Lab_12_MCMC_BlackJAX.ipynb

{
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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOBeRzu8XcicuzbSX9VWnVW",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/USCbiostats/PM520/blob/main/Lab_12_MCMC_BlackJAX.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "12UrCPML9_fV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install blackjax"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EIj4uu45-Jzd",
        "outputId": "4e46267c-efd5-4987-901d-3036db0718db"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting blackjax\n",
            "  Downloading blackjax-1.1.1-py3-none-any.whl (4.6 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m4.6/4.6 MB\u001b[0m \u001b[31m14.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: fastprogress>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from blackjax) (1.0.3)\n",
            "Requirement already satisfied: jax>=0.4.16 in /usr/local/lib/python3.10/dist-packages (from blackjax) (0.4.23)\n",
            "Requirement already satisfied: jaxlib>=0.4.16 in /usr/local/lib/python3.10/dist-packages (from blackjax) (0.4.23+cuda12.cudnn89)\n",
            "Collecting jaxopt>=0.8 (from blackjax)\n",
            "  Downloading jaxopt-0.8.3-py3-none-any.whl (172 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m172.3/172.3 kB\u001b[0m \u001b[31m12.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: optax>=0.1.7 in /usr/local/lib/python3.10/dist-packages (from blackjax) (0.2.2)\n",
            "Requirement already satisfied: typing-extensions>=4.4.0 in /usr/local/lib/python3.10/dist-packages (from blackjax) (4.10.0)\n",
            "Requirement already satisfied: ml-dtypes>=0.2.0 in /usr/local/lib/python3.10/dist-packages (from jax>=0.4.16->blackjax) (0.2.0)\n",
            "Requirement already satisfied: numpy>=1.22 in /usr/local/lib/python3.10/dist-packages (from jax>=0.4.16->blackjax) (1.25.2)\n",
            "Requirement already satisfied: opt-einsum in /usr/local/lib/python3.10/dist-packages (from jax>=0.4.16->blackjax) (3.3.0)\n",
            "Requirement already satisfied: scipy>=1.9 in /usr/local/lib/python3.10/dist-packages (from jax>=0.4.16->blackjax) (1.11.4)\n",
            "Requirement already satisfied: absl-py>=0.7.1 in /usr/local/lib/python3.10/dist-packages (from optax>=0.1.7->blackjax) (1.4.0)\n",
            "Requirement already satisfied: chex>=0.1.86 in /usr/local/lib/python3.10/dist-packages (from optax>=0.1.7->blackjax) (0.1.86)\n",
            "Requirement already satisfied: toolz>=0.9.0 in /usr/local/lib/python3.10/dist-packages (from chex>=0.1.86->optax>=0.1.7->blackjax) (0.12.1)\n",
            "Installing collected packages: jaxopt, blackjax\n",
            "Successfully installed blackjax-1.1.1 jaxopt-0.8.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 511
        },
        "id": "IF_-d-Wp944H",
        "outputId": "6b75ea29-d778-4508-d00f-a2baa9709e4e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x600 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "# warm up\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "import jax.scipy.stats as stats\n",
        "\n",
        "import blackjax\n",
        "\n",
        "\n",
        "seed = 0\n",
        "rng_key = jax.random.key(seed)\n",
        "\n",
        "# true values that generate our observations\n",
        "loc, scale = 10, 20\n",
        "observed = np.random.normal(loc, scale, size=1_000)\n",
        "\n",
        "\n",
        "# set up our density function\n",
        "def logdensity_fn(loc, log_scale, observed=observed):\n",
        "    \"\"\"Univariate Normal\"\"\"\n",
        "    scale = jnp.exp(log_scale)\n",
        "    logpdf = stats.norm.logpdf(observed, loc, scale)\n",
        "    return jnp.sum(logpdf)\n",
        "\n",
        "\n",
        "def logdensity(x):\n",
        "  return logdensity_fn(**x)\n",
        "\n",
        "\n",
        "# kernel params\n",
        "inv_mass_matrix = np.array([0.5, 0.01])\n",
        "num_integration_steps = 60\n",
        "step_size = 1e-3\n",
        "\n",
        "# set up our kernel\n",
        "hmc = blackjax.hmc(logdensity, step_size, inv_mass_matrix, num_integration_steps)\n",
        "\n",
        "# sample from posterior\n",
        "rng_key, sample_key = jax.random.split(rng_key)\n",
        "\n",
        "initial_position = {\"loc\": 1.0, \"log_scale\": 1.0}\n",
        "initial_state = hmc.init(initial_position)\n",
        "hmc_kernel = jax.jit(hmc.step)\n",
        "\n",
        "\n",
        "def inference_loop(rng_key, kernel, initial_state, num_samples):\n",
        "    @jax.jit\n",
        "    def one_step(state, rng_key):\n",
        "        state, _ = kernel(rng_key, state)\n",
        "        return state, state\n",
        "\n",
        "    keys = jax.random.split(rng_key, num_samples)\n",
        "    _, states = jax.lax.scan(one_step, initial_state, keys)\n",
        "\n",
        "    return states\n",
        "\n",
        "states = inference_loop(sample_key, hmc_kernel, initial_state, 10_000)\n",
        "\n",
        "mcmc_samples = states.position\n",
        "mcmc_samples[\"scale\"] = jnp.exp(mcmc_samples[\"log_scale\"]).block_until_ready()\n",
        "\n",
        "# visualize results\n",
        "fig, (ax, ax1) = plt.subplots(ncols=2, figsize=(15, 6))\n",
        "ax.plot(mcmc_samples[\"loc\"])\n",
        "ax.set_xlabel(\"Samples\")\n",
        "ax.set_ylabel(\"loc\")\n",
        "\n",
        "ax1.plot(mcmc_samples[\"scale\"])\n",
        "ax1.set_xlabel(\"Samples\")\n",
        "ax1.set_ylabel(\"scale\");"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Bayesian Logistic Regression, revisited"
      ],
      "metadata": {
        "id": "9fyyTkS3-9aI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import jax.numpy as jnp\n",
        "import blackjax\n",
        "\n",
        "from sklearn.datasets import make_biclusters\n",
        "\n",
        "\n",
        "plt.rcParams[\"axes.spines.right\"] = False\n",
        "plt.rcParams[\"axes.spines.top\"] = False\n",
        "plt.rcParams[\"figure.figsize\"] = (12, 8)\n",
        "\n",
        "seed = 0\n",
        "rng_key = jax.random.key(seed)\n",
        "\n",
        "# generate data\n",
        "num_points = 50\n",
        "X, rows, cols = make_biclusters(\n",
        "    (num_points, 2), 2, noise=0.6, random_state=314, minval=-3, maxval=3\n",
        ")\n",
        "y = rows[0] * 1.0  # y[i] = whether point i belongs to cluster 1\n",
        "\n",
        "# visualize data/labels\n",
        "colors = [\"tab:red\" if el else \"tab:blue\" for el in rows[0]]\n",
        "plt.scatter(*X.T, edgecolors=colors, c=\"none\")\n",
        "plt.xlabel(r\"$X_0$\")\n",
        "plt.ylabel(r\"$X_1$\");"
      ],
      "metadata": {
        "id": "clAXExbG_AEW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# set up likelihoods\n",
        "\n",
        "Phi = jnp.c_[jnp.ones(num_points)[:, None], X]\n",
        "N, M = Phi.shape\n",
        "\n",
        "\n",
        "def sigmoid(z):\n",
        "    return jnp.exp(z) / (1 + jnp.exp(z))\n",
        "\n",
        "\n",
        "def log_sigmoid(z):\n",
        "    return z - jnp.log(1 + jnp.exp(z))\n",
        "\n",
        "\n",
        "def logdensity_fn(w, alpha=1.0):\n",
        "    \"\"\"The log-probability density function of the posterior distribution of the model.\"\"\"\n",
        "    log_an = log_sigmoid(Phi @ w)\n",
        "    an = Phi @ w\n",
        "    log_likelihood_term = y * log_an + (1 - y) * jnp.log(1 - sigmoid(an))\n",
        "    prior_term = alpha * w @ w / 2\n",
        "\n",
        "    return -prior_term + log_likelihood_term.sum()\n",
        "\n",
        "\n",
        "# sample initial weights, w\n",
        "rng_key, init_key = jax.random.split(rng_key)\n",
        "\n",
        "w0 = jax.random.multivariate_normal(init_key, 0.1 + jnp.zeros(M), jnp.eye(M))\n",
        "rmh = blackjax.rmh(logdensity_fn, blackjax.mcmc.random_walk.normal(jnp.ones(M) * 0.05))\n",
        "initial_state = rmh.init(w0)\n",
        "\n",
        "# set up inference loop\n",
        "def inference_loop(rng_key, kernel, initial_state, num_samples):\n",
        "    @jax.jit\n",
        "    def one_step(state, rng_key):\n",
        "        state, _ = kernel(rng_key, state)\n",
        "        return state, state\n",
        "\n",
        "    keys = jax.random.split(rng_key, num_samples)\n",
        "    _, states = jax.lax.scan(one_step, initial_state, keys)\n",
        "\n",
        "    return states\n",
        "\n",
        "# perform inference and sample\n",
        "rng_key, sample_key = jax.random.split(rng_key)\n",
        "states = inference_loop(sample_key, rmh.step, initial_state, 5_000)"
      ],
      "metadata": {
        "id": "MxNSXAv6_Xbe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "burnin = 300\n",
        "\n",
        "fig, ax = plt.subplots(1, 3, figsize=(12, 2))\n",
        "for i, axi in enumerate(ax):\n",
        "    axi.plot(states.position[:, i])\n",
        "    axi.set_title(f\"$w_{i}$\")\n",
        "    axi.axvline(x=burnin, c=\"tab:red\")\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "do_74vBK_0vN"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}