diff --git a/blackjax/types.py b/blackjax/types.py index 7fee30540..d9a12b77d 100644 --- a/blackjax/types.py +++ b/blackjax/types.py @@ -9,4 +9,4 @@ # Once recursive typing is fully supported (https://github.com/python/mypy/issues/731), we can uncomment the line below. # PyTree = Union[Array, Iterable["PyTree"], Mapping[Any, "PyTree"]] -PRNGKey = Array +PRNGKey = jnp.ndarray diff --git a/notebooks/LogisticRegression.ipynb b/notebooks/LogisticRegression.ipynb new file mode 100644 index 000000000..a2a919e2f --- /dev/null +++ b/notebooks/LogisticRegression.ipynb @@ -0,0 +1,416 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "411b1c7b", + "metadata": {}, + "source": [ + "# Bayesian Logistic Regression\n", + "\n", + "In this notebook we demonstrate the use of the random walk Rosenbluth-Metropolis-Hasting algorithm on a simple logistic regression." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5dd85020", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import jax.random as random\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.datasets import make_biclusters\n", + "\n", + "import blackjax.rmh as rmh" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b5dcae54", + "metadata": {}, + "outputs": [], + "source": [ + "%config InlineBackend.figure_format = \"retina\"\n", + "plt.rcParams[\"axes.spines.right\"] = False\n", + "plt.rcParams[\"axes.spines.top\"] = False\n", + "plt.rcParams[\"figure.figsize\"] = (12, 8)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8c2348de", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Python implementation: CPython\n", + "Python version : 3.9.5\n", + "IPython version : 7.25.0\n", + "\n", + "jax : 0.2.26\n", + "jaxlib : 0.1.75\n", + "blackjax: 0.3.0\n", + "\n", + "Compiler : GCC 11.1.0\n", + "OS : Linux\n", + "Release : 5.12.12-zen1-1-zen\n", + "Machine : x86_64\n", + "Processor : \n", + "CPU cores : 8\n", + "Architecture: 64bit\n", + "\n" + ] + } + ], + "source": [ + "%load_ext watermark\n", + "%watermark -d -m -v -p jax,jaxlib,blackjax" + ] + }, + { + "cell_type": "markdown", + "id": "8d4de9e9", + "metadata": {}, + "source": [ + "## The data" + ] + }, + { + "cell_type": "markdown", + "id": "af5721c9", + "metadata": {}, + "source": [ + "We create two clusters of points using [scikit-learn's `make_bicluster` function](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_biclusters.html?highlight=bicluster%20data#sklearn.datasets.make_biclusters)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "21d667fe", + "metadata": {}, + "outputs": [], + "source": [ + "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" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "3f605888", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 480, + "width": 720 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "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\"$X_1$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8a11bbaa", + "metadata": {}, + "source": [ + "## The model" + ] + }, + { + "cell_type": "markdown", + "id": "c8767311", + "metadata": {}, + "source": [ + "We use a simple logistic regression model to infer to which cluster each of the points belongs. We note $y$ a binary variable that indicates whether a point belongs to the first cluster :\n", + "\n", + "$$\n", + "y \\sim \\operatorname{Bernoulli}(p)\n", + "$$\n", + "\n", + "The probability $p$ to belong to the first cluster commes from a logistic regression:\n", + "\n", + "$$\n", + "p = \\operatorname{logistic}(\\Phi\\,\\boldsymbol{w})\n", + "$$\n", + "\n", + "where $w$ is a vector of weights whose priors are a normal prior centered on 0:\n", + "\n", + "$$\n", + "\\boldsymbol{w} \\sim \\operatorname{Normal}(0, \\sigma)\n", + "$$\n", + "\n", + "And $\\Phi$ is the matrix that contains the data, so each row $\\Phi_{i,:}$ is the vector $\\left[1, X_0^i, X_1^i\\right]$" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f498cb13", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" + ] + } + ], + "source": [ + "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 logprob_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()" + ] + }, + { + "cell_type": "markdown", + "id": "3456f9ae", + "metadata": {}, + "source": [ + "## Posterior sampling\n", + "\n", + "We use `blackjax`'s Random Walk RMH kernel to sample from the posterior distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "e98bff54", + "metadata": {}, + "outputs": [], + "source": [ + "rng_key = random.PRNGKey(314)\n", + "\n", + "w0 = random.multivariate_normal(rng_key, 0.1 + jnp.zeros(M), jnp.eye(M))\n", + "initial_state = rmh.new_state(w0, logprob_fn)\n", + "mcmc_kernel = rmh.kernel(logprob_fn, sigma=jnp.ones(M) * 0.7)\n", + "mcmc_kernel = jax.jit(mcmc_kernel)" + ] + }, + { + "cell_type": "markdown", + "id": "b7d6c95d", + "metadata": {}, + "source": [ + "Since `blackjax` does not provide an inference loop we need to implement one ourselves:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "147888ca", + "metadata": {}, + "outputs": [], + "source": [ + "def inference_loop(rng_key, kernel, initial_state, num_samples):\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" + ] + }, + { + "cell_type": "markdown", + "id": "427bac07", + "metadata": {}, + "source": [ + "We can now run the inference:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "e7465b52", + "metadata": {}, + "outputs": [], + "source": [ + "_, rng_key = random.split(rng_key)\n", + "states = inference_loop(rng_key, mcmc_kernel, initial_state, 5_000)" + ] + }, + { + "cell_type": "markdown", + "id": "550be73b", + "metadata": {}, + "source": [ + "And display the trace:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "5edc2447", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 154, + "width": 709 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "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()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "865acf20", + "metadata": {}, + "outputs": [], + "source": [ + "chains = states.position[burnin:, :]\n", + "nsamp, _ = chains.shape" + ] + }, + { + "cell_type": "markdown", + "id": "cf120386", + "metadata": {}, + "source": [ + "### Predictive distribution\n", + "\n", + "Having infered the posterior distribution of the regression's coefficients we can compute the probability to belong to the first cluster at each position $(X_0, X_1)$." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "286ab4f8", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a meshgrid\n", + "xmin, ymin = X.min(axis=0) - 0.1\n", + "xmax, ymax = X.max(axis=0) + 0.1\n", + "step = 0.1\n", + "Xspace = jnp.mgrid[xmin:xmax:step, ymin:ymax:step]\n", + "_, nx, ny = Xspace.shape\n", + "\n", + "# Compute the average probability to belong to the first cluster at each point on the meshgrid\n", + "Phispace = jnp.concatenate([jnp.ones((1, nx, ny)), Xspace])\n", + "Z_mcmc = sigmoid(jnp.einsum(\"mij,sm->sij\", Phispace, chains))\n", + "Z_mcmc = Z_mcmc.mean(axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d14b079d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 480, + "width": 712 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.contourf(*Xspace, Z_mcmc)\n", + "plt.scatter(*X.T, c=colors)\n", + "plt.xlabel(r\"$X_0$\")\n", + "plt.ylabel(r\"$X_1$\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "blackjax-dev", + "language": "python", + "name": "blackjax-dev" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}