Revealing causality between heterogeneous data sources with deep restricted Boltzmann machines

Abstract

In a number of real life applications, scientists do not have access to temporal data, since budget for data acquisition is always limited. Here we challenge the problem of causal inference between groups of heterogeneous non-temporal observations obtained from multiple sources. We consider a family of probabilistic algorithms for causal inference based on an assumption that in case where X causes Y, P(X) and P(Y|X) are statistically independent. For a number of real world applications, deep learning methods were reported to achieve the most accurate empirical performance, what motivates us to use deep Boltzmann machines to approximate the marginal and conditional probabilities of heterogeneous observations as accurate as possible.We introduce a novel algorithm to infer causal relationships between blocks of variables. The proposed method was tested on a benchmark of multivariate cause-effect pairs. We show by our experiments that our method achieves the state-of-the-art empirical accuracy, and sometimes outperforms the state-of-the-art methods. An important part of our contribution is an application of the proposed algorithm to an original medical data set, where we explore relations between alimentary patters, human gut microbiome composition, and health status.