Noisy-OR Models with Latent Confounding

TL;DR

This paper investigates the identifiability of causal models with latent confounding using noisy-OR models, providing conditions for model identification and developing algorithms tested for accuracy and robustness.

Contribution

It extends identifiability results to noisy-OR causal models with latent confounding and negative influences, along with new learning algorithms.

Findings

Identification conditions for noisy-OR models with latent confounding.

Algorithms demonstrating accuracy, scalability, and robustness.

Extension of identifiability to models with negative influences.

Abstract

Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a `noisy-OR' parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness.