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The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…

Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery.…

If $X,Y,Z$ denote sets of random variables, two different data sources may contain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue that causal inference can help inferring properties of the 'unobserved joint distributions'…

The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional…

We are interested in learning causal relationships between pairs of random variables, purely from observational data. To effectively address this task, the state-of-the-art relies on strong assumptions regarding the mechanisms mapping…

Learning a causal effect from observational data is not straightforward, as this is not possible without further assumptions. If hidden common causes between treatment $X$ and outcome $Y$ cannot be blocked by other measurements, one…

The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints :…

Ordinal variables, such as on the Likert scale, are common in applied research. Yet, existing methods for causal inference tend to target nominal or continuous data. When applied to ordinal data, this fails to account for the inherent…

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current…

Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such…

The traditional two-stage approach to causal inference first identifies a single causal model (or equivalence class of models), which is then used to answer causal queries. However, this neglects any epistemic model uncertainty. In…

This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…

This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we…

This paper concerns the assessment of the effects of actions from a combination of nonexperimental data and causal assumptions encoded in the form of a directed acyclic graph in which some variables are presumed to be unobserved. We provide…

We consider modeling a binary response variable together with a set of covariates for two groups under observational data. The grouping variable can be the confounding variable (the common cause of treatment and outcome), gender,…

The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various…

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…

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…