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Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis
Ronan Perry · Julius von Kügelgen · Bernhard Schölkopf

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #323

Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the sparse mechanism shift hypothesis which posits that distribution shifts occur due to a small number of changing causal conditionals. Motivated by this idea, we apply it to learning causal structure from heterogeneous environments, where i.i.d. data only allows for learning an equivalence class of graphs without restrictive assumptions. We propose the Mechanism Shift Score (MSS), a score-based approach amenable to various empirical estimators, which provably identifies the entire causal structure with high probability if the sparse mechanism shifts hypothesis holds. Empirically, we verify behavior predicted by the theory and compare multiple estimators and score functions to identify the best approaches in practice. Compared to other methods, we show how MSS bridges a gap by both being nonparametric as well as explicitly leveraging sparse changes.

Author Information

Ronan Perry (University of Washington)
Julius von Kügelgen (Max Planck Institute for Intelligent Systems Tübingen & University of Cambridge)
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

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