Nov 13, 2023 · cs.LGJ/K move · Enter open · S save
Bijan Mazaheri, Spencer Gordon, Yuval Rabani, Leonard Schulman
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, USA · Fragment Data Technologies, San Francisco, California, USA · Department of Computer Science, Hebrew Univeristy of Jerusalem, Jerusalem, Israel · Computing and Mathmematical Sciences, California Institute of Technology, Pasadena, California, USA
Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a ``source'' which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.