From 9d950f75219fe82b1058ac585cc3b10833a4d2b9 Mon Sep 17 00:00:00 2001 From: Juan Orduz Date: Fri, 25 Oct 2024 13:00:14 +0200 Subject: [PATCH] init --- Python/bayesian_cuped.ipynb | 518 ++++++++++++++++++++++++++++++++++++ 1 file changed, 518 insertions(+) create mode 100644 Python/bayesian_cuped.ipynb diff --git a/Python/bayesian_cuped.ipynb b/Python/bayesian_cuped.ipynb new file mode 100644 index 0000000..8b089a1 --- /dev/null +++ b/Python/bayesian_cuped.ipynb @@ -0,0 +1,518 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import arviz as az\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import numpyro\n", + "import numpyro.distributions as dist\n", + "import pandas as pd\n", + "from jax import random\n", + "from numpyro.infer import MCMC, NUTS\n", + "\n", + "numpyro.set_host_device_count(n=4)\n", + "\n", + "az.style.use(\"arviz-darkgrid\")\n", + "plt.rcParams[\"figure.figsize\"] = [12, 7]\n", + "plt.rcParams[\"figure.dpi\"] = 100\n", + "plt.rcParams[\"figure.facecolor\"] = \"white\"\n", + "\n", + "rng_key = random.PRNGKey(seed=42)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class dgp_cuped:\n", + " \"\"\"\n", + " Data Generating Process: CUPED\n", + " \"\"\"\n", + "\n", + " def __init__(self, alpha=5, beta=0, gamma=3, delta=2):\n", + " self.alpha = alpha\n", + " self.beta = beta\n", + " self.gamma = gamma\n", + " self.delta = delta\n", + "\n", + " def generate_data(self, N=100, seed=1):\n", + " np.random.seed(seed)\n", + "\n", + " # Individuals\n", + " i = range(1, N + 1)\n", + "\n", + " # Treatment status\n", + " d = np.random.binomial(1, 0.5, N)\n", + "\n", + " # Individual outcome pre-treatment\n", + " y0 = self.alpha + self.beta * d + np.random.normal(0, 1, N)\n", + " y1 = y0 + self.gamma + self.delta * d + np.random.normal(0, 1, N)\n", + "\n", + " # Generate the dataframe\n", + " df = pd.DataFrame({\"i\": i, \"ad_campaign\": d, \"revenue0\": y0, \"revenue1\": y1})\n", + "\n", + " return df" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " i ad_campaign revenue0 revenue1\n", + "0 1 0 5.315635 8.359304\n", + "1 2 1 2.977799 7.751485\n", + "2 3 0 4.693796 9.025253\n", + "3 4 0 5.827975 8.540667\n", + "4 5 0 5.230095 8.910165" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = dgp_cuped().generate_data()\n", + "df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.7914301325347406" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(\n", + " np.mean(df.loc[df.ad_campaign == True, \"revenue1\"])\n", + " - np.mean(df.loc[df.ad_campaign == False, \"revenue1\"])\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "ad_campaign = df.ad_campaign.to_numpy()\n", + "revenue0 = df.revenue0.to_numpy()\n", + "revenue1 = df.revenue1.to_numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def cuped_model(ad_campaign, revenue0, revenue1):\n", + " n_samples = len(ad_campaign)\n", + " intercept_target = numpyro.sample(\"intercept_target\", dist.Normal(0, 2))\n", + " theta = numpyro.sample(\"theta\", dist.Normal(0, 2))\n", + " sigma_theta = numpyro.sample(\"sigma_theta\", dist.HalfCauchy(2))\n", + "\n", + " mu_target = intercept_target + theta * revenue0\n", + "\n", + " with numpyro.plate(\"target_conditioning\", n_samples):\n", + " numpyro.sample(\n", + " \"revenue1_pred\", dist.Normal(mu_target, sigma_theta), obs=revenue1\n", + " )\n", + "\n", + " revenue_cuped = numpyro.deterministic(\n", + " \"revenue_cuped\", revenue1 - theta * (revenue0 - jnp.mean(revenue0))\n", + " )\n", + "\n", + " intercept_cuped = numpyro.sample(\"intercept_cuped\", dist.Normal(0, 2))\n", + " beta_cuped = numpyro.sample(\"beta_cuped\", dist.Normal(0, 3))\n", + "\n", + " with numpyro.plate(\"cuped_conditioning\", len(ad_campaign)):\n", + " numpyro.sample(\n", + " \"revenue_cuped_pred\",\n", + " dist.Normal(intercept_cuped + beta_cuped * ad_campaign, 1),\n", + " obs=revenue_cuped,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "cluster_target_conditioning\n", + "\n", + "target_conditioning\n", + "\n", + "\n", + "cluster_cuped_conditioning\n", + "\n", + "cuped_conditioning\n", + "\n", + "\n", + "\n", + "intercept_target\n", + "\n", + "intercept_target\n", + "\n", + "\n", + "\n", + "revenue1_pred\n", + "\n", + "revenue1_pred\n", + "\n", + "\n", + "\n", + "intercept_target->revenue1_pred\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "theta\n", + "\n", + "theta\n", + "\n", + "\n", + "\n", + "revenue_cuped\n", + "\n", + "revenue_cuped\n", + "\n", + "\n", + "\n", + "theta->revenue_cuped\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "theta->revenue1_pred\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "sigma_theta\n", + "\n", + "sigma_theta\n", + "\n", + "\n", + "\n", + "sigma_theta->revenue1_pred\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "intercept_cuped\n", + "\n", + "intercept_cuped\n", + "\n", + "\n", + "\n", + "revenue_cuped_pred\n", + "\n", + "revenue_cuped_pred\n", + "\n", + "\n", + "\n", + "intercept_cuped->revenue_cuped_pred\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "beta_cuped\n", + "\n", + "beta_cuped\n", + "\n", + "\n", + "\n", + "beta_cuped->revenue_cuped_pred\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "distribution_description_node\n", + "intercept_target ~ Normal\n", + "theta ~ Normal\n", + "sigma_theta ~ HalfCauchy\n", + "revenue1_pred ~ Normal\n", + "revenue_cuped ~ Deterministic\n", + "intercept_cuped ~ Normal\n", + "beta_cuped ~ Normal\n", + "revenue_cuped_pred ~ Normal\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "numpyro.render_model(\n", + " cuped_model,\n", + " model_args=(ad_campaign, revenue0, revenue1),\n", + " render_distributions=True,\n", + " render_params=True,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "6654e04b092b4071afaa739dd484eb10", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + " 0%| | 0/3500 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "az.plot_posterior(idata, var_names=[\"theta\"], ax=ax)\n", + "ax.set_title(r\"Posterior distribution of $\\theta$\");" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "az.plot_posterior(idata, var_names=[\"beta_cuped\"], ref_val=2.0, ax=ax)\n", + "ax.set_title(\"Posterior distribution of Revenue CUPED Effect Estimate\");" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "default", + "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": "3.11.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}