Incorporating Sum Constraints into Multitask Gaussian Processes

TL;DR

This paper introduces a method to incorporate sum constraints into multitask Gaussian processes, ensuring constraints are met with high precision and improving prediction accuracy over standard models.

Contribution

It presents a novel approach to embed linear and nonlinear sum constraints into Gaussian processes by conditioning the prior, enhancing model fidelity and accuracy.

Findings

Constraints are fulfilled with high precision.

The method improves overall prediction accuracy.

Applicable to both linear and nonlinear constraints.

Abstract

Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of the outputs to be constant. This is achieved by conditioning the prior distribution on the constraint fulfillment. The approach allows for both linear and nonlinear constraints. We demonstrate that the constraints are fulfilled with high precision and that the construction can improve the overall prediction accuracy as compared to the standard Gaussian process.