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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# GLM in PyMC3: Out-Of-Sample Predictions\n",
- "\n",
- "In this notebook I explore the [glm](https://docs.pymc.io/api/glm.html) module of [PyMC3](https://docs.pymc.io/). I am particularly interested in the model definition using [patsy](https://patsy.readthedocs.io/en/latest/) formulas, as it makes the model evaluation loop faster (easier to include features and/or interactions). There are many good resources on this subject, but most of them evaluate the model in-sample. For many applications we require doing predictions on out-of-sample data. This experiment was motivated by the discussion of the thread [\"Out of sample\" predictions with the GLM sub-module](https://discourse.pymc.io/t/out-of-sample-predictions-with-the-glm-sub-module/773) on the (great!) forum [discourse.pymc.io/](https://discourse.pymc.io/), thank you all for your input!\n",
- "\n",
- "**Resources**\n",
- "\n",
- "\n",
- "- [PyMC3 Docs: Example Notebooks](https://docs.pymc.io/nb_examples/index.html)\n",
- " \n",
- " - In particular check [GLM: Logistic Regression](https://docs.pymc.io/notebooks/GLM-logistic.html)\n",
- "\n",
- "- [Bambi](https://bambinos.github.io/bambi/), a more complete implementation of the GLM submodule which also allows for mixed-effects models.\n",
- "\n",
- "- [Bayesian Analysis with Python (Second edition) - Chapter 4](https://github.com/aloctavodia/BAP/blob/master/code/Chp4/04_Generalizing_linear_models.ipynb)\n",
- "- [Statistical Rethinking](https://xcelab.net/rm/statistical-rethinking/)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Prepare Notebook"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n"
- ]
- }
- ],
- "source": [
- "import matplotlib.pyplot as plt\n",
- "import numpy as np\n",
- "import pandas as pd\n",
- "import seaborn as sns\n",
- "\n",
- "sns.set_style(style=\"darkgrid\", rc={\"axes.facecolor\": \".9\", \"grid.color\": \".8\"})\n",
- "sns.set_palette(palette=\"deep\")\n",
- "sns_c = sns.color_palette(palette=\"deep\")\n",
- "\n",
- "import arviz as az\n",
- "import patsy\n",
- "import pymc3 as pm\n",
- "\n",
- "from pymc3 import glm\n",
- "\n",
- "plt.rcParams[\"figure.figsize\"] = [7, 6]\n",
- "plt.rcParams[\"figure.dpi\"] = 100"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Generate Sample Data\n",
- "\n",
- "We want to fit a logistic regression model where there is a multiplicative interaction between two numerical features."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
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