Using Unlabeled Data to Discover Bivariate Causality with Deep Restricted Boltzmann Machines

Abstract

An important question in microbiology is whether treatment causes changes in gut flora, and whether it also affects metabolism. The reconstruction of causal relations purely from non-temporal observational data is challenging. We address the problem of causal inference in a bivariate case, where the joint distribution of two variables is observed. We consider, in particular, data on discrete domains. The state-of-the-art causal inference methods for continuous data suffer from high computational complexity. Some modern approaches are not suitable for categorical data, and others need to estimate and fix multiple hyper-parameters. In this contribution, we introduce a novel method of causal inference which is based on the widely used assumption that if X causes Y, then P(X) and P(Y|X) are independent. We propose to explore a semi-supervised approach where P(Y|X) and P(X) are estimated from labeled and unlabeled data respectively, whereas the marginal probability is estimated potentially from much more (cheap unlabeled) data than the conditional distribution. We validate the proposed method on the standard cause-effect pairs. We illustrate by experiments on several benchmarks of biological network reconstruction that the proposed approach is very competitive in terms of computational time and accuracy compared to the state-of-the-art methods. Finally, we apply the proposed method to an original medical task where we study whether drugs confound human metagenome.