notebooks/bayesian_linear_regression_full_rank.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GJcMJWZDBy2h"
      },
      "source": [
        "# Bayesian Linear Regression fit using full-rank Gaussian VI vs closed-form solution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compared to MFVI, here LR weight and bias samples come from the same (multi-parameter) sampler sampling from a full-rank Gaussian."
      ]
    },
    {
      "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 jointly with full-rank\n",
        " Gaussian"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [],
      "source": [
        "sampler, variational_params1, aux_objs = sampling.create_multiparameter_sampler(sampling.create_gaussian_tril_sampler, model.named_parameters())\n",
        "\n",
        "names = tuple(n for n, _ in model.named_parameters())\n",
        "parameters2sampler[names] = sampler\n",
        "variational_params.extend(variational_params1.items())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**Note, we use only one sampler returning joint samples for all parameters.**"
      ]
    },
    {
      "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',\n",
              "  '0.bias'): <function reparameterized.sampling.multiparameter._multiparameter_sampler_unpack.<locals>.wrapped_sampler(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": [
              "[('loc', torch.Size([2])),\n",
              " ('unnormalized_diag', torch.Size([2])),\n",
              " ('cov_tril', torch.Size([2, 2]))]"
            ]
          },
          "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',\n",
              "  '0.bias'): tensor([4.9681, 3.7646, 2.2191], 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 = -7679.90 (= -7670.15 [+] -16.85 [-] -7.10)\n",
            "epoch=1: elbo = -1701.48 (= -1698.93 [+] -5.65 [-] -3.10)\n",
            "epoch=2: elbo = -891.89 (= -892.04 [+] -1.87 [-] -2.02)\n",
            "epoch=3: elbo = -1105.49 (= -1105.17 [+] -2.60 [-] -2.28)\n",
            "epoch=4: elbo = -873.46 (= -874.02 [+] -1.89 [-] -2.44)\n",
            "epoch=5: elbo = -990.65 (= -990.94 [+] -2.11 [-] -2.40)\n",
            "epoch=6: elbo = -6138.66 (= -6126.93 [+] -16.88 [-] -5.15)\n",
            "epoch=7: elbo = -1324.17 (= -1323.88 [+] -2.84 [-] -2.54)\n",
            "epoch=8: elbo = -1495.00 (= -1492.59 [+] -6.90 [-] -4.49)\n",
            "epoch=9: elbo = -1468.23 (= -1467.12 [+] -3.39 [-] -2.28)\n",
            "epoch=1000: elbo = -428.35 (= -404.89 [+] -25.52 [-] -2.07)\n",
            "epoch=2000: elbo = -381.09 (= -347.89 [+] -32.62 [-]  0.57)\n",
            "epoch=3000: elbo = -376.25 (= -342.97 [+] -31.80 [-]  1.48)\n",
            "epoch=4000: elbo = -376.90 (= -343.32 [+] -31.83 [-]  1.75)\n",
            "epoch=5000: elbo = -376.97 (= -346.65 [+] -29.52 [-]  0.81)\n",
            "epoch=6000: elbo = -377.97 (= -345.99 [+] -32.82 [-] -0.85)\n",
            "epoch=7000: elbo = -376.58 (= -342.77 [+] -31.76 [-]  2.05)\n",
            "epoch=8000: elbo = -376.69 (= -340.81 [+] -33.19 [-]  2.68)\n",
            "epoch=9000: elbo = -375.80 (= -339.78 [+] -34.76 [-]  1.26)\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(0.3891, grad_fn=<MeanBackward0>),\n",
              " tensor(7.8643, 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": "markdown",
      "metadata": {},
      "source": [
        "Compare covariance:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "pj-hoGZ1A9Ba"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.0018352 , 0.00256277],\n",
              "       [0.00256277, 0.06240231]])"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "SN"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor([[0.0019, 0.0031],\n",
              "        [0.0031, 0.0590]], grad_fn=<SqueezeBackward0>)"
            ]
          },
          "execution_count": 37,
          "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": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
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