Causal Discovery with Latent Confounding

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This field seeks causal graphs and effects from observed variables when unmeasured common causes can create misleading dependencies. Methods use graphical models such as maximal ancestral graphs, conditional-independence and inequality constraints, rank or cumulant structure, and score-based or structural-equation models; many rely on assumptions such as sparsity, linearity, or particular noise distributions. Interventions, differences across environments, and time-series variation can add identifying information, while benchmarks test graph recovery in synthetic and real-world settings, including cyclic systems and selection bias. A central challenge is that distinct causal structures can imply the same observed data, so researchers must determine what is identifiable under each assumption and how to scale discovery without costly interventions.

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Causal Discovery in Mixtures of Populations
Nov 13, 2023Bijan Mazaheri, Spencer Gordon, Yuval Rabani +1Latent Variable Models Causal Discovery
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 +1

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Causal Discovery in Mixtures of Populations

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+1

Latent Variable Models Causal Discovery Causal Identifiability Causal Discovery with Latent Confounding Causal Inference with Unobserved Confounding

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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.