# Relaxation of the EM Algorithm via Quantum Annealing for Gaussian Mixture Models

## TL;DR

This paper introduces DQAEM, a novel algorithm combining quantum annealing with EM to improve Gaussian mixture model optimization, reducing local optima trapping and enhancing stability.

## Contribution

It presents the DQAEM algorithm that integrates quantum annealing into EM, providing theoretical stability and demonstrating improved performance in Gaussian mixture models.

## Key findings

- DQAEM outperforms traditional EM in avoiding local optima.
- Theoretical proof of stability for DQAEM.
- Numerical simulations confirm efficiency improvements.

## Abstract

We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. The expectation-maximization (EM) algorithm is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.