Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning

• URL: http://arxiv.org/abs/2406.06348v2
• Date: Wed, 24 Jul 2024 16:13:45 GMT
• Title: Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning
• Authors: Ashka Shah, Adela DePavia, Nathaniel Hudson, Ian Foster, Rick Stevens,
• Abstract summary: Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to $104$ variables.
• Score: 0.742246975663779
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way -- without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure -- a set of learned or existing candidate hypotheses -- to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to ${10^4}$ variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces.

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