Reduced rank regression models with latent variables in Bayesian functional data analysis

Abstract

In functional data analysis (FDA) it is of interest to generalize techniques of multivariate analysis like canonical correlation analysis or regression to functions which are often observed with noise. In the proposed Bayesian approach to FDA two tools are combined: (i) a special Demmler-Reinsch like basis of interpolation splines to represent functions parsimoniously and flexibly; (ii) latent variable models initially introduced for probabilistic principal components analysis or canonical correlation analysis of the corresponding coefficients. In this way partial curves and non-Gaussian measurement error schemes can be handled. Bayesian inference is based on a variational algorithm such that computations are straight forward and fast corresponding to an idea of FDA as a toolbox for explorative data analysis. The performance of the approach is illustrated with synthetic and real data sets.