# Deterministic Quantum Annealing Expectation-Maximization Algorithm

## TL;DR

This paper introduces the DQAEM algorithm, a quantum annealing-based extension of EM, which improves maximum likelihood estimation by overcoming local optima issues, demonstrated through numerical simulations.

## Contribution

The paper proposes the DQAEM algorithm, integrating quantum annealing with EM to enhance global optimization in maximum likelihood estimation.

## Key findings

- DQAEM outperforms EM in numerical simulations.
- DQAEM reduces dependence on initial configurations.
- DQAEM effectively finds better optima in MLE tasks.

## Abstract

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial configurations and fails to find the global optimum. On the other hand, in the field of physics, quantum annealing (QA) was proposed as a novel optimization approach. Motivated by QA, we propose a quantum annealing extension of EM, which we call the deterministic quantum annealing expectation-maximization (DQAEM) algorithm. We also discuss its advantage in terms of the path integral formulation. Furthermore, by employing numerical simulations, we illustrate how it works in MLE and show that DQAEM outperforms EM.