A distance covariance-based kernel for nonlinear causal clustering in heterogeneous populations

A distance covariance-based kernel for nonlinear causal clustering in heterogeneous populations

Abstract

We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and social sciences. To this end, we introduce a distance covariance-based kernel designed specifically to measure the similarity between the underlying nonlinear causal structures of different samples. Indeed, we prove that the corresponding feature map is a statistically consistent estimator of nonlinear independence structure, rendering the kernel itself a statistical test for the hypothesis that sets of samples come from different generating causal structures. Even stronger, we prove that the kernel space is isometric to the space of causal ancestral graphs, so that distance between samples in the kernel space is guaranteed to correspond to distance between their generating causal structures. This kernel thus enables us to perform clustering to identify the homogeneous subpopulations, for which we can then learn causal structures using existing methods. Though we focus on the theoretical aspects of the kernel, we also evaluate its performance on synthetic data and demonstrate its use on a real gene expression data set.

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Authors
  • Markham, Alex
  • Das, Richeek
  • Grosse-Wentrup, Moritz
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
1st conference on Causal Learning and Reasoning (CLeaR) 2022
Divisions
Neuroinformatics
Subjects
Kuenstliche Intelligenz
Event Location
Eureka, CA, USA
Event Type
Conference
Event Dates
11-13 Apr 2022
Series Name
Proceedings of Machine Learning Research
Publisher
PMLR
Page Range
pp. 542-558
Date
2022
Official URL
https://proceedings.mlr.press/v177/markham22a.html
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