Existing identification results in proximal causal inference often focus on marginal interventional distributions using standard outcome or treatment bridge functions. These methods do not generally identify joint interventional distributions that contain all proxy variables that were used to define the corresponding bridge functions. In many applications, however, these joint interventional distributions are a natural target of interest. We introduce extended bridge functions and derive new identification results for joint interventional distributions that may retain all relevant proxy variables. We then apply these results to proximal identification algorithms, where interventional kernels naturally arise as intermediate objects, yielding a generalized framework based on kernel operations.
Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated a…
The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator. Such problems include analyses of path-specific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (po-calculus), a natural generalizati…
Proximal Mediation Analysis with Unmeasured Treatment-Induced Confounding
Center for Applied Statistics and School of Statistics, Renmin University of China（中国人民大学统计学院与应用统计中心）；Department of Biostatistics & Medical Informatics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物统计与医学信息学系）
Interventional effects have been proposed as a solution to the unidentifiability of natural (in)direct effects under mediator-outcome confounders affected by the exposure. Such confounders are an intrinsic characteristic of studies with time-varying exposures and mediators, yet the generalization of the interventional effect framework to the time-varying case has received little attention in the literature. We present an identification result for interventional effects in a general longitudinal data structure that allows flexibility in the specification of treatment-outcome, treatment-mediator…
We consider the problem of identifying intermediate variables (or mediators) that regulate the effect of a treatment on a response variable. While there has been significant research on this classical topic, little work has been done when the set of potential mediators is high-dimensional (HD). A further complication arises when these mediators are interrelated (with unknown dependencies). In particular, we assume that the causal structure of the treatment, the confounders, the potential mediators and the response is a (possibly unknown) directed acyclic graph (DAG). HD DAG models have previou…
Can Large Language Models Help Experimental Design for Causal Discovery?
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；Hong Kong Baptist University（香港浸会大学）；The University of Sydney（悉尼大学）；Carnegie Mellon University（卡内基梅隆大学）
Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be…
Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability distribution for the interventional distribution resulting from the action. In many cases an identifiability algorithm may return a complicated expression that contains variables that are in fact unnecessary. In practice this can lead to additional computational burden and increased bias or inefficiency of estimates when dealing with measurement error or missing dat…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）
Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the spa…
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more genera…
