend((n+\":\"+vn, vp) for vn, vp in variational_params1.items())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3_7JDyMt1R2W"
      },
      "source": [
        "# Preview sample"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "samplers:\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "{'0.weight': <function reparameterized.sampling.gaussian.create_factorized_gaussian_sampler.<locals>.sample_factorized_gaussian(n_samples=1)>,\n",
              " '0.bias': <function reparameterized.sampling.gaussian.create_factorized_gaussian_sampler.<locals>.sample_factorized_gaussian(n_samples=1)>}"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(\"samplers:\")\n",
        "display(parameters2sampler)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "variational parameters:\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "[('0.weight:loc', torch.Size([1, 1])),\n",
              " ('0.weight:unnormalized_scale', torch.Size([1, 1])),\n",
              " ('0.bias:loc', torch.Size([1])),\n",
              " ('0.bias:unnormalized_scale', torch.Size([1]))]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "print(\"variational parameters:\")\n",
        "display([(vn, vp.shape) for vn, vp in variational_params])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "WVRjL_Vb3Cyc"
      },
      "outputs": [],
      "source": [
        "parameters_samples, nlls = r.sample_parameters(parameters2sampler.items(), 3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nAElvBuKsutz",
        "outputId": "9906dfbf-fb99-44eb-c0f1-bbeedda8266d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "parameters' sample:\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "{'0.weight': torch.Size([3, 1, 1]), '0.bias': torch.Size([3, 1])}"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "print(\"parameters' sample:\")\n",
        "{n: s.shape for n, s in parameters_samples.items()}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cBNkS9FM1V6g",
        "outputId": "a72458d3-c921-45db-fb8d-deea62b85f9f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "parameters' NLLs:\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "{'0.weight': tensor([1.5438, 0.6501, 3.4862], grad_fn=<NegBackward0>),\n",
              " '0.bias': tensor([1.0825, 2.5185, 1.1836], grad_fn=<NegBackward0>)}"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "print(\"parameters' NLLs:\")\n",
        "nlls"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QkAbLF_UVB3s",
        "outputId": "a47fe134-088d-4be0-8104-e3a7fd4382ae"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "torch.Size([6, 64, 1])"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "r.sample_predictive(x, model, parameters_samples, predictive_distribution_sampler, n_samples=2, flatten_samples_dims=True).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wMK1M-vcYxkv",
        "outputId": "291b25f9-3f8f-40a1-e040-edde416bbabf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "torch.Size([3, 64])"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "r.predictive_likelihoods(x, y, model, parameters_samples, predictive_distribution_log_lik).shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VqLQg7NvguxA"
      },
      "source": [
        "## Learning"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 332
        },
        "id": "cD4dC0iFctTB",
        "outputId": "a246291e-f201-48ff-db00-0ea2c00ec530"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "parameters_samples, nlls = r.sample_parameters(parameters2sampler.items(), 10)\n",
        "xs = linspace1(x)\n",
        "ys = r.sample_predictive(xs, model, parameters_samples, \n",
        "                        sampler=predictive_distribution_sampler, \n",
        "                        n_samples=1, \n",
        "                       )\n",
        "\n",
        "plot_fit(x, y, xs, ys)\n",
        "plt.title(\"before learning\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HgRQ6dDMJYer",
        "outputId": "b88b19fd-06f6-41e0-9836-95702e68bd30"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "epoch=0: elbo = -1129.31 (= -1133.66 [+] -2.36 [-] -6.70)\n",
            "epoch=1: elbo = -710.74 (= -708.95 [+] -4.48 [-] -2.69)\n",
            "epoch=2: elbo = -1230.81 (= -1228.98 [+] -3.42 [-] -1.59)\n",
            "epoch=3: elbo = -1655.00 (= -1653.23 [+] -3.62 [-] -1.85)\n",
            "epoch=4: elbo = -1341.47 (= -1338.57 [+] -4.91 [-] -2.01)\n",
            "epoch=5: elbo = -1328.17 (= -1327.40 [+] -2.73 [-] -1.96)\n",
            "epoch=6: elbo = -828.05 (= -830.04 [+] -2.73 [-] -4.71)\n",
            "epoch=7: elbo = -1742.15 (= -1739.37 [+] -4.88 [-] -2.10)\n",
            "epoch=8: elbo = -623.39 (= -620.28 [+] -7.16 [-] -4.04)\n",
            "epoch=9: elbo = -886.78 (= -886.07 [+] -2.55 [-] -1.83)\n",
            "epoch=1000: elbo = -389.11 (= -358.64 [+] -32.01 [-] -1.55)\n",
            "epoch=2000: elbo = -377.95 (= -342.22 [+] -34.61 [-]  1.12)\n",
            "epoch=3000: elbo = -376.57 (= -343.23 [+] -31.34 [-]  2.00)\n",
            "epoch=4000: elbo = -377.00 (= -343.45 [+] -31.33 [-]  2.22)\n",
            "epoch=5000: elbo = -376.11 (= -344.42 [+] -30.54 [-]  1.16)\n",
            "epoch=6000: elbo = -377.49 (= -343.79 [+] -34.29 [-] -0.59)\n",
            "epoch=7000: elbo = -376.65 (= -342.50 [+] -32.02 [-]  2.13)\n",
            "epoch=8000: elbo = -376.71 (= -340.81 [+] -33.20 [-]  2.69)\n",
            "epoch=9000: elbo = -375.65 (= -339.95 [+] -34.42 [-]  1.28)\n"
          ]
        }
      ],
      "source": [
        "optimized_parameters = [vp for _, vp in variational_params]\n",
        "optimizer = torch.optim.Adam(optimized_parameters, lr=0.01) \n",
        "\n",
        "n_posterior_samples = 1\n",
        "n_epochs = 10000\n",
        "\n",
        "for e in range(n_epochs):\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    # sampling from approximate posterior\n",
        "    parameters_samples, posterior_nlls = r.sample_parameters(parameters2sampler, n_samples=n_posterior_samples)\n",
        "    posterior_nlls = torch.stack(list(posterior_nlls.values()))  # out shape: n_param_groups x n_posterior_samples\n",
        "    log_q = -posterior_nlls.sum(0)\n",
        "\n",
        "    # priors\n",
        "    prior_nlls = r.estimate_parameters_nll(parameters2nllfunc, parameters_samples)\n",
        "    prior_nlls = torch.stack(list(prior_nlls.values()))  # out shape: n_param_groups x n_posterior_samples\n",
        "    log_p = -prior_nlls.sum(0)\n",
        "\n",
        "    # estimating likelihoods of observed y\n",
        "    logliks = r.predictive_likelihoods(x, y, model, parameters_samples, predictive_distribution_log_lik)\n",
        "    assert logliks.shape==torch.Size([n_posterior_samples, len(y)])\n",
        "    logliks = logliks.sum(1) # sum over data points\n",
        "    \n",
        "    elbo = logliks+log_p-log_q\n",
        "    elbo = elbo.mean()  # average over posterior samples\n",
        "\n",
        "    loss_vi = -elbo\n",
        "    loss_vi.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    if e<10 or e%1000==0:\n",
        "        print(f\"epoch={e}: elbo = {elbo: .2f} (= {logliks.mean(): .2f} [+] {log_p.mean(): .2f} [-] {log_q.mean(): .2f})\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "parameters_samples, nlls = r.sample_parameters(parameters2sampler, 10)\n",
        "xs = linspace1(x)\n",
        "ys = r.sample_predictive(xs, model, parameters_samples, \n",
        "                        sampler=predictive_distribution_sampler, \n",
        "                        n_samples=1, \n",
        "                       )\n",
        "\n",
        "plot_fit(x, y, xs, ys)\n",
        "plt.title(\"after learning\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FMLYtaZFBoFm"
      },
      "source": [
        "# Linear Regression Bayesian true (closed-form) posterior"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O_qCizafZv1z"
      },
      "source": [
        "See Bishop's book"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "1yIXrPEr7dDU"
      },
      "outputs": [],
      "source": [
        "psi = np.hstack([x_data, np.ones(x_data.shape)])\n",
        "t = y_data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "elCPvgtiEQwf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "((64, 2), (64, 1))"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "psi.shape, t.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "KH-ZfaL-_hwr"
      },
      "outputs": [],
      "source": [
        "#likelihood precision:\n",
        "beta = 1./(LIKELIHOOD_SIGMA*LIKELIHOOD_SIGMA)\n",
        "\n",
        "#prior:\n",
        "S0 = np.eye(psi.shape[-1])\n",
        "m0 = np.zeros(psi.shape[-1]).reshape(-1, 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "wsl3q5Ys7_sJ"
      },
      "outputs": [],
      "source": [
        "SN = np.linalg.inv( np.linalg.inv(S0) + beta*np.dot(psi.T, psi) ) # covariance matrix (Bishop 3.50)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "YPZEyITg_uld"
      },
      "outputs": [],
      "source": [
        "mN = np.dot(SN, np.dot(np.linalg.inv(S0), m0) + beta*np.dot(psi.T, t)) # means (Bishop 3.51)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compare expectations (means):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "jqLCbzz5AmTr"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.37413242],\n",
              "       [7.83990305]])"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "mN"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor(0.3909, grad_fn=<MeanBackward0>),\n",
              " tensor(7.8558, grad_fn=<MeanBackward0>))"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# empirically estimate means for the VI solution:\n",
        "parameters_samples, nlls = r.sample_parameters(parameters2sampler.items(), n_samples=1000000)\n",
        "parameters_samples['0.weight'].mean(), parameters_samples['0.bias'].mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor([[0.3909]], requires_grad=True), tensor([7.8557], requires_grad=True))"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# extract means directly from variational parameters:\n",
        "\n",
        "variational_params_d = dict(variational_params)\n",
        "l1, l2 = variational_params_d['0.weight:loc'], variational_params_d['0.bias:loc'], \n",
        "l1, l2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compare covariance:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "pj-hoGZ1A9Ba"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.0018352 , 0.00256277],\n",
              "       [0.00256277, 0.06240231]])"
            ]
          },
          "execution_count": 37,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "SN"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor([[ 1.9555e-03, -1.7786e-06],\n",
              "        [-1.7786e-06,  5.3761e-02]], grad_fn=<SqueezeBackward0>)"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# empirically estimate covariance matrix for the VI solution:\n",
        "parameters_samples, nlls = r.sample_parameters(parameters2sampler.items(), n_samples=1000000)\n",
        "samples_weight, samples_bias = parameters_samples['0.weight'].flatten(), parameters_samples['0.bias'].flatten()\n",
        "samples = torch.stack([samples_weight, samples_bias], dim=0)\n",
        "torch.cov(samples)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**Note, we used MFVI and off-diagonal covariances are 0.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "um_HOFQK-lEz"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor([[0.0020]], grad_fn=<MulBackward0>),\n",
              " tensor([0.0538], grad_fn=<MulBackward0>))"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# extract diagonal variances directly from variational parameters:\n",
        "s1, s2 = softplus(variational_params_d['0.weight:unnormalized_scale']), softplus(variational_params_d['0.bias:unnormalized_scale'])\n",
        "s1*s1, s2*s2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [
        "-C2DLYqynn54"
      ],
      "provenance": []
    },
    "gpuClass": "standard",
    "kernelspec": {
      "display_name": "Python 3.8.5 ('base')",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    },
    "vscode": {
      "interpreter": {
        "hash": "72dff520818572b45c401a256658ee25fa99b55260abeb0336ef1b1e43b37267"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}