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https://github.com/ArthurDanjou/ml_exercises.git
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add causal model notebook
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franzi
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exercises/causal_model.ipynb
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250
exercises/causal_model.ipynb
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "ethical-chinese",
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"metadata": {},
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"source": [
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"# Learning a causal model\n",
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"\n",
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"The following example is adapted from \"Elements of Causal Inference\" by Jonas Peters, Dominik Janzig, and Bernhard Schölkopf (2017).\n",
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"See also Jonas Peters great [4-part lecture series on causality](https://www.youtube.com/watch?v=zvrcyqcN9Wo)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "transsexual-moore",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn.linear_model import LinearRegression, LassoLars"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "canadian-problem",
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"metadata": {},
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"outputs": [],
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"source": [
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"def sample_data(seed=None, n=10000, data_drift=False, concept_drift=False):\n",
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" # generate a sample from the distribution entailed by the causal graph\n",
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" np.random.seed(seed)\n",
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" # C, A, K\n",
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" C = np.random.randn(n)\n",
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" A = 0.8*np.random.randn(n)\n",
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" K = A + 0.1*np.random.randn(n)\n",
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" # X with and without data drift\n",
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" if data_drift:\n",
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" X = C - 2*A + 2.0*np.random.randn(n)\n",
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" else:\n",
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" X = C - 2*A + 0.2*np.random.randn(n)\n",
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" # F \n",
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" F = 3*X + 0.8*np.random.randn(n)\n",
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" # D with and without concept drift\n",
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" if concept_drift:\n",
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" D = 2*X + 0.5*np.random.randn(n)\n",
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" else:\n",
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" D = -2*X + 0.5*np.random.randn(n)\n",
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" # G, Y \n",
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" G = D + 0.5*np.random.randn(n)\n",
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" Y = 2*K - D + 0.2*np.random.randn(n)\n",
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" # H with and without data drift\n",
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" if data_drift:\n",
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" H = 0.5*Y + 1.0*np.random.randn(n)\n",
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" else:\n",
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" H = 0.5*Y + 0.1*np.random.randn(n) \n",
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" # put all in a nice dataframe\n",
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" 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",
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" return df\n",
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"\n",
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"def test_model(input_vars, df_train, df_test):\n",
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" # fit model with given variables\n",
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" lm = LinearRegression().fit(df_train[input_vars], df_train[[\"Y\"]])\n",
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" # check model fit and coefficients\n",
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" # true coefficients would be all values on the edges multiplied from the path from X to Y\n",
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" 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"
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]
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},
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{
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"cell_type": "markdown",
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"id": "revised-millennium",
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"metadata": {},
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"source": [
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"## Train & evaluate the model"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "southwest-printing",
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"metadata": {},
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"outputs": [],
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"source": [
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"# generate train and test data with different random seeds\n",
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"df_train = sample_data(1)\n",
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"df_test = sample_data(2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "transparent-sacrifice",
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"metadata": {},
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"outputs": [],
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"source": [
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"# (1) missing relevant input feature K -> wrong coefficient for X\n",
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"test_model([\"X\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "colonial-wagner",
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"metadata": {},
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"outputs": [],
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"source": [
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"# (2) all the right input features -> correct coefficients\n",
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"test_model([\"X\", \"K\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "wireless-corner",
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"metadata": {},
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"outputs": [],
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"source": [
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"# (3) additional input feature D, which has a more direct influence on Y than X\n",
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"test_model([\"X\", \"K\", \"D\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "supposed-yugoslavia",
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"metadata": {},
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"outputs": [],
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"source": [
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"# (4) additional input feature H, which is dependent on (i.e. highly correlated with) Y\n",
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"test_model([\"X\", \"K\", \"H\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "welcome-appraisal",
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"metadata": {
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"lines_to_next_cell": 2
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},
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"outputs": [],
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"source": [
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"# (5) regularized model with all inputs -> chooses dependent variable H instead of causal influences\n",
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"input_vars = [c for c in df_train.columns if c != \"Y\"]\n",
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"lm = LassoLars(alpha=0.003).fit(df_train[input_vars], df_train[\"Y\"])\n",
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"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))]))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "collectible-hands",
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"metadata": {},
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"source": [
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"## Data & Concept Drifts"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "quiet-groove",
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"metadata": {},
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"outputs": [],
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"source": [
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"# generate test data with a data drift in X and H\n",
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"df_test = sample_data(2, data_drift=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "greatest-cliff",
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"metadata": {},
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"outputs": [],
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"source": [
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"# model (2): true relationship between X and Y -> test performance equally good\n",
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"test_model([\"X\", \"K\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "indoor-celebrity",
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"metadata": {},
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"outputs": [],
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"source": [
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"# model (4): variable dependent on but not causal of Y -> test performance a lot worse\n",
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"test_model([\"X\", \"K\", \"H\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "endless-detective",
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"metadata": {},
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"outputs": [],
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"source": [
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"# generate test data with a concept drift in D, i.e., on the way from X to Y\n",
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"df_test = sample_data(2, concept_drift=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "korean-penguin",
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"metadata": {},
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"outputs": [],
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"source": [
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"# model (2): causal relationship between X and Y changed -> test performance catastrophic\n",
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"test_model([\"X\", \"K\"], df_train, df_test)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "blessed-passenger",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"encoding": "# -*- coding: utf-8 -*-",
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"notebook_metadata_filter": "-all"
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},
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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