The goal of this paper is to design a causal inference method accounting for complex interactions between causal factors. The proposed method relies on a category theoretical reformulation of the definitions of dependent variables, independent variables and latent variables in terms of products and arrows in the category of unlabeled partitions. Throughout the paper, we demonstrate how the proposed method accounts for possible hidden variables, such as environmental variables or noise, and how it can be interpreted statistically in terms of $p$-values. This interpretation, from category theory to statistics, is implemented through a collection of propositions highlighting the functorial properties of ANOVA. We use these properties in combination with our category theoretical framework to provide solutions to causal inference problems with both sound algebraic and statistical properties. As an application, we show how the proposed method can be used to design a combinatorial genome-wide association algorithm for the field of genetics.
We present a method for estimating causal effects in time series data when fine-grained information about the outcome of interest is available. Specifically, we examine what we call the split-door setting, where the outcome variable can be split into two parts: one that is potentially affected by the cause being studied and another that is independent of it, with both parts sharing the same (unobserved) confounders. We show that under these conditions, the problem of identification reduces to that of testing for independence among observed variables, and present a method that uses this approac…
There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite populations, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the physical randomization of the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the average causal effect. Practically, however, these two views result in identical v…
We generalize the proximal g-formula of Miao, Geng, and Tchetgen Tchetgen (2018) for causal inference under unobserved confounding using proxy variables. Specifically, we show that the formula holds true for all causal models in a certain equivalence class, and this class contains models in which the total number of levels for the set of unobserved confounders can be arbitrarily larger than the number of levels of each proxy variable. Although straightforward to obtain, the result can be significant for applications. Simulations corroborate our formal arguments.
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Bernstein Center Freiburg, University of Freiburg（弗赖堡大学伯恩斯坦弗莱堡中心）
Pattern recognition in neuroimaging distinguishes between two types of models: encoding- and decoding models. This distinction is based on the insight that brain state features, that are found to be relevant in an experimental paradigm, carry a different meaning in encoding- than in decoding models. In this paper, we argue that this distinction is not sufficient: Relevant features in encoding- and decoding models carry a different meaning depending on whether they represent causal- or anti-causal relations. We provide a theoretical justification for this argument and conclude that causal infer…
The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a z…
In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are based on modelling of the treatment assignment mechanism and their doubly robust extensions have been difficult to motivate using formal Bayesian arguments, in principle, for likelihood-based inferences, the treatment assignment model can play no part in inferences concerning the expected outcomes if the models are assumed to be correctly specified. On the other…
University of Virginia（弗吉尼亚大学）；Global Infectious Disease Institute, University of Virginia（弗吉尼亚大学全球传染病研究所）
To mitigate the spread of COVID-19 pandemic, decision-makers and public authorities have announced various non-pharmaceutical policies. Analyzing the causal impact of these policies in reducing the spread of COVID-19 is important for future policy-making. The main challenge here is the existence of unobserved confounders (e.g., vigilance of residents). Besides, as the confounders may be time-varying during COVID-19 (e.g., vigilance of residents changes in the course of the pandemic), it is even more difficult to capture them. In this paper, we study the problem of assessing the causal effects …
University at Buffalo（布法罗大学）；University of Georgia（佐治亚大学）；Alibaba Group（阿里巴巴集团）；University of Virginia（弗吉尼亚大学）
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under t…
We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional `likelihood times prior' posterior inference; in addition, most methods rely on parametric and distributional assumptions, and presumed correct specification. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision…
We give a category-theoretic treatment of causal models that formalizes the syntax for causal reasoning over a directed acyclic graph (DAG) by associating a free Markov category with the DAG in a canonical way. This framework enables us to define and study important concepts in causal reasoning from an abstract and "purely causal" point of view, such as causal independence/separation, causal conditionals, and decomposition of intervention effects. Our results regarding these concepts abstract away from the details of the commonly adopted causal models such as (recursive) structural equation mo…
