A QUBO Model for Gaussian Process Variance Reduction

TL;DR

This paper introduces a novel QUBO model for selecting measurement locations in Gaussian Processes to reduce variance, enabling potential quantum computing solutions and showing promising empirical results.

Contribution

It proposes a new QUBO formulation for Gaussian Process variance reduction, bridging spatial modeling with quantum annealing methods.

Findings

QUBO solutions are comparable or better than existing techniques

Empirical results demonstrate the effectiveness of the QUBO model

First step towards quantum-based sampling optimization in Gaussian Processes

Abstract

Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function. Current state of the art techniques select such set to minimize the posterior variance of the Gaussian process. We explore the feasibility of solving this problem by proposing a novel Quadratic Unconstrained Binary Optimization (QUBO) model. In recent years this QUBO formulation has gained increasing attention since it represents the input for the specialized quantum annealer D-Wave machines. Hence, our contribution takes an important first step towards the sampling optimization of Gaussian processes in the context of quantum computation. Results of our empirical evaluation shows that the optimum of the QUBO objective function we derived represents a good solution for the above mentioned problem. In fact we are able to obtain comparable and in some cases better results than the widely used submodular technique.