{
"cells": [
{
"cell_type": "markdown",
"id": "d68537ba",
"metadata": {},
"source": [
"(BART_introduction)=\n",
"# Bayesian Additive Regression Trees: Introduction\n",
":::{post} Dec 21, 2021\n",
":tags: BART, non-parametric, regression \n",
":category: intermediate, explanation\n",
":author: Osvaldo Martin\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "7c087cca",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running on PyMC v4.3.0\n"
]
}
],
"source": [
"from pathlib import Path\n",
"\n",
"import arviz as az\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import pymc as pm\n",
"import pymc_bart as pmb\n",
"\n",
"print(f\"Running on PyMC v{pm.__version__}\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "25cf7b45",
"metadata": {},
"outputs": [],
"source": [
"RANDOM_SEED = 5781\n",
"np.random.seed(RANDOM_SEED)\n",
"az.style.use(\"arviz-darkgrid\")"
]
},
{
"cell_type": "markdown",
"id": "444df604",
"metadata": {},
"source": [
"## BART overview"
]
},
{
"cell_type": "markdown",
"id": "86f379df",
"metadata": {},
"source": [
"Bayesian additive regression trees (BART) is a non-parametric regression approach. If we have some covariates $X$ and we want to use them to model $Y$, a BART model (omitting the priors) can be represented as:\n",
"\n",
"$$Y = f(X) + \\epsilon$$\n",
"\n",
"where we use a sum of $m$ [regression trees](https://en.wikipedia.org/wiki/Decision_tree_learning) to model $f$, and $\\epsilon$ is some noise. In the most typical examples $\\epsilon$ is normally distributed, $\\mathcal{N}(0, \\sigma)$. So we can also write:\n",
"\n",
"$$Y \\sim \\mathcal{N}(\\mu=BART(X), \\sigma)$$\n",
"\n",
"In principle nothing restricts us to use a sum of trees to model other relationship. For example we may have:\n",
"\n",
"$$Y \\sim \\text{Poisson}(\\mu=BART(X))$$\n",
"\n",
"One of the reason BART is Bayesian is the use of priors over the regression trees. The priors are defined in such a way that they favor shallow trees with leaf values close to zero. A key idea is that a single BART-tree is not very good at fitting the data but when we sum many of these trees we get a good and flexible approximation."
]
},
{
"cell_type": "markdown",
"id": "e239c2c0",
"metadata": {},
"source": [
"## Coal mining with BART\n",
"\n",
"To better understand BART in practice we are going to use the oldie but goldie coal mining disaster dataset. One of the classic examples in PyMC. Instead of thinking this problem as a switch-point model with two Poisson distribution, as in the original PyMC example. We are going to think this problem as a non-parametric regression with a Poisson response (this is usually discussed in terms of [Poisson processes](https://en.wikipedia.org/wiki/Poisson_point_process) or [Cox processes](https://en.wikipedia.org/wiki/Cox_process), but we are OK without going into those technicalities). For a similar example but with Gaussian processes see [1](https://github.com/aloctavodia/BAP/blob/master/code/Chp7/07_Gaussian%20process.ipynb) or [2](https://research.cs.aalto.fi/pml/software/gpstuff/demo_lgcp.shtml). Because our data is just a single column with dates, we need to do some pre-processing. We are going to discretize the data, just as if we were building a histogram. We are going to use the centers of the bins as the variable $X$ and the counts per bin as the variable $Y$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "85bdba1b",
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" coal = np.loadtxt(Path(\"..\", \"data\", \"coal.csv\"))\n",
"except FileNotFoundError:\n",
" coal = np.loadtxt(pm.get_data(\"coal.csv\"))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5d1221b3",
"metadata": {},
"outputs": [],
"source": [
"# discretize data\n",
"years = int(coal.max() - coal.min())\n",
"bins = years // 4\n",
"hist, x_edges = np.histogram(coal, bins=bins)\n",
"# compute the location of the centers of the discretized data\n",
"x_centers = x_edges[:-1] + (x_edges[1] - x_edges[0]) / 2\n",
"# xdata needs to be 2D for BART\n",
"x_data = x_centers[:, None]\n",
"# express data as the rate number of disaster per year\n",
"y_data = hist / 4"
]
},
{
"cell_type": "markdown",
"id": "98e0da5c",
"metadata": {},
"source": [
"In PyMC a BART variable can be defined very similar to other random variables. One important difference is that we have to pass ours Xs and Ys to the BART variable. Here we are also making explicit that we are going to use a sum over 20 trees (`m=20`). Low number of trees like 20 could be good enough for simple models like this and could also work very good as a quick approximation for more complex models in particular during the iterative or explorative phase of modeling. In those cases once we have more certainty about the model we really like we can improve the approximation by increasing `m`, in the literature is common to find reports of good results with numbers like 50, 100 or 200."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "6ac663f0",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Multiprocess sampling (4 chains in 4 jobs)\n",
"PGBART: [μ_]\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"
\n",
" "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 20 seconds.\n"
]
}
],
"source": [
"with pm.Model() as model_coal:\n",
" μ_ = pmb.BART(\"μ_\", X=x_data, Y=y_data, m=20)\n",
" μ = pm.Deterministic(\"μ\", np.abs(μ_))\n",
" y_pred = pm.Poisson(\"y_pred\", mu=μ, observed=y_data)\n",
" idata_coal = pm.sample(random_seed=RANDOM_SEED)"
]
},
{
"cell_type": "markdown",
"id": "1e967bf5",
"metadata": {},
"source": [
"The white line in the following plot shows the median rate of accidents. The darker orange band represent the HDI 50% and the lighter one the 94%. We can see a rapid decrease of coal accidents between 1880 and 1900. Feel free to compare these results with those in the original {ref}`pymc:pymc_overview` example."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1c715dbe",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
"rates = idata_coal.posterior[\"μ\"]\n",
"rate_mean = idata_coal.posterior[\"μ\"].mean(dim=[\"draw\", \"chain\"])\n",
"ax.plot(x_centers, rate_mean, \"w\", lw=3)\n",
"az.plot_hdi(x_centers, rates, smooth=False)\n",
"az.plot_hdi(x_centers, rates, hdi_prob=0.5, smooth=False, plot_kwargs={\"alpha\": 0})\n",
"ax.plot(coal, np.zeros_like(coal) - 0.5, \"k|\")\n",
"ax.set_xlabel(\"years\")\n",
"ax.set_ylabel(\"rate\");"
]
},
{
"cell_type": "markdown",
"id": "81f778de",
"metadata": {},
"source": [
"In the previous plot the white line is the median over 4000 posterior draws, and each one of those posterior draws is a sum over `m=20` trees. \n",
"\n",
"\n",
"The following figure shows two samples from the posterior of $\\mu$. We can see that these functions are not smooth. This is fine and is a direct consequence of using regression trees. Trees can be seen as a way to represent stepwise functions, and a sum of stepwise functions is just another stepwise function. Thus, when using BART we just need to know that we are assuming that a stepwise function is a good enough approximation for our problem. In practice this is often the case because we sum over many trees, usually values like 50, 100 or 200. Additionally, we often average over the posterior distribution. All this makes the \"steps smoother\", even when we never really have an smooth function as for example with Gaussian processes (splines). A nice theoretical result, tells us that in the limit of $m \\to \\infty$ the BART prior converges to a [nowheredifferentiable](https://en.wikipedia.org/wiki/Weierstrass_function) Gaussian process.\n",
"\n",
"The following figure shows two samples of $\\mu$ from the posterior."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0c982c16",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.step(x_data, idata_coal.posterior[\"μ\"].sel(chain=0, draw=[3, 10]).T);"
]
},
{
"cell_type": "markdown",
"id": "8633b7b4",
"metadata": {},
"source": [
"The next figure shows 3 trees. As we can see these are very simple function and definitely not very good approximators by themselves. Inspecting individuals trees is generally not necessary when working with BART, we are showing them just so we can gain further intuition on the inner workins of BART."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "252054ff",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bart_trees = μ_.owner.op.all_trees\n",
"for i in [0, 1, 2]:\n",
" plt.step(x_data[:, 0], [bart_trees[0][i].predict(x) for x in x_data])"
]
},
{
"cell_type": "markdown",
"id": "c7d04e15",
"metadata": {},
"source": [
"## Biking with BART"
]
},
{
"cell_type": "markdown",
"id": "abf8c799-b89e-48dc-a1c9-8366325a530a",
"metadata": {},
"source": [
"To explore other features offered by BART in PyMC. We are now going to move on to a different example. In this example we have data about the number of bikes rental in a city, and we have chosen four covariates; the hour of the day, the temperature, the humidity and whether is a workingday or a weekend. This dataset is a subset of the [bike_sharing_dataset](http://archive.ics.uci.edu/ml/datasets/Bike+Sharing+Dataset)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "099f4c0e",
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" bikes = pd.read_csv(Path(\"..\", \"data\", \"bikes.csv\"))\n",
"except FileNotFoundError:\n",
" bikes = pd.read_csv(pm.get_data(\"bikes.csv\"))\n",
"\n",
"X = bikes[[\"hour\", \"temperature\", \"humidity\", \"workingday\"]]\n",
"Y = bikes[\"count\"]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "5f8410b2",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Multiprocess sampling (4 chains in 4 jobs)\n",
"CompoundStep\n",
">NUTS: [α]\n",
">PGBART: [μ]\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"
\n",
" "
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 85 seconds.\n"
]
}
],
"source": [
"with pm.Model() as model_bikes:\n",
" α = pm.Exponential(\"α\", 1 / 10)\n",
" μ = pmb.BART(\"μ\", X, Y)\n",
" y = pm.NegativeBinomial(\"y\", mu=np.abs(μ), alpha=α, observed=Y)\n",
" idata_bikes = pm.sample(random_seed=RANDOM_SEED)"
]
},
{
"cell_type": "markdown",
"id": "5daefd3e",
"metadata": {},
"source": [
"### Partial dependence plots"
]
},
{
"cell_type": "markdown",
"id": "99fd44df",
"metadata": {},
"source": [
"To help us interpret the results of our model we are going to use partial dependence plot. This is a type of plot that shows the marginal effect that one covariate has on the predicted variable. That is, what is the effect that a covariate $X_i$ has of $Y$ while we average over all the other covariates ($X_j, \\forall j \\not = i$). This type of plot are not exclusive of BART. But they are often used in the BART literature. PyMC-BART provides an utility function to make this plot from the inference data."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "9bb3955d-98d6-40b0-ab1c-10082459f72a",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/osvaldo/anaconda3/lib/python3.9/site-packages/arviz/plots/hdiplot.py:156: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
" hdi_data = hdi(y, hdi_prob=hdi_prob, circular=circular, multimodal=False, **hdi_kwargs)\n",
"/home/osvaldo/anaconda3/lib/python3.9/site-packages/pymc_bart/utils.py:266: FutureWarning: hdi currently interprets 2d data as (draw, shape) but this will change in a future release to (chain, draw) for coherence with other functions\n",
" hdi = az.hdi(nyi)\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmb.plot_dependence(μ, X=X, Y=Y, grid=(2, 2), var_discrete=[3]);"
]
},
{
"cell_type": "markdown",
"id": "3a86b72b",
"metadata": {},
"source": [
"From this plot we can see the main effect of each covariate on the predicted value. This is very useful we can recover complex relationship beyond monotonic increasing or decreasing effects. For example for the `hour` covariate we can see two peaks around 8 and and 17 hs and a minimum at midnight.\n",
"\n",
"When interpreting partial dependence plots we should be careful about the assumptions in this plot. First we are assuming variables are independent. For example when computing the effect of `hour` we have to marginalize the effect of `temperature` and this means that to compute the partial dependence value at `hour=0` we are including all observed values of temperature, and this may include temperatures that are actually not observed at midnight, given that lower temperatures are more likely than higher ones. We are seeing only averages, so if for a covariate half the values are positively associated with predicted variable and the other half negatively associated. The partial dependence plot will be flat as their contributions will cancel each other out. This is a problem that can be solved by using individual conditional expectation plots `pmb.plot_dependence(..., kind=\"ice\")`. Notice that all this assumptions are assumptions of the partial dependence plot, not of our model! In fact BART can easily accommodate interaction of variables Although the prior in BART regularizes high order interactions). For more on interpreting Machine Learning model you could check the \"Interpretable Machine Learning\" book {cite:p}`molnar2019`.\n",
"\n",
"Finally like with other regression methods we should be careful that the effects we are seeing on individual variables are conditional on the inclusion of the other variables. So for example, while `humidity` seems to be mostly flat, meaning that this covariate has an small effect of the number of used bikes. This could be the case because `humidity` and `temperature` are correlated to some extend and once we include `temperature` in our model `humidity` does not provide too much extra information. Try for example fitting the model again but this time with `humidity` as the single covariate and then fitting the model again with `hour` as a single covariate. You should see that the result for this single-variate models will very similar to the previous figure for the `hour` covariate, but less similar for the `humidity` covariate."
]
},
{
"cell_type": "markdown",
"id": "54e31c66",
"metadata": {},
"source": [
"### Variable importance\n",
"\n",
"As we saw in the previous section a partial dependence plot can visualize give us an idea of how much each covariable contributes to the predicted outcome. But BART itself leads to a simple heuristic to estimate variable importance. That is simple count how many times a variable is included in all the regression trees. The intuition is that if a variable is important they it should appears more often in the fitted trees that less important variables. While this heuristic seems to provide reasonable results in practice, there is not too much theory justifying this procedure, at least not yet.\n",
"\n",
"The following plot shows the relative importance in a scale from 0 to 1 (less to more importance) and the sum of the individual importance is 1. See that, at least in this case, the relative importance qualitative agrees with the partial dependence plot.\n",
"\n",
"Additionally, PyMC-BART provides a novel method to assess the variable importance. You can see an example in the bottom panel. On the x-axis we have the number of covariables and on the y-axis the square of the Pearson correlation coefficient between the predictions made for the full-model (all variables included) and the restricted-models, those with only a subset of the variables. The components are included following the relative variable importance order, as show in the top panel. Thus, in this example 1 component means `hour`, two components means `hour` and `temperature`, 3 components `hour`, `temperature`and `humidity`. Finally, four components means `hour`, `temperature`, `humidity`, `workingday`, i.e., the full model. Hence, from the next figure we can see that even a model with a single component, `hour`, is very close to the full model. Even more, the model with two components `hour`, and `temperature` is on average indistinguishable from the full model. The error bars represent the 94 \\% HDI from the posterior predictive distribution. It is important to notice that to compute these correlations we do not resample the models, instead the predictions of the restricted-models are approximated by *prunning* variables from the full-model."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "2bb3d9f8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmb.plot_variable_importance(idata_bikes, μ, X, samples=100);"
]
},
{
"cell_type": "markdown",
"id": "219cde48-b626-4325-afc0-2a2881fc5683",
"metadata": {},
"source": [
"## Authors\n",
"* Authored by Osvaldo Martin in Dec, 2021 ([pymc-examples#259](https://github.com/pymc-devs/pymc-examples/pull/259))\n",
"* Updated by Osvaldo Martin in May, 2022 ([pymc-examples#323](https://github.com/pymc-devs/pymc-examples/pull/323))\n",
"* Updated by Osvaldo Martin in Sep, 2022\n",
"* Updated by Osvaldo Martin in Nov, 2022"
]
},
{
"cell_type": "markdown",
"id": "3c184bc8",
"metadata": {},
"source": [
"## References\n",
"\n",
":::{bibliography}\n",
":filter: docname in docnames\n",
"\n",
"martin2021bayesian\n",
"quiroga2022bart\n",
":::"
]
},
{
"cell_type": "markdown",
"id": "2c557ed8",
"metadata": {},
"source": [
"## Watermark"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "608086f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Last updated: Thu Nov 03 2022\n",
"\n",
"Python implementation: CPython\n",
"Python version : 3.9.13\n",
"IPython version : 8.4.0\n",
"\n",
"pymc : 4.3.0\n",
"pymc_bart : 0.2.0\n",
"numpy : 1.23.0\n",
"pandas : 1.4.4\n",
"matplotlib: 3.5.2\n",
"arviz : 0.13.0\n",
"\n",
"Watermark: 2.3.0\n",
"\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -n -u -v -iv -w"
]
},
{
"cell_type": "markdown",
"id": "4b02674f-26ad-4c07-bf60-eb8edd1c520b",
"metadata": {},
"source": [
":::{include} ../page_footer.md\n",
":::"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.13"
},
"vscode": {
"interpreter": {
"hash": "d5f0cba85daacbebbd957da1105312a62c58952ca942f7218a10e4aa5f415a19"
}
}
},
"nbformat": 4,
"nbformat_minor": 5
}