Revealing causality between heterogeneous data sources with deep restricted Boltzmann machines

Nataliya Sokolovska, Karine Clément, Jean-Daniel Zucker

Abstract: Highlights • Inferring causal relations between blocks of heterogeneous observations is challenging but possible. • A causal direction can be inferred from estimated marginal and conditional probabilities of random variables from a data set. • Conditional and marginal probability distributions can be estimated from data using deep restricted Boltzmann machines. • Distance correlation is used as the independence measure. 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. Previous article in issue Next article in issue