Ilkka Huopaniemi, Helsinki University of Technology, Department of Information and Computer Science, Finland
Tommi Suvitaival, Helsinki University of Technology, Department of Information and Computer Science, Finland
Janne Nikkila, Helsinki University of Technology, Department of Information and Computer Science, Finland
Matej Oresic, VTT Technical Research Centre of Finland, Espoo, Finland
Samuel Kaski, Helsinki University of Technology, Department of Information and Computer Science, Finland

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Abstract

We present a Bayesian model for two-way ANOVA-type analysis of high-dimensional, small sample-size datasets with highly correlated groups of variables. Modern cellular measurement methods are a main application area; typically the task is differential analysis between diseased and healthy samples, complicated by additional covariates requiring a multi-way analysis. The main complication is the combination of high dimensionality and low sample size, which renders classical multivariate techniques useless. We introduce a hierarchical model which does dimensionality reduction by assuming that the input variables come in similarly-behaving groups, and performs an ANOVA-type decomposition for the set of reduced-dimensional latent variables. We apply the methods to study lipidomic profiles of a recent large-cohort human diabetes study.