{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running on PyMC v4.4.0+213.g85ca9123f.dirty\n" ] } ], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pymc as pm\n", "\n", "print(f\"Running on PyMC v{pm.__version__}\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "az.style.use(\"arviz-darkgrid\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(model_comparison)=\n", "# Model comparison\n", "\n", "To demonstrate the use of model comparison criteria in PyMC, we implement the **8 schools** example from Section 5.5 of Gelman et al (2003), which attempts to infer the effects of coaching on SAT scores of students from 8 schools. Below, we fit a **pooled model**, which assumes a single fixed effect across all schools, and a **hierarchical model** that allows for a random effect that partially pools the data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data include the observed treatment effects (`y`) and associated standard deviations (`sigma`) in the 8 schools." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "y = np.array([28, 8, -3, 7, -1, 1, 18, 12])\n", "sigma = np.array([15, 10, 16, 11, 9, 11, 10, 18])\n", "J = len(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pooled model" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [mu]\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [12000/12000 00:02<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 3 seconds.\n" ] } ], "source": [ "with pm.Model() as pooled:\n", " # Latent pooled effect size\n", " mu = pm.Normal(\"mu\", 0, sigma=1e6)\n", "\n", " obs = pm.Normal(\"obs\", mu, sigma=sigma, observed=y)\n", "\n", " trace_p = pm.sample(2000)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "az.plot_trace(trace_p);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hierarchical model" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [eta, mu, tau]\n" ] }, { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
\n", " \n", " 100.00% [12000/12000 00:09<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 10 seconds.\n" ] } ], "source": [ "with pm.Model() as hierarchical:\n", " eta = pm.Normal(\"eta\", 0, 1, shape=J)\n", " # Hierarchical mean and SD\n", " mu = pm.Normal(\"mu\", 0, sigma=10)\n", " tau = pm.HalfNormal(\"tau\", 10)\n", "\n", " # Non-centered parameterization of random effect\n", " theta = pm.Deterministic(\"theta\", mu + tau * eta)\n", "\n", " obs = pm.Normal(\"obs\", theta, sigma=sigma, observed=y)\n", "\n", " trace_h = pm.sample(2000, target_accept=0.9)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "az.plot_forest(trace_h, var_names=\"theta\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Leave-one-out Cross-validation (LOO)\n", "\n", "LOO cross-validation is an estimate of the out-of-sample predictive fit. In cross-validation, the data are repeatedly partitioned into training and holdout sets, iteratively fitting the model with the former and evaluating the fit with the holdout data. Vehtari et al. (2016) introduced an efficient computation of LOO from MCMC samples (without the need for re-fitting the data). This approximation is based on importance sampling. The importance weights are stabilized using a method known as Pareto-smoothed importance sampling (PSIS).\n", "\n", "### Widely-applicable Information Criterion (WAIC)\n", "\n", "WAIC (Watanabe 2010) is a fully Bayesian criterion for estimating out-of-sample expectation, using the computed log pointwise posterior predictive density (LPPD) and correcting for the effective number of parameters to adjust for overfitting.\n", "\n", "By default ArviZ uses LOO, but WAIC is also available.\n", "\n", "### Model log-likelihood\n", "\n", "In order to compute LOO and WAIC, ArviZ needs access to the model elemwise loglikelihood for every posterior sample. We can add it via {func}`~pymc.compute_log_likelihood`. Alternatively we can pass `idata_kwargs={\"log_likelihood\": True}` to {func}`~pymc.sample` to have it computed automatically at the end of sampling." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with pooled:\n", " pm.compute_log_likelihood(trace_p)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Computed from 8000 posterior samples and 8 observations log-likelihood matrix.\n", "\n", " Estimate SE\n", "elpd_loo -30.55 1.10\n", "p_loo 0.67 -\n", "------\n", "\n", "Pareto k diagnostic values:\n", " Count Pct.\n", "(-Inf, 0.5] (good) 8 100.0%\n", " (0.5, 0.7] (ok) 0 0.0%\n", " (0.7, 1] (bad) 0 0.0%\n", " (1, Inf) (very bad) 0 0.0%" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pooled_loo = az.loo(trace_p)\n", "\n", "pooled_loo" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with hierarchical:\n", " pm.compute_log_likelihood(trace_h)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/ricardo/miniconda3/envs/pymc/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n", " warnings.warn(\n" ] }, { "data": { "text/plain": [ "Computed from 8000 posterior samples and 8 observations log-likelihood matrix.\n", "\n", " Estimate SE\n", "elpd_loo -30.82 1.07\n", "p_loo 1.17 -\n", "\n", "There has been a warning during the calculation. Please check the results.\n", "------\n", "\n", "Pareto k diagnostic values:\n", " Count Pct.\n", "(-Inf, 0.5] (good) 1 12.5%\n", " (0.5, 0.7] (ok) 6 75.0%\n", " (0.7, 1] (bad) 1 12.5%\n", " (1, Inf) (very bad) 0 0.0%" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hierarchical_loo = az.loo(trace_h)\n", "\n", "hierarchical_loo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ArviZ includes two convenience functions to help compare LOO for different models. The first of these functions is `compare`, which computes LOO (or WAIC) from a set of traces and models and returns a DataFrame." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/ricardo/miniconda3/envs/pymc/lib/python3.10/site-packages/arviz/stats/stats.py:802: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n", " warnings.warn(\n" ] }, { "data": { "text/html": [ "
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rankelpd_loop_looelpd_diffweightsedsewarningscale
pooled0-30.5541720.6704580.0000001.01.1027050.000000Falselog
hierarchical1-30.8218141.1674350.2676410.01.0707270.239078Truelog
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" ], "text/plain": [ " rank elpd_loo p_loo elpd_diff weight se \\\n", "pooled 0 -30.554172 0.670458 0.000000 1.0 1.102705 \n", "hierarchical 1 -30.821814 1.167435 0.267641 0.0 1.070727 \n", "\n", " dse warning scale \n", "pooled 0.000000 False log \n", "hierarchical 0.239078 True log " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_comp_loo = az.compare({\"hierarchical\": trace_h, \"pooled\": trace_p})\n", "df_comp_loo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have many columns, so let's check out their meaning one by one:\n", "\n", "\n", "0. The index is the names of the models taken from the keys of the dictionary passed to `compare(.)`.\n", "\n", "1. **rank**, the ranking of the models starting from 0 (best model) to the number of models.\n", "\n", "2. **loo**, the values of LOO (or WAIC). The DataFrame is always sorted from best LOO/WAIC to worst. \n", "\n", "3. **p_loo**, the value of the penalization term. We can roughly think of this value as the estimated effective number of parameters (but do not take that too seriously).\n", "\n", "4. **d_loo**, the relative difference between the value of LOO/WAIC for the top-ranked model and the value of LOO/WAIC for each model. For this reason we will always get a value of 0 for the first model.\n", "\n", "5. **weight**, the weights assigned to each model. These weights can be loosely interpreted as the probability of each model being true (among the compared models) given the data.\n", "\n", "6. **se**, the standard error for the LOO/WAIC computations. The standard error can be useful to assess the uncertainty of the LOO/WAIC estimates. By default these errors are computed using stacking.\n", "\n", "7. **dse**, the standard errors of the difference between two values of LOO/WAIC. The same way that we can compute the standard error for each value of LOO/WAIC, we can compute the standard error of the differences between two values of LOO/WAIC. Notice that both quantities are not necessarily the same, the reason is that the uncertainty about LOO/WAIC is correlated between models. This quantity is always 0 for the top-ranked model.\n", "\n", "8. **warning**, If `True` the computation of LOO/WAIC may not be reliable.\n", "\n", "9. **loo_scale**, the scale of the reported values. The default is the log scale as previously mentioned. Other options are deviance -- this is the log-score multiplied by -2 (this reverts the order: a lower LOO/WAIC will be better) -- and negative-log -- this is the log-score multiplied by -1 (as with the deviance scale, a lower value is better)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second convenience function takes the output of `compare` and produces a summary plot in the style of the one used in the book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath (check also [this port](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3) of the examples in the book to PyMC)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "az.plot_compare(df_comp_loo, insample_dev=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The empty circle represents the values of LOO and the black error bars associated with them are the values of the standard deviation of LOO. \n", "\n", "The value of the highest LOO, i.e the best estimated model, is also indicated with a vertical dashed grey line to ease comparison with other LOO values.\n", "\n", "For all models except the top-ranked one we also get a triangle indicating the value of the difference of WAIC between that model and the top model and a grey error bar indicating the standard error of the differences between the top-ranked WAIC and WAIC for each model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpretation\n", "\n", "Though we might expect the hierarchical model to outperform a complete pooling model, there is little to choose between the models in this case, given that both models gives very similar values of the information criteria. This is more clearly appreciated when we take into account the uncertainty (in terms of standard errors) of LOO and WAIC.\n", "\n", "## Reference\n", "\n", "[Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6), 997–1016.](https://doi.org/10.1007/s11222-013-9416-2)\n", "\n", "[Vehtari, A, Gelman, A, Gabry, J. (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing](http://link.springer.com/article/10.1007/s11222-016-9696-4)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last updated: Thu Dec 08 2022\n", "\n", "Python implementation: CPython\n", "Python version : 3.10.8\n", "IPython version : 8.3.0\n", "\n", "xarray : 2022.6.0\n", "pytensor: 2.8.10\n", "\n", "pymc : 4.4.0+213.g85ca9123f.dirty\n", "arviz : 0.13.0\n", "numpy : 1.22.3\n", "matplotlib: 3.5.2\n", "\n", "Watermark: 2.3.1\n", "\n" ] } ], "source": [ "%load_ext watermark\n", "\n", "%watermark -n -u -v -iv -w -p xarray,pytensor" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "interpreter": { "hash": "baf205d70af30bf8b721a304f5a44beb31bf8af014f6b7340f1a7ae004926653" }, "kernelspec": { "display_name": "pymc", "language": "python", "name": "pymc" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }