Related papers: Interpreting Unconditional Quantile Regression wit…

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug…

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…

Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables…

This paper deals with the problem of evaluating the causal effect using observational data in the presence of an unobserved exposure/ outcome variable, when cause-effect relationships between variables can be described as a directed acyclic…

Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these…

Despite their enormous predictive power, machine learning models are often unsuitable for applications in regulated industries such as finance, due to their limited capacity to provide explanations. While model-agnostic frameworks such as…

A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature…

Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if ?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that…

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…

When inferring the causal effect of one variable on another from correlational data, a common practice by professional researchers as well as lay decision makers is to control for some set of exogenous confounding variables. Choosing an…

Treatment effect heterogeneity is of a great concern when evaluating policy impact: "is the treatment Pareto-improving?", "what is the proportion of people who are better off under the treatment?", etc. However, even in the simple case of a…

Model explanations based on pure observational data cannot compute the effects of features reliably, due to their inability to estimate how each factor alteration could affect the rest. We argue that explanations should be based on the…

Credit assignment in reinforcement learning is the problem of measuring an action's influence on future rewards. In particular, this requires separating skill from luck, i.e. disentangling the effect of an action on rewards from that of…

We study policy counterfactuals that impose path restrictions on a policy instrument over a finite window. Under a sequential intervention design, we define two counterfactual objects, policy-peg impulse responses and policy-path effects,…

We propose a counterfactual Kaplan-Meier estimator that incorporates exogenous covariates and unobserved heterogeneity of unrestricted dimensionality in duration models with random censoring. Under some regularity conditions, we establish…

Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…

This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…

Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome's dependence structure need to be considered. We focus on the case of binary outcomes…