From fdb3b1c2654aa0c94732bd794981f0b11fa25d1a Mon Sep 17 00:00:00 2001 From: franzi Date: Fri, 20 Aug 2021 11:47:53 +0200 Subject: [PATCH] add causal model notebook --- exercises/causal_model.ipynb | 250 +++++++++++++++++++++++++++++++++++ 1 file changed, 250 insertions(+) create mode 100644 exercises/causal_model.ipynb diff --git a/exercises/causal_model.ipynb b/exercises/causal_model.ipynb new file mode 100644 index 0000000..f48d96a --- /dev/null +++ b/exercises/causal_model.ipynb @@ -0,0 +1,250 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ethical-chinese", + "metadata": {}, + "source": [ + "# Learning a causal model\n", + "\n", + "The following example is adapted from \"Elements of Causal Inference\" by Jonas Peters, Dominik Janzig, and Bernhard Schölkopf (2017).\n", + "See also Jonas Peters great [4-part lecture series on causality](https://www.youtube.com/watch?v=zvrcyqcN9Wo)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "transsexual-moore", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.linear_model import LinearRegression, LassoLars" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "canadian-problem", + "metadata": {}, + "outputs": [], + "source": [ + "def sample_data(seed=None, n=10000, data_drift=False, concept_drift=False):\n", + " # generate a sample from the distribution entailed by the causal graph\n", + " np.random.seed(seed)\n", + " # C, A, K\n", + " C = np.random.randn(n)\n", + " A = 0.8*np.random.randn(n)\n", + " K = A + 0.1*np.random.randn(n)\n", + " # X with and without data drift\n", + " if data_drift:\n", + " X = C - 2*A + 2.0*np.random.randn(n)\n", + " else:\n", + " X = C - 2*A + 0.2*np.random.randn(n)\n", + " # F \n", + " F = 3*X + 0.8*np.random.randn(n)\n", + " # D with and without concept drift\n", + " if concept_drift:\n", + " D = 2*X + 0.5*np.random.randn(n)\n", + " else:\n", + " D = -2*X + 0.5*np.random.randn(n)\n", + " # G, Y \n", + " G = D + 0.5*np.random.randn(n)\n", + " Y = 2*K - D + 0.2*np.random.randn(n)\n", + " # H with and without data drift\n", + " if data_drift:\n", + " H = 0.5*Y + 1.0*np.random.randn(n)\n", + " else:\n", + " H = 0.5*Y + 0.1*np.random.randn(n) \n", + " # put all in a nice dataframe\n", + " df = pd.DataFrame(np.vstack([C, A, K, X, F, D, G, Y, H]).T, columns=[\"C\", \"A\", \"K\", \"X\", \"F\", \"D\", \"G\", \"Y\", \"H\"])\n", + " return df\n", + "\n", + "def test_model(input_vars, df_train, df_test):\n", + " # fit model with given variables\n", + " lm = LinearRegression().fit(df_train[input_vars], df_train[[\"Y\"]])\n", + " # check model fit and coefficients\n", + " # true coefficients would be all values on the edges multiplied from the path from X to Y\n", + " print(f\"R^2 (train): {lm.score(df_train[input_vars], df_train[['Y']]):0.3f}; (test): {lm.score(df_test[input_vars], df_test[['Y']]):0.3f} => Y ~ {lm.intercept_[0]:0.3f} + \" + \" + \".join([f\"{lm.coef_[0, i]:0.3f} * {input_vars[i]}\" for i in range(len(input_vars))]))\n" + ] + }, + { + "cell_type": "markdown", + "id": "revised-millennium", + "metadata": {}, + "source": [ + "## Train & evaluate the model" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "southwest-printing", + "metadata": {}, + "outputs": [], + "source": [ + "# generate train and test data with different random seeds\n", + "df_train = sample_data(1)\n", + "df_test = sample_data(2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "transparent-sacrifice", + "metadata": {}, + "outputs": [], + "source": [ + "# (1) missing relevant input feature K -> wrong coefficient for X\n", + "test_model([\"X\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "colonial-wagner", + "metadata": {}, + "outputs": [], + "source": [ + "# (2) all the right input features -> correct coefficients\n", + "test_model([\"X\", \"K\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "wireless-corner", + "metadata": {}, + "outputs": [], + "source": [ + "# (3) additional input feature D, which has a more direct influence on Y than X\n", + "test_model([\"X\", \"K\", \"D\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "supposed-yugoslavia", + "metadata": {}, + "outputs": [], + "source": [ + "# (4) additional input feature H, which is dependent on (i.e. highly correlated with) Y\n", + "test_model([\"X\", \"K\", \"H\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "welcome-appraisal", + "metadata": { + "lines_to_next_cell": 2 + }, + "outputs": [], + "source": [ + "# (5) regularized model with all inputs -> chooses dependent variable H instead of causal influences\n", + "input_vars = [c for c in df_train.columns if c != \"Y\"]\n", + "lm = LassoLars(alpha=0.003).fit(df_train[input_vars], df_train[\"Y\"])\n", + "print(f\"R^2 (train): {lm.score(df_train[input_vars], df_train['Y']):0.3f}; (test): {lm.score(df_test[input_vars], df_test['Y']):0.3f} => Y ~ {lm.intercept_:0.3f} + \" + \" + \".join([f\"{lm.coef_[i]:0.3f} * {input_vars[i]}\" for i in range(len(input_vars))]))" + ] + }, + { + "cell_type": "markdown", + "id": "collectible-hands", + "metadata": {}, + "source": [ + "## Data & Concept Drifts" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "quiet-groove", + "metadata": {}, + "outputs": [], + "source": [ + "# generate test data with a data drift in X and H\n", + "df_test = sample_data(2, data_drift=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "greatest-cliff", + "metadata": {}, + "outputs": [], + "source": [ + "# model (2): true relationship between X and Y -> test performance equally good\n", + "test_model([\"X\", \"K\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "indoor-celebrity", + "metadata": {}, + "outputs": [], + "source": [ + "# model (4): variable dependent on but not causal of Y -> test performance a lot worse\n", + "test_model([\"X\", \"K\", \"H\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "endless-detective", + "metadata": {}, + "outputs": [], + "source": [ + "# generate test data with a concept drift in D, i.e., on the way from X to Y\n", + "df_test = sample_data(2, concept_drift=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "korean-penguin", + "metadata": {}, + "outputs": [], + "source": [ + "# model (2): causal relationship between X and Y changed -> test performance catastrophic\n", + "test_model([\"X\", \"K\"], df_train, df_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "blessed-passenger", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "encoding": "# -*- coding: utf-8 -*-", + "notebook_metadata_filter": "-all" + }, + "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": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}