Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume -, Issue -, Pages -Publisher
OXFORD UNIV PRESS
DOI: 10.1093/jrsssb/qkad071
Keywords
causal additive models; graphical models; nonlinear causal discovery; pervasive confounding; spectral deconfounding
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Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. In this article, we present a provably consistent method to estimate causal relationships in the nonlinear, pervasive confounding setting by utilizing additional structure among the confounders and considering both confounders and nonlinear effects explicitly.
Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical scenarios. Without additional assumptions about the unobserved variables, it is not possible to recover any causal relationships from observational data. Fortunately, in many applied settings, additional structure among the confounders can be expected. In particular, pervasive confounding is commonly encountered and has been utilised for consistent causal estimation in linear causal models. In this article, we present a provably consistent method to estimate causal relationships in the nonlinear, pervasive confounding setting. The core of our procedure relies on the ability to estimate the confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, prove its consistency in recovering a correct ordering of the DAG, and empirically compare it to previous approaches. We demonstrate improved performance on both simulated and real datasets by explicitly accounting for both confounders and nonlinear effects.
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