Speaker: Luis Damiano, PhD Candidate, Department of Statistics, Iowa State University

Title: Automatic Relevance Determination for Gaussian Process Regression with Functional Inputs

Abstract: In the context of Gaussian process regression, it is common to treat functional inputs as vectors. The parameter space becomes prohibitively complex as the functional input resolution increases, which hinders automatic relevance determination. Generalizing work for time-varying inputs, we introduce the automatic dynamic relevance determination (ADRD) framework to enforce smoothness on the predictive relevance profile over the index space with only a limited number of parameters. Fully Bayesian estimation is carried out to identify relevant regions of the functional input space and validation is performed to benchmark against traditional vector-input model specifications. In a case study for surrogate modeling, we find that ADRD outperforms models with input dimension reduction via functional principal component analysis. Furthermore, the predictive power is comparable to high-dimensional models, in terms of both mean prediction and uncertainty, with 10 times fewer tuning parameters. Last, ADRD rules out erratic patterns associated with vector-input models.