Bounded Regression with Gaussian Process Projection

TL;DR

This paper introduces a novel Gaussian process projection method for bounded regression functions, ensuring predictions respect bounds with efficient computation and superior performance demonstrated through simulations and real data.

Contribution

It proposes a new projection approach for Gaussian processes that enforces bound constraints while maintaining computational efficiency and improved predictive performance.

Findings

The method guarantees predictions within bounds everywhere.

It maintains computational efficiency comparable to standard Gaussian processes.

Simulation results show superior performance over competitors.

Abstract

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian process is first imposed on the regression function whose posterior distribution is then projected onto the bounded space. The resulting projected measure is then used for inference. The projected sample path has closed form which facilitates efficient computations. In particular, our projection approach maintains a comparable computational efficiency with that of the original GP. The proposed method yield predictions that respects bound constraints everywhere, while allows varying bounds across the input domain. An extensive simulation study is carried out which demonstrates that the performance of our approach dominates that of the competitors. An application to real data set is also considered.