diff --git a/gaussian_processes/pymc3.ipynb b/gaussian_processes/pymc3.ipynb new file mode 100644 index 0000000..825e9c9 --- /dev/null +++ b/gaussian_processes/pymc3.ipynb @@ -0,0 +1,243 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n" + ] + } + ], + "source": [ + "import pymc3 as pm\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from pymc3.gp.util import plot_gp_dist\n", + "\n", + "#https://docs.pymc.io/notebooks/GP-Marginal.html" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(5)\n", + "x = np.linspace(0, 10)[:, None]\n", + "y = np.sin(x)\n", + "\n", + "X = np.random.choice(x.flatten(), 7, replace=False)[:, None]\n", + "Y = np.sin(X)\n", + "\n", + "plt.plot(x, y)\n", + "plt.plot(X, Y, 'o')" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "Only 100 samples in chain.\n", + "Sequential sampling (1 chains in 1 job)\n", + "NUTS: [f*, ls]\n", + "100%|██████████| 150/150 [03:43<00:00, 1.05it/s]\n", + "The acceptance probability does not match the target. It is 0.9064175024104284, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "The chain reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n", + "Only one chain was sampled, this makes it impossible to run some convergence checks\n" + ] + } + ], + "source": [ + "with pm.Model() as model:\n", + " ls = pm.HalfCauchy('ls', beta=5)\n", + " \n", + " # zero mean\n", + " mean = pm.gp.mean.Constant(0)\n", + " # input_dim = the total columns of X\n", + " cov = pm.gp.cov.ExpQuad(input_dim=1, ls=ls)\n", + " \n", + " # The GP\n", + " gp = pm.gp.Marginal(mean , cov)\n", + " \n", + " # Observed data\n", + " f = gp.marginal_likelihood('y_obs', X, Y.flatten(), noise=0)\n", + " \n", + " # Conditional GP\n", + " f_star = gp.conditional('f*', x) \n", + " step = pm.NUTS()\n", + "\n", + " trace = pm.sample(chains=1, step=step, tune=50, draws=100)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1000/1000 [00:01<00:00, 891.40it/s]\n" + ] + } + ], + "source": [ + "with model:\n", + " pred_samples = pm.sample_ppc(trace, vars=[f_star, f], samples=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot the results\n", + "fig = plt.figure(figsize=(12,5))\n", + "ax = fig.gca()\n", + "\n", + "plot_gp_dist(ax, pred_samples[\"f*\"], x)\n", + "plt.plot(X, Y, 'o')" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n" + ] + } + ], + "source": [ + "with model:\n", + " prior_pc = pm.sample_prior_predictive(samples=100)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}