Non-colliding Gaussian Process Regressions

Abstract

Imposing constraints on models has been a way to incorporate prior information to develop more realistic models and/or compensate for the lack of data. In this thesis, we propose a way to impose a “non-colliding constraint” on Gaussian process regression when modelling multiple (unknown) functions at the same time. The non-colliding constraint prevents the situation where the predictions from different regressions intersect with each other. This is a desirable property when the physical process that we are trying to model exhibits a multi-layered structure such as in stratigraphy or when the underlying functions should not intersect, for example the highest, and lowest temperature of a given time period. We show that the non-colliding problem can be reformulated to modelling a sequence of Gaussian process regressions with inequality constraints. We then use a piecewise linear approximation approach proposed by López-Lopera et al. (2018) to achieve this. Through an extensive simulation study, we show that our method is able to produce more realistic models that reflect the prior information of no collisions, as well as smaller errors with less variability than the standard Gaussian process regression especially when the training set is small.