How do causal forests deal with overfitting?
To deal with overfitting, causal forests use an honesty condition, whereby a tree is honest, if for each training sample ( i) it only uses the response (Y ᵢ) to estimate the within-leaf treatment effect or to decide where to place the split, but not both ( Jacob, 2021 ).
What is the causal Forest approach and why is it useful?
What is nice about the causal forest approach, too, is that we could make this an actual variable in our data set and include that information, so it no longer becomes a “use an HTE algorithm or target people with neutral attitudes” scenario—we can do both by providing the causal forest an indicator for whether or not their attitudes are neutral.
How can I estimate the number of causal forests?
The grf package has a causal_forest function that can be used to estimate causal forests. Additional functions afterwards can estimate, for example, the average_treatment_effect (). See help (package='grf') for more options.
How reliable are the confidence intervals in causal forests?
The major selling point of causal forests is the reliability of the confidence intervals, for reasons previously discussed in the theoretical explanation of causal forests. Essentially, the asymptotic normality of the estimator should result in small confidence intervals.
How to create a causal forest?
What are the advantages of tree and forest based estimators?
How many sets of data are used in Jacob's cate survey?
What is the difference between a change in treatment and an intervention?
Why use honest trees?
What is the difference of conditional and cate?
What is Causal Effect?
See more
About this website
What are causal forests?
Causal forests are a causal inference learning method that are an extension of Random Forests. In random forests, the data is repeatedly split in order to minimize prediction error of an outcome variable.
How does causal forest work?
While a random forest is built from decision trees , a causal forest is built from causal trees, where the causal trees learn a low-dimensional representation of treatment effect heterogeneity . Importantly, the splitting criterion optimizes for finding splits associated with treatment effect heterogeneity.
What is treatment effect heterogeneity?
Heterogeneity of treatment effect (HTE) is the nonrandom, explainable variability in the direction and magnitude of treatment effects for individuals within a population.
What is conditional average treatment effect?
Heterogenous treatment effects If the average treatment effects are different, SUTVA is violated. A per-subgroup ATE is called a "conditional average treatment effect" (CATE), i.e. the ATE conditioned on membership in the subgroup. CATE can be used as an estimate if SUTVA does not hold.
What is causal tree?
In summary, the causal factor tree is an investigation/analysis tool that is used to display a logical hierarchy of all the causes leading to a given effect or consequence. When gaps in knowledge are encountered, the tree exposes the gap, but does not provide any means to resolve it; other tools are required.
What is causal inference in statistics?
Causal inference refers to an intellectual discipline that considers the assumptions, study designs, and estimation strategies that allow researchers to draw causal conclusions based on data.
What are treatment effects in research?
A 'treatment effect' is the average causal effect of a binary (0–1) variable on an outcome variable of scientific or policy interest.
What is homogeneous treatment effect?
A homogeneous treatment effects model. The magnitude and direction of the treatment effect is the same for all patients, regardless of any other patient characteristics. Models that allow the treatment effect to be different for different individuals are referred to as heterogeneous treatment effect models.
What is treatment effect in RCT?
To estimate a treatment effect in an RCT, the analysis has to be adjusted for the baseline value of the outcome variable. A proper adjustment is not achieved by performing a regular repeated measures analysis (method 2) or by the regular analysis of changes (method 3).
What is the average causal effect?
In this article, the authors review Rubin's definition of an average causal effect (ACE) as the average difference between potential outcomes under different treatments. The authors distinguish an ACE and a regression coefficient.
How is treatment effect measured?
CONTINUOUS MEASURES When a trial uses a continuous measure, such as blood pressure, the treatment effect is often calculated by measuring the difference in mean improvement in blood pressure between groups. In these cases (if the data are normally distributed), a t-test is commonly used.
What is the difference between ATE and ATT?
ATE is the average treatment effect, and ATT is the average treatment effect on the treated. The ATT is the effect of the treatment actually applied.
Causal forests: A tutorial in high-dimensional causal inference
IntroPotential outcomesAlgorithmSample splitRegularization + confoundingBART Causal inference: A missing data problem Potential employment Education Treated No job training Job training Treatment e ect
[1902.07409] Estimating Treatment Effects with Causal Forests: An ...
We apply causal forests to a dataset derived from the National Study of Learning Mindsets, and consider resulting practical and conceptual challenges. In particular, we discuss how causal forests use estimated propensity scores to be more robust to confounding, and how they handle data with clustered errors.
Using Causal Forests To Predict Treatment Heterogeneity: An Application ...
This article presents a step-by-step explanation for applied researchers regarding how the algorithm predicts treatment effects based on observables.
causal_forest: Causal forest in grf: Generalized Random Forests
Causal forest Description. Trains a causal forest that can be used to estimate conditional average treatment effects tau(X). When the treatment assignment W is binary and unconfounded, we have tau(X) = E[Y(1) - Y(0) | X = x], where Y(0) and Y(1) are potential outcomes corresponding to the two possible treatment states.
Using causal forests to assess heterogeneity in cost‐effectiveness ...
1 INTRODUCTION. The standard cost-effectiveness analysis (CEA) in health care settings, which compares the mean difference in health benefits over the mean difference in costs between alternative treatments, is increasingly being used to inform decisions on reimbursement and guidelines of pharmaceuticals and/or health care services in many jurisdictions across the world (Chalkidou et al., 2009 ...
What is the honest causal forest?
The honest causal forest (Athey & Imbens, 2016; Athey, Tibshirani, & Wager, 2018; Wager & Athey, 2018) is a random forest made up of honest causal trees, and the “random forest” part is fit just like any other random forest (e.g., resampling, considering a subset of predictors, averaging across many trees). Because of this, I will assume you know how decision trees and random forests work; I will focus on what makes the honest causal tree unique from a typical decision tree by answering two questions: What makes it causal? What makes it honest?
How to get the causal effect?
Under this framework, getting the true causal effect requires actual magic: We take our world, split it into two universes, have an individual in Universe 1 go through the treatment and that same person in Universe 2 go through a placebo, then compare the outcomes from Universes 1 and 2. This impossibility is what Holland (1986) referred to as “the fundamental problem of causal inference.”
What is trans_therm_pre?
The trans_therm_pre variable gives us a chance to compare a causal forest to the neutral or uncertrain targeting approach I discussed at the beginning of this post. This alternative strategy would involve finding, for instance, the people with attitudes that were higher than the 25th percentile but lower than the 75th percentile. What is nice about the causal forest approach, too, is that we could make this an actual variable in our data set and include that information, so it no longer becomes a “use an HTE algorithm or target people with neutral attitudes” scenario—we can do both by providing the causal forest an indicator for whether or not their attitudes are neutral. I code this below. I get the quantiles for trans_therm_pre, then I make a logical variable for if someone is in the middle 50% of the distribution, then I convert the logical vector to numeric by multiplying it by 1 and assign it to the data frame dat:
What is the goal of the Rubin causal model?
The goal is to estimate the causal effect for an individual: Y (Treatment) - Y (Control). Most papers I’ve read proposing, implementing, or reviewing algorithms that do this generally frame this problem within the Rubin causal model (a.k.a., potential outcomes model). This approach defines causality strictly: It is the value we would have observed if a person was in the treatment, minus what we would have observed if a person was in the control. There’s a problem here, since a person can only be in one condition at a time. If someone is assigned to the control condition, we never observe the outcome if they had been in the treatment condition (and vice versa). Note that this is why the “would have” language is used, which highlights that these outcomes are “potential.”
How to find the average treatment effect?
So what do we do? One solution is to get two large groups of people that are similar to one another, assign one of these groups to the treatment, the other to the control, and then compare the expected outcome ( e.g., mean response or probability of a behavior occurring) between the two groups. This gives us the average treatment effect (ATE)—the lift across all people in the sample. When I say that the two groups are “similar,” I mean that we assume miscellaneous characteristics about these people that could influence either (a) what treatment they experienced or (b) their potential outcomes Y (Treatment) and Y (Control) have been accounted for. The gold standard for doing this is conducting a randomized experiment, where people are chosen at random to be either in the control or treatment condition. Since I am only going to consider estimating HTEs within the realm of an experiment, I don’t discuss ensuring this assumption further.
How much lift did the half of the sample with the biggest predicted treatment effects yield?
From these results, we can see that including the half of the sample with the biggest predicted treatment effects yielded a 2.05 lift, including just those that had neutral attitudes gave us a lift of 0.89, and choosing half of the sample randomly gave us 0.25.
What is an unsupervised approach?
Unsupervised approaches generally take p number of variables and a user-input k number of groups, then maximize the variance between groups and/or minimize the variance within the k groups on these p variables. Other algorithms, like my favorite DBSCAN, use a non-parametric procedure to group points together that are nearby in p -dimensional space. Note that some measure of Y may or may not be present in the variables used for clustering.
Abstract
To estimate treatment heterogeneity in two randomized controlled trials of a youth summer jobs program, we implement Wager and Athey's (2015) causal forest algorithm. We provide a step-by-step explanation targeted at applied researchers of how the algorithm predicts treatment effects based on observables.
JEL Classification
C21 Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
lbuckley13 commented on May 15, 2018
I have the same question as you. The best answer that I've found was published by a group at Mt. Sinai Medical School using a neutral randomized controlled trial of a weight loss intervention in patients with type 2 diabetes mellitus.
swager commented on May 18, 2018
Also, as to the original question of looking for variables that are associated with treatment heterogeneity, I often try something like this:
jtibshirani commented on May 30, 2018
Concerning the OOB predictions, here's what I propose: by default, we should calculate OOB automatically during training, and return them as part of the forest object ( forest$oob_predictions = predict_oob (...) ).
Zaw5009 commented on Jun 25, 2018
Hi, I am looking to calculate ATEs (and their SEs) for predicted deciles based on predictions from a causal forest. A version of this is done in the Uplift package, but in that package 1) causal forests aren't used and 2) you have to bootstrap SEs.
Zaw5009 commented on Jul 5, 2018
I have not tried the bootstrapping approach, but this solves my problem. I can just plug in the values from the holdout group to obtain lift deciles and then calculate the ATEs and their accompanying SEs for each predicted lift decile. Thanks!
swager commented on Jul 6, 2018
Thanks a lot @markhwhiteii! We'll make sure this functionality is included in the next release.
tianshengwang commented on Jan 31, 2020
Also, as to the original question of looking for variables that are associated with treatment heterogeneity, I often try something like this:
What is the second objective of Causal Tree Learning?
The second key objective that a Causal Tree learning’s splitting criterion must incorporate is the expected accuracy of a CATE estimation made within a particular leaf. If leaves are not split in a way that cleanly separates groups of individuals with disparate outcomes, the accuracy of a resultant heterogeneous treatment effect estimation may significantly diminish.
How does decision tree learning work for causal inference?
The splitting step of decision tree learning for causal inference consists of defining a set of rules for splitting observed individuals into buckets by values of variables defining their characteristics . This step generally consists of an algorithm similar to that of decision tree learning, which also aims to split observed individuals into groups given the values of variables describing their characteristics. However, in the splitting step of decision tree learning for heterogeneous treatment effect estimation, an analyst is not interested in estimating a particular value. To aid in understanding, one can think of this splitting step as very similar to the subclassification strategy for CATE estimation as discussed in my previous blog post. While subclassification generally consists of splitting observed individuals by arbitrary characteristics, such as their decade of birth as shown in Figure 1, the splitting step of decision tree learning for causal inference optimizes a subclassification strategy to maximize the accuracy of a subsequent average treatment effect estimation.
What is overfitting in decision tree learning?
Another challenge Athey and Imbens encountered when trying to design a decision tree learning algorithm which could be applied to heterogeneous treatment effect estimation, is overfitting, a phenomenon that occurs when a calculated estimation does not extrapolate well to a general population. When sampled data is used as input in the splitting step of decision tree learning for causal inference, splits are made to optimize for the accuracy of estimated treatment effects within each leaf. If that same data is used in a subsequent estimation step, the accuracy of a resultant CATE estimation may not generalize well to data outside of an analyzed sample, which has not been included in the calculation of said optimal splits.
How do Athey and Imbens solve the overfitting problem?
Athey and Imbens resolve the overfitting problem by leveraging an estimation strategy known as honesty in the causal inference literature . At the beginning of a causal tree learning process the data measuring the characteristics and behaviors of observed individuals is separated into two subsamples, a splitting subsample and an estimating subsample.
What is Causal Tree Learning?
In this post, I will discuss Causal Tree Learning, a machine learning technique developed by the economists Susan Athey and Guido Imbens for automatically estimating heterogeneous treatment effects conditional on a large number of confounding variables . Causal Tree Learning leverages a machine learning algorithm known as decision tree learning to identify an optimal strategy for splitting observed individuals into groups to estimate heterogeneous treatment effects. Causal Tree Learning has been leveraged for a variety of use cases, most prominently to estimate the value of specific search advertising spots on Bing and for understanding the effects of different education policies on high school students of different backgrounds. For example, with Causal Tree Learning I could precisely identify estimated effects of my airline brand ads on individuals with particular characteristics described by their Past Behavior, Demographic Data, and Psychographic Data. The formulation of Causal Tree Learning by Athey and Imbens utilizes two foundational concepts in heterogeneous treatment effects and decision tree learning, which I will describe before explaining how the method can be used for exceptionally accurate causal effect estimation.
What is a splitting subsample?
The splitting subsample is used in the splitting step of causal inference with decision trees and, as previously described, is leveraged to build a causal tree.
What is the accuracy of a decision tree?
The accuracy of a decision tree refers to the frequency with which a decision tree estimation of a particular value is correct. Traditionally, decision trees are leveraged to estimate the value of a target variable, which is the quantity or class a decision tree attempts to predict.
What happens to out-of-sample cases in a tree?
Any future, out-of-sample cases (such as those used after deploying the model) will be dropped down the tree and assigned the predicted treatment effect for the node in which they end are placed.
What framework do authors use to modify the Conventional Cart?
In the previous two sections before this quotation, Modifying Conventional CART for Treatment Effects and Modifying the Honest Approach, the authors use the Rubin causal model/potential outcomes framework to derive an estimation for the treatment effect.
What is the criterion for splitting a tree?
The criterion for splitting is such that tree leafs are "big".
What is cross validated?
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
How to create a causal forest?
To create a causal forest from causal trees, it is necessary to estimate a weighting function and use the resulting weights to solve a local generalized method of moments (GMM) model to estimate the CATE. To deal with overfitting, causal forests use an honesty condition, whereby a tree is honest, if for each training sample ( i) it only uses the response (Y ᵢ) to estimate the within-leaf treatment effect or to decide where to place the split, but not both ( Jacob, 2021 ). Sample-splitting is used to create honest trees, where half the data is used to estimate the tree structure, a splitting subsample, and the other half is used to estimate the treatment effect in each leaf, an estimating subsample. The prediction of treatment effects is the difference in the average outcomes between the treated and the control observations of the estimating subsample in terminal leaves.
What are the advantages of tree and forest based estimators?
An advantage of tree and forest-based estimators like the causal forest, is the availability of interpretability tests such as Shapley (SHAP) values. The economist, Lloyd Shapley, won the Nobel Prize in economics for developing the concept for SHapley Additive exPlanations values, which are derived from cooperative game theory. For an introduction to this interpretability measure, I suggest this Medium post.
How many sets of data are used in Jacob's cate survey?
In Jacob’s CATE survey, twenty sets were run and the average CATE was reported to be around 1300. The causal forest built here will return CATE values between 1200 and 1400, a range which agrees with Jacob’s average CATE result.
What is the difference between a change in treatment and an intervention?
To show that a treatment causes an outcome , a change in treatment should cause a change in outcome (Y) while all other covariates are kept constant; this type of change in treatment is referred to as an intervention. The causal diagrams below for randomized controlled trials (RCT), show how the average treatment effect (ATE) is calculated as the effect of the treatment on the outcome, and the CATE is the effect of the treatment on the outcome, conditional on covariates.
Why use honest trees?
Using honest trees allows for asymptotic normality in the estimator used to estimate the variance of the estimates, which then allows for reliable confidence intervals of the parameters estimated ( Wager & Athey 2017 ). This is important, because to obtain an accurate estimate, the bias should asymptotically disappear, such that the confidence intervals are minimized. A necessary step, since it is not possible to actually observe treatment effects, therefore, traditional mean squared error cannot be used to evaluate performance and determine confidence intervals. Since the bias vanishes asymptotically, the causal forest estimates are consistent and asymptotically Gaussian, which means that together with the estimator for the asymptotic variance (honest trees), valid confidence intervals are ensured. In this tutorial, I make use of Microsoft Research’s EconML Python library to implement causal forests, the documentation provides an overview of the formal methodology behind their double machine learning implementation of causal forests.
What is the difference of conditional and cate?
The CATE or 𝜏 ( x) is the difference of conditional means: 𝜇₁ ( x) — 𝜇₀ ( x ). Image from Jacob (2021).
What is Causal Effect?
Causal effect is defined as the magnitude by which an outcome variable (Y) is changed by a unit-level interventional change in treatment , in other words, the difference between outcomes in the real world and the counterfactual world.