FULLY BAYESIAN TENSOR-BASED REGRESSION

N-way (or multiway) Partial Least Squares (NPLS) regression is a successful algorithm for solving ill-conditioned and high-dimensional problems. However, the selection of the latent space dimensionality, when performed manually, becomes a critical issue in the presence of irrelevant, redundant and noisy information and can lead to overfitting, and when using cross-validation one can still not guarantee a good predictive performance. We propose a fully Bayesian N-way partial least squares regression (BNPLS) with an automatic relevance determination (ARD) prior on the factor matrices so that the number of latent components can be determined automatically without requiring specific assumptions. Using synthetic data, we compare the performance of BNPLS with conventional NPLS, standard partial least squared (PLS) and state-of-the-art higher-order PLS (HOPLS). Results show that BNPLS consistently achieves a better or comparable performance.