{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# R-Learner\n", "R-Learner provides a general framework for estimating causal effects using Machine Learning (ML) algorithms. \n", "\n", "The use of adaptive ML methods for causal inference is appealing because they can handle high-dimensinal data with minimal assumptions on the functional form. However, the inference might be tricky since ML methods trade off variance for bias, and thus might produce biased estimator for the treatment effect. \n", "Here we will briefly describe the theory behind R-Learner and its implementation in causallib.\n", "\n", "We formalize the problem in the potential outcome framework. \n", "\n", "$X_i$ denotes the individual features, $Y_i$ the observed outcome, and $A_i\\in \\{0, 1\\}$ is the treatment assignment. The potential outcome $\\{Y_i(0),Y_i(1)\\}$, corresponding to the outcome that we would have observed given the treatment $A_i$. We write the conditional response surface as $\\mu_{a}(x)=E[Y(a)|X=x]$, for $a\\in\\{0,1\\}$.\n", "\n", "We aim to estimate the Average Treatment Effect (ATE), \n", "$$\\tau = E[Y(1)-Y(0)]$$ \n", "and the Conditional Average Treatment Effect (CATE), \n", "$$\\tau(x)=E[Y(1)-Y(0)|X=x]$$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Semi-parametric setup\n", "Consider the partially linear form: \n", "$$ Y_i(a)=\\mu_{0}(X_i) +a\\tau(X_i)+\\varepsilon_i $$\n", "where $\\varepsilon_i$ is an error term, assuming zero conditional mean $E[\\varepsilon_i|X_i,A_i]=0$. \n", "\n", "We can write the conditional mean outcome as follows: \n", "$$ m(X_i)=E[Y_i|X=x]=\\mu_{0}(X_i) +e(X_i)\\tau(X_i)$$\n", "where $e(X_i)=Pr[A_i=1|X=x]$ is the propensity model.\n", "\n", "Given this setup, we can re-write the function of $\\tau(x)$:\n", "$$ Y_i-m(X_i)=[A_i-e(X_i)]\\tau(X_i)+\\varepsilon_i$$\n", "This decomposition was first introduced by [Robinson](https://www.jstor.org/stable/pdf/1912705.pdf?casa_token=95zyuy2cbqYAAAAA:XFOeNcCphsIkNDismjRHwPCp795ALdHwOACPDkc2f7xkDKwtilZglJmwp-UMuUVarf_J9B50LEkbDwjKvBJfrxfRgBuIQNllQ26X59xichd_9mhslLE) at 1988. [Chernozukov et al.](https://ifs.org.uk/uploads/cemmap/wps/cwp491616.pdf) developed the partially linear (and also the interactive) modelling through the concept of score function and momemt conditions to obtain an estimate of the ATE. Recently, [Nie & Wager](https://arxiv.org/pdf/1712.04912.pdf), utilized this decomposition to create a loss function (named as *R-loss*), that can be optimized in order to estimate the CATE. In addition, they presented error bound for heterogeneous treatment effect via non-parametric kernel regression.\n", "\n", "Note that by this construction we are allowing the relation between $X$ and $Y$ and $X$ and $A$ to be non-linear and complex, but still restricting the model estimating the effect to be additive and linear." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimating the effect\n", "Basically, R-Learner is a two-stages procedure:\n", "1. First, estimating the \"nuisance models\". In this context, nuisance means that we do not directly care about the correctness of our estimate of $e(X)$ and $m(X)$, as far as we get a good estimate for the causal effects.\n", " - treatment_model - regressing $A$ on $X$ in order to obtain an esimtate of $\\hat{e}(X)$\n", " - outcome_model - regressing $Y$ on $X$ in order to obtain an esimtate of $\\hat{m}(X)$\n", "2. Then, minimize the R-loss:\n", "$$ \\tau^*(\\cdot) = argmin_{\\tau}\\left\\{ E\\left[(Y_i-\\hat{m}(X_i)) - (A_i-\\hat{e}(X_i))\\tau(X_i) \\right] \\right\\}$$\n", "\n", "In principle this method is a regression of residuals, which has a long history in the statistics literature.\n", "The residuals simplify the effect estimation since most of the variance is already explained by the nuisance model, thus the effect model is left with a simpler modelling problem.\n", "Note that the covariates used for fitting the effect model in the second stage do not have to be the same set of covariates that is required to remove confounding. For example, they can be smaller set of factors we care for the most when examining how heterogeneous the effect is in these strata\n", "\n", "A common technique to avoid bias from overfitting is cross-fitting, where the predicted value of the nuisance models for the $i$-th data point is fitted using a subsample of the data that does not contain the $i$-th data point. For example, we can split the data into two folds. Using one fold for stage (1) and the second fold for stage (2), and then run the same procedure but with switched folds (i.e. fold two for stage (1) and fold one for stage (2))." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from collections import defaultdict\n", "import seaborn as sns\n", "sns.set_palette(\"deep\")\n", "%matplotlib inline\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "from sklearn.linear_model import LinearRegression, LogisticRegression, LassoCV\n", "from sklearn.ensemble import RandomForestRegressor\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.model_selection import GridSearchCV\n", "from sklearn.metrics import mean_squared_error\n", "\n", "\n", "from causallib.estimation import StratifiedStandardization, Standardization\n", "from causallib.estimation import RLearner" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation study for estimating the Average Treatment Effect (ATE)\n", "We are examining three kinds of simulations:\n", "1. SI1 - the response surface is relatively simple, but the treatment assigment is highly imbalanced. In addition, the effect is given as a step function, dependent on one covariate. \n", "2. SI3 - complex nonlinear, balanced groups. The response surface is nonlinear and the effect is heterogeneous, but the treatment assignment is fully-randomized, with probability $0.5$ to be in one of the groups.\n", "3. dml - complex response and treatment mechanism. The true individual effect is homogenous and was set to $\\tau=0.5$.\n", "\n", "Simulations SI1 & SI3 are based on the paper: [\"Supporting Information: Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning\"](), and Simulation dml appeared as an introductory example in [\"Double machine learning for treatment and causal parameters\"](https://ifs.org.uk/uploads/cemmap/wps/cwp491616.pdf). \n", "\n", "As a benchmark we are presenting the results of R-Learner, comparing to S-Learner (Standardization) and T-Learner (Stratified Standardization). \n", "Note that we are showing results with 100 simulations runs, which might take some time to run on your local computer. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def _generate_X(n, d, seed=0):\n", " rng = np.random.RandomState(seed)\n", " sigma = np.array([[0.7**(np.abs(i-j)) for i in range(d)]\n", " for j in range(d)])\n", " X = pd.DataFrame(rng.multivariate_normal(np.zeros(d), sigma, size=n))\n", " return X\n", " \n", "def generate_data_SI1(n=500, d=20, seed=0):\n", " '''\n", " Simulation SI1 - linear response and imbalanced treatment assignment\n", " '''\n", " rng = np.random.RandomState(seed)\n", " X = _generate_X(n, d, seed)\n", " a = pd.Series(rng.binomial(1, 0.02, n))\n", " \n", " beta = rng.uniform(-5, 5, size=(d,)) \n", " mu_0 = np.dot(X, beta) + 5 * np.array(X.iloc[:, 0]>0.5)\n", " mu_1 = mu_0 + 8 * np.array(X.iloc[:, 1]>0.1)\n", " tau = mu_1 - mu_0\n", " y = a * mu_1 + (1-a) * mu_0 + rng.normal(size=(n,))\n", " return {\"X\": X, \"a\": a, \"y\": y, \"tau\": tau, 'mu_0':mu_0, 'mu_1':mu_1}\n", "\n", "def generate_data_SI3(n=500, d=20, seed=0):\n", " \"\"\"\n", " Simulation SI3 - non-linear response and randomized treatment assignment with probability 0.5\n", " \"\"\"\n", " def _univariate_non_linear(x):\n", " return 2/(1+np.exp(-12*(x-0.5)))\n", " \n", " rng = np.random.RandomState(seed)\n", " X = _generate_X(n, d, seed)\n", " a = pd.Series(rng.binomial(1, 0.5, n))\n", " \n", " x1_nl, x2_nl = _univariate_non_linear(X.iloc[:,0]), _univariate_non_linear(X.iloc[:,1]) \n", " mu_0 = -0.5 * np.multiply(x1_nl, x2_nl)\n", " mu_1 = 0.5 * np.multiply(x1_nl, x2_nl)\n", " tau = mu_1 - mu_0\n", " y = a * mu_1 + (1-a) * mu_0 + rng.normal(size=(n,))\n", " return {\"X\": X, \"a\": a, \"y\": y, \"tau\": tau, 'mu_0':mu_0, 'mu_1':mu_1}\n", "\n", "def generate_data_dml(n=500, d=20, binary_treatment=True, seed=0): \n", " \"\"\"\n", " Simulation dml - complex response and treatment assignment with homogeneous effect\n", " \"\"\"\n", " from scipy.special import expit\n", " def m(x):\n", " return x.iloc[:,0] + 0.25 * expit(x.iloc[:, 2]) \n", "\n", " def g(x):\n", " return expit(x.iloc[:,0]) + 0.25 * x.iloc[:, 2]\n", "\n", " rng = np.random.RandomState(seed)\n", " err = rng.normal(0, 1, 2*n)\n", " eps, eta = err[:n], err[n:] \n", " tau = 0.5\n", " \n", " X = _generate_X(n, d, seed)\n", " M = m(X)\n", " a = 1*(pd.Series(M + eps) > 0.1) if binary_treatment else pd.Series(M + eps) \n", " \n", " mu_0 = g(X)\n", " mu_1 = tau + mu_0\n", " y = pd.Series(np.dot(tau, a) + mu_0 + eta) \n", " return {\"X\": X, \"a\": a, \"y\": y, \"tau\": tau, 'mu_0':mu_0, 'mu_1':mu_1}\n", "\n", "def simulation_runner(data_generating_func, n_repetitions=100):\n", " \"\"\"\n", " Generating results of estimated effect for all of the models\n", " \"\"\"\n", " results = list()\n", " for seed in range(n_repetitions):\n", " data = data_generating_func(seed)\n", " for model_name, model in models.items():\n", " model.fit(data['X'], data['a'], data['y'])\n", " # estimate Average Treatment Effect\n", " pop = model.estimate_population_outcome(data['X'], data['a'])\n", " effect = model.estimate_effect(pop.loc[1], pop.loc[0])['diff']\n", " results.append((effect, model_name))# , data['tau'].mean()\n", " results.append((np.mean(data['tau']), 'True_ATE'))\n", " df_results=pd.DataFrame(results,columns=['effect','method'])#, 'true_effect'])\n", " return df_results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Models\n", "We show only a small search of hyperparmeters, but in practice the search can be much more extensive, including also different ML algorithms for the outcome\\treatment model." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "# nuisance models\n", "treatment_model = LogisticRegression(max_iter=2000)\n", "outcome_model = GridSearchCV(RandomForestRegressor(), \n", " {'max_depth':[2,4,6]}, n_jobs=-1, cv=3)\n", "\n", "# causal models\n", "models = {\n", " 'R-Learner': RLearner(outcome_model=outcome_model, \n", " treatment_model=treatment_model, \n", " effect_model=LinearRegression(fit_intercept=False), \n", " effect_covariates=list(), # homogeneous effect\n", " n_splits=2, \n", " refit=False),\n", " 'S-Learner': Standardization(outcome_model),\n", " 'T-Learner': StratifiedStandardization(outcome_model),\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation SI1\n", "Simple response with imbalanced treatment assignment" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data_generating_func = lambda seed: generate_data_SI1(n=500, d=20, seed=seed)\n", "df_results = simulation_runner(data_generating_func, 100)\n", "\n", "# plot the estimated effects\n", "fig, ax = plt.subplots(ncols=1, figsize=(9,5))\n", "sns.boxplot(data=df_results.loc[df_results.method != 'True_ATE',:], \n", " y='effect', \n", " x='method', \n", " linewidth=0.8, \n", " ax=ax)\n", "ax.axhline(df_results.loc[df_results.method == 'True_ATE','effect'].mean(), \n", " color='black',\n", " ls='--', \n", " label='True ATE')\n", "ax.legend(fontsize=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be seen, both T-Learner and R-Learner achived an unbiased estimate, but T-Learner has greater variance. Recall that T-Learner estimates each response surface (treated/untreated) separately and without utilizing across-group information, which can reduce statistical power in such highly-imbalanced settings and increase the variance. In addition, S-Learner resulted in highly biased estimate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation SI3\n", "Randomized agginment with complex non-linear response and heterogenous effect" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data_generating_func = lambda seed: generate_data_SI3(n=300, d=20, seed=seed)\n", "df_results = simulation_runner(data_generating_func)\n", "\n", "# plot the estimated effects\n", "fig, ax = plt.subplots(ncols=2, figsize=(14,5))\n", "sns.kdeplot(data=df_results, x='effect', hue='method', ax=ax[0])\n", "sns.boxplot(data=df_results, y='effect', x='method', linewidth=0.8, ax=ax[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this simulation it is best to seperate the effect estimation problem into two problems of estimating the response surface of the treated and the untreated, since there is nothing to learn from the treatment assignment mechnism. T-Learner, which follows this exact strategy performs very well, but only slightly better than R-Learner. Note that these results were achieved even though we restricted the estimated effect of R-Learner to be homogeneous. On the other hand, S-Learner uses a single learner and assumes homogeneity as well, pools all of the data in order to learn that the responses of the groups are in fact quite different. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation dml" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data_generating_func = lambda seed: generate_data_dml(n=400, d=20, seed=seed)\n", "df_results = simulation_runner(data_generating_func)\n", "\n", "fig, ax = plt.subplots(ncols=2, figsize=(14,5))\n", "sns.kdeplot(data=df_results.loc[df_results.method != 'True_ATE',:], \n", " x='effect', hue='method', ax=ax[0])\n", "ax[0].axvline(df_results.loc[df_results.method == 'True_ATE','effect'].mean(), \n", " color='black',ls='--', label='True_ATE')\n", "sns.boxplot(data=df_results.loc[df_results.method != 'True_ATE',:], \n", " y='effect', x='method', linewidth=0.8, ax=ax[1])\n", "ax[1].axhline(df_results.loc[df_results.method == 'True_ATE','effect'].mean(), \n", " color='black',ls='--', label='True_ATE')\n", "ax[1].legend(['True_ATE']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this simulation, both the response surface and the treatment assignment mechanism are complex and non-linear. Naive implementation of S-Learner or T-Learner leads to biased estimated effect. The R-learner, which is characterized with doubly-robust property permitting the use of slowly converging nuisance models, achieves the lowest effect estimation error. In particular, this property requires that only the product of the approximation errors of the treatment and outcome nuisance models will be $n^{-1/2}$, in order to obtain a root-n estimate to the effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Computing the Conditional Average Treatment Effect (CATE)\n", "\n", "We present differences in the models based on the data of simulation SI1. We consider two types of models for R-Learner: \n", "\n", "(1) R-Leraner_hom: assuming homogenous effect, i.e., the model predicts the same individual effect for all units.\n", "\n", "(2) R-Learner_het: assuming that the effect is linearly dependent on the covariates (acting as effect-modifiers). " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [], "source": [ "# set nuisance models\n", "treatment_model = LogisticRegression(max_iter=4000, solver='liblinear',penalty='l1')\n", "outcome_model = LassoCV(max_iter=8000, cv=2)\n", "\n", "# causal model\n", "models = {\n", " 'R-Learner_het': RLearner(outcome_model=outcome_model, \n", " treatment_model=treatment_model,\n", " effect_model=LassoCV(max_iter=8000, cv=2, fit_intercept=False), \n", " effect_covariates=list(np.arange(1,20)), \n", " n_splits=2, \n", " refit=False),\n", " 'R-Learner_hom': RLearner(outcome_model=outcome_model,\n", " treatment_model=treatment_model,\n", " effect_model=LinearRegression(fit_intercept=False), \n", " effect_covariates=list(), \n", " n_splits=2, \n", " refit=False),\n", " 'S-Learner': Standardization(outcome_model),\n", " 'T-Learner': StratifiedStandardization(outcome_model),\n", "}\n", "\n", "poly = PolynomialFeatures(degree=2, include_bias=False)\n", "results = list()\n", "for n_sample in [400, 700, 1000, 1500, 2000, 3000, 4000]:\n", " for i in range(50):\n", " data = generate_data_SI1(n=n_sample, d=20, seed=i)\n", " data['X'] = pd.DataFrame(poly.fit_transform(data['X']))\n", " for model_name, model in models.items():\n", " model.fit(data['X'], data['a'], data['y'])\n", " ind_outcome = model.estimate_individual_outcome(data['X'], data['a'])\n", " effect = model.estimate_effect(ind_outcome.loc[:,1], ind_outcome.loc[:,0], \n", " agg='individual')['diff']\n", " mse = mean_squared_error(data['tau'], effect)\n", " results.append((mse, model_name, n_sample))\n", "df_results=pd.DataFrame(results,columns=['mse','method', 'n_sample'])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(ncols=2, figsize=(18,6))\n", "\n", "df_results.loc[:,'log(mse)'] = np.log(df_results.loc[:,'mse'])\n", "gdf = df_results.groupby(['method', 'n_sample']).mean().reset_index()\n", "gdf['log(mse)'] = np.log(gdf['mse'])\n", "sns.lineplot(data=gdf, x='n_sample', y='log(mse)', hue='method', marker='o', ax=ax[0])#, alpha=0.8) \n", "sns.boxplot(data=df_results, y='log(mse)', x='method', hue='n_sample', linewidth=0.8, ax=ax[1])\n", "ax[0].legend(title='models', fontsize=12, loc=1)\n", "ax[1].legend(title='n samples', fontsize=12, loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that for large sample size, R-Learner_het achieves the lowest effect estimation error. Introduction of heterogeneity increases the number of parameters to be estimated, leading to a large variance in the estimated effect (more apparent when the sample size is small). Therefore, it is important to be careful in choosing an effect_model, and to restrict its complexity in order to control the variance of the estimated effect.\n", "\n", "In addition, R-Learner_hom and S-Learner both assume homogeneity, converging to the same effect, but R-Learner_hom does so at a faster rate. T-Learner in this case achieves the poorest results, mainly because of the great variability in estimating the response surface of the treated with small samples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we present plots of the estimated effect vs. $X_2$. \n", "Recall that the effect is truly dependent on this variable, $\\tau(x)=8 \\cdot I_{X_2>0.1}$, where $I$ is an indicator function." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(ncols=3, figsize=(16,4),sharey=True)\n", "t_ind_out = models['T-Learner'].estimate_individual_outcome(data['X'], data['a'])\n", "effects = {'T-Learner': models['T-Learner'].estimate_effect(t_ind_out.loc[:,1], t_ind_out.loc[:,0], agg='individual')['diff'],\n", " 'R-learner_hom': models['R-Learner_hom'].estimate_individual_effect(data['X']),\n", " 'R-learner_het': models['R-Learner_het'].estimate_individual_effect(data['X'])\n", " }\n", "ax[0].set_ylabel('effect')\n", "for i, model in enumerate(effects):\n", " ax[i].scatter(data['X'].iloc[:,1], effects[model], label=model)\n", " ax[i].scatter(data['X'].iloc[:,1], data['tau'], label='true effect')\n", " ax[i].set_title(f'True and estimated effect vs. $X_2$\\nn=4,000')\n", " ax[i].set_xlabel('$X_2$')\n", " ax[i].legend(fontsize=12)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A great model for the estimated effect should capture the fact that the true individual effect is equals to $8$ when $X_2$ is greater than 0.1.\n", "\n", "As can be seen, T-Learner captured a positive trend, with $X_2$ increasing the estimated effect increasing as well. However, the variance is relatively large. On the other hand, R-Learner_het has captured the same trend in much more compelling way. Since the effect_model in R-Learner_het is a simple LinearRegression, it cannot perfectly estimate the non-linearity of the step-function. R-Learner_hom estimates a constant effect for all units, which is unable to capture any dependence on the features, resulted in an averaged effect." ] } ], "metadata": { "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": "3.7.10" } }, "nbformat": 4, "nbformat_minor": 4 }