Bayesian Multi-Way Models for Data Translation in Computational Biology

The inference of differences between samples is a fundamental problem in computational biology and many other sciences. Hypothesis about a complex system can be studied via a controlled experiment. The design of the controlled experiment sets the conditions, or covariates, for the system in such a way that their effect on the system can be studied through independent measurements. When the number of measured variables is high and the variables are correlated, the assumptions of standard statistical methods are no longer valid. In this thesis, computational methods are presented to this problem and its follow-up problems.

A similar experiment done on different systems, such as multiple biological species, leads to multiple "views" of the experiment outcome, observed in different data spaces or domains. However, cross-domain experimentation brings uncertainty about the similarity of the systems and their outcomes. Thus, a new question emerges: which of the covariate effects generalize across the domains? In this thesis, novel computational methods are presented for the integration of data views, in order to detect weaker covariate effects and to generalize covariate effects to views with unobserved data.

Five main contributions to the inference of covariate effects are presented: (1) When the data are high-dimensional and collinear, the problem of false discovery is curbed by assuming a cluster structure on the observed variables and by handling the uncertainty with Bayesian methods. (2) Prior information about the measurement process can be used to further improve the inference of covariate effects for metabolomic experiments by modeling the multiple layers of uncertainty in the mass spectral data. (3-4) When the data come from multiple measurement sources on the same subjects - that is, from data views with co-occurring samples - it is unknown, whether the covariate effects generalize across the views and whether the outcome of a new intervention can be generalized to a view with no observed data on that intervention. These problems are shown to be possible to solve by assuming a shared generative process for the multiple data views. (5) When the data come from different domains with no co-occurring samples, the inference of between-domain dependencies is not possible in the same way as with co-occurring samples. It is shown that even in this situation, it is possible to identify covariate effects that generalize across the domains, when the experimental design at least weakly binds the domains together. Then, effects that generalize are identified by assuming a shared generative process for the covariate effects.