Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning
<|reference_start|>Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning: 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.<|reference_end|>
@article{shah2024causal,
    title={Causal Discovery over High-Dimensional Structured Hypothesis Spaces with
  Causal Graph Partitioning},
    author={Ashka Shah, Adela DePavia, Nathaniel Hudson, Ian Foster, Rick Stevens},
    journal={arXiv preprint arXiv:2406.06348},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06348},
    primaryClass={cs.LG cs.DC stat.ME}
}