{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Thinning MCMC outputs\n", "\n", "This notebook illustrates how to use `pbnn.utils.misc.thinning_fn` for thinning a MCMC output." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import blackjax\n", "import flax.linen as nn\n", "import jax\n", "import jax.numpy as jnp\n", "import jax.random as jr\n", "import jax.scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from jax.flatten_util import ravel_pytree\n", "from matplotlib.gridspec import GridSpec\n", "\n", "from pbnn.mcmc.langevin import sgld\n", "from pbnn.utils.analytical_functions import gramacy_function\n", "from pbnn.utils.plot import plot_on_axis\n", "from pbnn.utils.misc import thinning_fn\n", "\n", "%load_ext watermark" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n" ] } ], "source": [ "n = 100\n", "noise_level = 0.1\n", "\n", "np.random.seed(0)\n", "X = 20 * np.random.rand(n, 1)\n", "X_test = np.linspace(0, 20, 200)[:, None]\n", "X, X_test = jnp.array(X), jnp.array(X_test)\n", "\n", "noise, noise_test = (\n", " np.random.randn(n, 1) * noise_level,\n", " np.random.randn(len(X_test), 1) * noise_level,\n", ")\n", "\n", "y = gramacy_function(X, noise)\n", "y_test = gramacy_function(X_test, noise_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the network, loglikelihood and logprior " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# define loglikelihood et logprior\n", "class MLP(nn.Module):\n", " \"\"\"Simple MLP.\"\"\"\n", "\n", " hidden_features: int\n", " out_features: int\n", "\n", " @nn.compact\n", " def __call__(self, x):\n", " x = nn.Dense(\n", " features=self.hidden_features,\n", " kernel_init=nn.initializers.normal(),\n", " bias_init=nn.initializers.normal(),\n", " )(x)\n", " x = nn.tanh(x)\n", " x = nn.Dense(\n", " features=self.hidden_features,\n", " kernel_init=nn.initializers.normal(),\n", " bias_init=nn.initializers.normal(),\n", " )(x)\n", " x = nn.tanh(x)\n", " x = nn.Dense(\n", " features=self.out_features,\n", " kernel_init=nn.initializers.normal(),\n", " bias_init=nn.initializers.normal(),\n", " )(x)\n", " return x\n", "\n", "\n", "network = MLP(hidden_features=50, out_features=1)\n", "\n", "\n", "def loglikelihood_fn(parameters, data, sig_noise: float = noise_level):\n", " \"\"\"Gaussian log-likelihood\"\"\"\n", " X, y = data\n", " return -jnp.sum(\n", " 0.5 * (y - network.apply({\"params\": parameters}, X)) ** 2 / sig_noise**2\n", " )\n", "\n", "\n", "def logprior_fn(parameters):\n", " \"\"\"Compute the value of the log-prior density function.\"\"\"\n", " flat_params, _ = ravel_pytree(parameters)\n", " return jnp.sum(stats.norm.logpdf(flat_params))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run the SGLD algorithm" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# set some hyperparameters\n", "step_size = 1e-6\n", "num_iterations = 100_000\n", "burnin = 80_000\n", "batch_size = 32\n", "\n", "# generate initial positions\n", "rng_key = jr.PRNGKey(0)\n", "keys = jr.split(rng_key)\n", "\n", "init_positions = network.init(keys[0], X)[\"params\"]\n", "\n", "# run SGLD\n", "positions, ravel_fn, predict_fn = sgld(\n", " X=X,\n", " y=y,\n", " loglikelihood_fn=loglikelihood_fn,\n", " logprior_fn=logprior_fn,\n", " init_positions=init_positions,\n", " batch_size=batch_size,\n", " step_size=step_size,\n", " num_iterations=num_iterations,\n", " rng_key=keys[1],\n", ")\n", "\n", "# remove burnin\n", "positions = jax.tree_util.tree_map(lambda xx: xx[burnin:], positions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Thinning\n", "\n", "The MCMC output is thinned by minimizing the energy distance using the function `thinning_fn`. Here, we thin the MCMC output of size 20000 into a subsample of size 2000." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# thin the MCMC output\n", "rpositions = ravel_fn(positions)\n", "idx = thinning_fn(rpositions, size=2000)\n", "\n", "# filter with the indices\n", "positions = jax.tree_util.tree_map(lambda xx: xx[idx], positions)\n", "\n", "# predict\n", "f_predictions = predict_fn(network, positions, X_test).squeeze()\n", "\n", "# generate the noisy predictions\n", "_, key = jr.split(keys[1])\n", "y_predictions = f_predictions + noise_level * jr.normal(\n", " key, shape=(len(f_predictions), 1)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot the prediction intervals" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(constrained_layout=True, figsize=(5, 4))\n", "gs = GridSpec(nrows=1, ncols=1, figure=fig)\n", "alpha = 0.05\n", "\n", "mean_prediction = jnp.median(y_predictions, axis=0)\n", "qlow = jnp.quantile(y_predictions, 0.5 * alpha, axis=0)\n", "qhigh = jnp.quantile(y_predictions, (1 - 0.5 * alpha), axis=0)\n", "\n", "ax = fig.add_subplot(gs[0])\n", "plot_on_axis(ax, X_test, y_test, mean_prediction, qlow, qhigh, title=f\"sgld\")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Author: Brian Staber\n", "\n", "Last updated: Tue Feb 27 2024\n", "\n", "Python implementation: CPython\n", "Python version : 3.11.7\n", "IPython version : 8.21.0\n", "\n", "blackjax : 1.1.0\n", "jax : 0.4.23\n", "matplotlib: 3.8.2\n", "flax : 0.8.0\n", "numpy : 1.26.3\n", "\n", "Watermark: 2.4.3\n", "\n" ] } ], "source": [ "%reload_ext watermark\n", "%watermark -n -u -v -iv -w -a 'Brian Staber'" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 2 }