Linearly constrained Gaussian processes

TL;DR

This paper introduces a method to incorporate known linear constraints into Gaussian processes by transforming the target function, ensuring constraints are always satisfied in predictions and samples.

Contribution

It proposes a novel transformation-based approach to explicitly embed linear constraints into Gaussian process models, with a constructive design procedure.

Findings

Successfully applied to simulated data

Validated on real-world datasets

Guarantees constraint satisfaction in predictions

Abstract

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.