Relaxation of the EM Algorithm via Quantum Annealing

TL;DR

This paper introduces a quantum annealing-enhanced EM algorithm that leverages quantum fluctuations to escape local optima in nonconvex maximum likelihood estimation problems, improving convergence and solution quality.

Contribution

It proposes a novel deterministic quantum annealing EM algorithm that incorporates quantum fluctuations to address nonconvexity issues in maximum likelihood estimation.

Findings

The quantum annealing EM algorithm guarantees convergence.

Numerical experiments show improved efficiency over traditional EM.

Quantum fluctuations help escape local optima in nonconvex problems.

Abstract

The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm fails to give the optimal estimate by being trapped by local optima. In order to deal with this difficulty, we propose a deterministic quantum annealing EM algorithm by introducing the mathematical mechanism of quantum fluctuations into the conventional EM algorithm because quantum fluctuations induce the tunnel effect and are expected to relax the difficulty of nonconvex optimization problems in the maximum likelihood estimation problems. We show a theorem that guarantees its convergence and give numerical experiments to verify its efficiency.