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This paper serves as a starting point for machine learning researchers, engineers and students who are interested in but not yet familiar with causal inference. We start by laying out an important set of assumptions that are collectively…

Machine Learning · Computer Science 2024-08-28 Daniel Jiwoong Im , Kyunghyun Cho

Causal discovery and causal effect estimation are two fundamental tasks in causal inference. While many methods have been developed for each task individually, statistical challenges arise when applying these methods jointly: estimating…

Methodology · Statistics 2024-08-21 Paula Gradu , Tijana Zrnic , Yixin Wang , Michael I. Jordan

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…

Machine Learning · Statistics 2015-05-20 David Lopez-Paz , Krikamol Muandet , Bernhard Schölkopf , Ilya Tolstikhin

This paper provides a nonparametric framework for causal inference with categorical outcomes under binary treatment and binary instrument settings. I decompose the observed joint probability of outcomes and treatment into marginal…

Econometrics · Economics 2025-11-11 Onil Boussim

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…

Artificial Intelligence · Computer Science 2019-11-01 Sam Witty , Alexander Lew , David Jensen , Vikash Mansinghka

We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero…

Methodology · Statistics 2022-02-01 Gianluca Detommaso , Michael Brückner , Philip Schulz , Victor Chernozhukov

This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and,…

Machine Learning · Statistics 2020-05-27 Virginia Aglietti , Xiaoyu Lu , Andrei Paleyes , Javier González

In recent years the search for a proper formal definition of actual causation -- i.e., the relation of cause-effect as it is instantiated in specific observations, rather than general causal relations -- has taken on impressive proportions.…

Artificial Intelligence · Computer Science 2015-03-04 Sander Beckers , Joost Vennekens

The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this paper, we consider the identifiability of state-based causal effects: how an intervention on a particular state of…

Machine Learning · Computer Science 2026-02-24 Yizuo Chen , Adnan Darwiche

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…

Machine Learning · Computer Science 2024-12-02 Yuhang Liu , Zhen Zhang , Dong Gong , Mingming Gong , Biwei Huang , Anton van den Hengel , Kun Zhang , Javen Qinfeng Shi

In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the…

Methodology · Statistics 2021-04-20 Zhichao Jiang , Peng Ding

An individual has been subjected to some exposure and has developed some outcome. Using data on similar individuals, we wish to evaluate, for this case, the probability that the outcome was in fact caused by the exposure. Even with the best…

Statistics Theory · Mathematics 2017-06-16 Rossella Murtas , Alexander Philip Dawid , Monica Musio

In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects…

Methodology · Statistics 2021-05-28 Iavor Bojinov , Ashesh Rambachan , Neil Shephard

A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism…

Methodology · Statistics 2020-09-24 Eric J Tchetgen Tchetgen , Andrew Ying , Yifan Cui , Xu Shi , Wang Miao

We propose a simple definition of an explanation for the outcome of a classifier based on concepts from causality. We compare it with previously proposed notions of explanation, and study their complexity. We conduct an experimental…

Machine Learning · Computer Science 2020-05-26 Leopoldo Bertossi , Jordan Li , Maximilian Schleich , Dan Suciu , Zografoula Vagena

Methods to identify cause-effect relationships currently mostly assume the variables to be scalar random variables. However, in many fields the objects of interest are vectors or groups of scalar variables. We present a new constraint-based…

Methodology · Statistics 2022-12-02 Jonas Wahl , Urmi Ninad , Jakob Runge

We develop methodology for causal inference in observational studies when using propensity score subclassification on data constructed with probabilistic record linkage techniques. We focus on scenarios where covariates and binary treatment…

Methodology · Statistics 2018-04-03 Joan Heck Wortman , Jerome P. Reiter

Sound educational policy recommendations require valid estimates of causal effects, but observational studies in physics education research sometimes have loosely specified causal hypotheses. The connections between the observational data…

Physics Education · Physics 2021-09-22 M. B. Weissman

In this paper we explore representations of temporal knowledge based upon the formalism of Causal Probabilistic Networks (CPNs). Two different ?continuous-time? representations are proposed. In the first, the CPN includes variables…

Artificial Intelligence · Computer Science 2013-04-08 Carlo Berzuini , Riccardo Bellazzi , Silvana Quaglini

The Causal Effect (CE) is a numerical measure of causal influence of variables on observed results. Despite being widely used in many areas, only preliminary attempts have been made to use CE as an attribution score in data management, to…

Databases · Computer Science 2025-09-23 Felipe Azua , Leopoldo Bertossi