Gaussian Processes for the inference of partially known mechanistic models used for clinical trial data analysis

Abstract

Abstract: Gaussian Processes (GPs) generalize the multivariate normal distribution to the infinite dimensional case, enabling the definition of prior distributions over function spaces. As such, they constitute one of the workhorses of Bayesian Inference for regression, classification, or even black-box optimization tasks. GPs have been successfully applied to the prediction of treatment effect, for inferring covariate effects from longitudinal data, or to predict whether T cells receptors can recognize specified epitopes. In this talk, I will cover the basics about GPs, highlight several analogies with other statistical methods and mention some extensions to handle complex behaviors like heterogeneity or non-stationarity. Next, I will discuss how GPs can aid for inferring partially known mechanistic models, based on heterogeneous data. Such models could describe the dynamics of antibodies response, for instance. The idea is to augment our current knowledge of the dynamics with GPs to account for unknown behaviors, but in a nonparametric fashion, thus providing an alternative to the classical nonlinear mixed effect framework.