LETTER Communicated by Jo-Anne Ting Bayesian Sparse Partial Least Squares

Partial least squares (PLS) is a class of methods that makes use of a set of latent or unobserved variables to model the relation between (typically) two sets of input and output variables, respectively. Several flavors, de-pending on how the latent variables or components are computed, have been developed over the last years. In this letter, we propose a Bayesian formulation of PLS along with some extensions. In a nutshell, we provide sparsity at the input space level and an automatic estimation of the op-timal number of latent components. We follow the variational approach to infer the parameter distributions. We have successfully tested the pro-posed methods on a synthetic data benchmark and on electrocorticogram data associated with several motor outputs in monkeys.