Robust Probabilistic Multivariate Calibration Model

In this paper we propose a robust probabilistic multivariate calibration (RPMC) model in an attempt to identify linear relationships between two sets of observed variables contaminated with outliers. Instead of the Gaussian assumptions that predominate in classical statistical models, RPMC is closely related with the multivariate Student's t-distribution over noises and latent variables. As a result, RPMC lowers the effect of outlying data points by regulating the thickness of the distribution tails. RPMC is essentially a robustified version of the supervised probabilistic principal component analysis (SPPCA) that recently emerged. We show that RPMC encompasses probabilistic PCA and SPPCA as limiting cases. We also derive an efficient EM algorithm for parameter estimation in RPMC. Based on the probabilistic description of latent variables, we present a procedure for the detection of outliers. The experimental results from both simulated examples and real life datasets show the effectiveness and robustness of the proposed approach.