{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Model comparison\n", "\n", "To demonstrate the use of model comparison criteria in PyMC3, 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": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import pymc3 as pm\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn-darkgrid')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data include the observed treatment effects and associated standard deviations in the 8 schools." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "J = 8\n", "y = np.array([28, 8, -3, 7, -1, 1, 18, 12])\n", "sigma = np.array([15, 10, 16, 11, 9, 11, 10, 18])" ] }, { "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 (2 chains in 2 jobs)\n", "NUTS: [mu]\n", "100%|██████████| 1500/1500 [00:01<00:00, 1003.81it/s]\n" ] } ], "source": [ "with pm.Model() as pooled:\n", " mu = pm.Normal('mu', 0, sd=1e6)\n", " \n", " obs = pm.Normal('obs', mu, sd=sigma, observed=y)\n", " \n", " trace_p = pm.sample(1000)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(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 (2 chains in 2 jobs)\n", "NUTS: [tau_log__, mu, eta]\n", "100%|██████████| 1500/1500 [00:03<00:00, 484.03it/s]\n" ] } ], "source": [ "with pm.Model() as hierarchical:\n", " \n", " eta = pm.Normal('eta', 0, 1, shape=J)\n", " mu = pm.Normal('mu', 0, sd=1e6)\n", " tau = pm.HalfCauchy('tau', 5)\n", " \n", " theta = pm.Deterministic('theta', mu + tau*eta)\n", " \n", " obs = pm.Normal('obs', theta, sd=sigma, observed=y)\n", " \n", " trace_h = pm.sample(1000)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace_h, varnames=['mu']);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.forestplot(trace_h, varnames=['theta']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "61.120811331601089" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pooled_waic = pm.waic(trace_p, pooled)\n", " \n", "pooled_waic.WAIC" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "61.229456725964631" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hierarchical_waic = pm.waic(trace_h, hierarchical)\n", " \n", "hierarchical_waic.WAIC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyMC3 includes two convenience functions to help compare WAIC for different models. The first of this functions is `compare`, this one computes WAIC (or LOO) from a set of traces and models and returns a DataFrame." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "hierarchical.name = 'hierarchical'\n", "pooled.name = 'pooled'" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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WAICpWAICdWAICweightSEdSEwarning
pooled61.120.67012.2100
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" ], "text/plain": [ " WAIC pWAIC dWAIC weight SE dSE warning\n", "pooled 61.12 0.67 0 1 2.21 0 0\n", "hierarchical 61.23 0.94 0.11 0 2.01 0.27 1" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_comp_WAIC = pm.compare({hierarchical: trace_h, pooled: trace_p})\n", "df_comp_WAIC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have many columns so let check one by one the meaning of them:\n", "\n", "\n", "1. The first column clearly contains the values of WAIC. The DataFrame is always sorted from lowest to highest WAIC. The index reflects the order in which the models are passed to this function.\n", "\n", "2. The second column is the estimated effective number of parameters. In general, models with more parameters will be more flexible to fit data and at the same time could also lead to overfitting. Thus we can interpret pWAIC as a penalization term, intuitively we can also interpret it as measure of how flexible each model is in fitting the data. \n", "\n", "3. The third column is the relative difference between the value of WAIC for the top-ranked model and the value of WAIC for each model. For this reason we will always get a value of 0 for the first model.\n", "\n", "4. Sometimes when comparing models, we do not want to select the \"best\" model, instead we want to perform predictions by averaging along all the models (or at least several models). Ideally we would like to perform a weighted average, giving more weight to the model that seems to explain/predict the data better. There are many approaches to perform this task, one of them is to use Akaike weights based on the values of WAIC for each model. These weights can be loosely interpreted as the probability of each model (among the compared models) given the data. One caveat of this approach is that the weights are based on point estimates of WAIC (i.e. the uncertainty is ignored).\n", "\n", "5. The fifth column records the standard error for the WAIC computations. The standard error can be useful to assess the uncertainty of the WAIC estimates. Nevertheless, caution need to be taken because the estimation of the standard error assumes normality and hence could be problematic when the sample size is low.\n", "\n", "6. In the same way that we can compute the standard error for each value of WAIC, we can compute the standard error of the differences between two values of WAIC. Notice that both quantities are not necessarily the same, the reason is that the uncertainty about WAIC is correlated between models. This quantity is always 0 for the top-ranked model.\n", "\n", "7. Finally we have the last column named \"warning\". A value of 1 indicates that the computation of WAIC may not be reliable, this warning is based on an empirical determined cutoff value and need to be interpreted with caution. For more details you can read this [paper](https://arxiv.org/abs/1507.04544)." ] }, { "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 PyMC3)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.compareplot(df_comp_WAIC);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The empty circle represents the values of WAIC and the black error bars associated with them are the values of the standard deviation of WAIC. \n", "\n", "The value of the lowest WAIC is also indicated with a vertical dashed grey line to ease comparison with other WAIC values.\n", "\n", "The filled black dots are the in-sample deviance of each model, which for WAIC is 2 pWAIC from the corresponding WAIC value.\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 errobar indicating the standard error of the differences between the top-ranked WAIC and WAIC for each model." ] }, { "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, which are corrected using Pareto-smoothed importance sampling (PSIS) to provide an estimate of point-wise out-of-sample prediction accuracy." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "61.159472594603194" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pooled_loo = pm.loo(trace_p, pooled)\n", " \n", "pooled_loo.LOO" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/fonnescj/Repos/pymc3/pymc3/stats.py:293: UserWarning: Estimated shape parameter of Pareto distribution is\n", " greater than 0.7 for one or more samples.\n", " You should consider using a more robust model, this is because\n", " importance sampling is less likely to work well if the marginal\n", " posterior and LOO posterior are very different. This is more likely to\n", " happen with a non-robust model and highly influential observations.\n", " happen with a non-robust model and highly influential observations.\"\"\")\n" ] }, { "data": { "text/plain": [ "61.336245930247486" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hierarchical_loo = pm.loo(trace_h, hierarchical)\n", " \n", "hierarchical_loo.LOO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use `compare` with LOO." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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LOOpLOOdLOOweightSEdSEwarning
pooled61.160.69012.2100
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\n", "
" ], "text/plain": [ " LOO pLOO dLOO weight SE dSE warning\n", "pooled 61.16 0.69 0 1 2.21 0 0\n", "hierarchical 61.34 0.99 0.18 0 2.03 0.25 1" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_comp_LOO = pm.compare({hierarchical: trace_h, pooled: trace_p}, ic='LOO')\n", "df_comp_LOO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The columns return the equivalent values for LOO, notice that in this example we get two warnings. Also notice that the order of the models is not the same as the one for WAIC.\n", "\n", "We can also plot the results" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.compareplot(df_comp_LOO);" ] }, { "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, giving 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 WAIC and LOO.\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.](http://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)" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }