  We extend multi-way, multivariate ANOVA-type analysis to cases where one
covariate is the view, with features of each view coming from different,
high-dimensional domains. The different views are assumed to be connected by
having paired samples; this is a common setup in recent bioinformatics
experiments, of which we analyze metabolite profiles in different conditions
(disease vs. control and treatment vs. untreated) in different tissues (views).
We introduce a multi-way latent variable model for this new task, by extending
the generative model of Bayesian canonical correlation analysis (CCA) both to
take multi-way covariate information into account as population priors, and by
reducing the dimensionality by an integrated factor analysis that assumes the
metabolites to come in correlated groups.
