Deterministic quantum annealing expectation-maximization algorithm

Abstract

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.

Quantum expectation-maximization algorithm

“…In Refs. [15,16], we have succeeded in improving the performances of the EM algorithm and VB. However, the aim of Refs.…”

“…The expectation-maximization (EM) algorithm [9,10,12] and variational Bayes (VB) inference [9,10] with the GMM are often used to improve the clustering, since the general GMM can deal with a wider class of data sets. Recently, one of the authors proposed quantum-inspired algorithms for the EM algorithm [13][14][15] and VB [16]. In Refs.…”

“…However, the aim of Refs. [15,16] is to make use of quantum fluctuations as a numerical tool and not to provide a quantum speedup over a classical algorithm; as a result, the computational costs are almost the same.…”

Quantum extension of variational Bayes inference

“…However, it is also known that VB and SAVB often fail to estimate appropriate parameters of an assumed model depending on prior distributions and initial conditions.In the field of physics, the study of quantum computation and how to exploit it for machine learning are getting popular. For example, while experimentalists are intensively developing quantum machines [9-13], theorists are developing quantum error correction schemes [14-18] and quantum algorithms [19][20][21][22][23][24][25][26][27][28][29]. In particular, the study of quantum annealing (QA) has a history for more than two decades [22][23][24][25] and is still progressing [26].In this Letter, by focusing on QA and VB, we devise a quantum-mechanically inspired algorithm that works on a classical computer in practical time and achieves a considerable improvement over VB and SAVB.…”

“…In the field of physics, the study of quantum computation and how to exploit it for machine learning are getting popular. For example, while experimentalists are intensively developing quantum machines [9][10][11][12][13], theorists are developing quantum error correction schemes [14][15][16][17][18] and quantum algorithms [19][20][21][22][23][24][25][26][27][28][29]. In particular, the study of quantum annealing (QA) has a history for more than two decades [22][23][24][25] and is still progressing [26].…”