Title: Relaxation of the EM Algorithm via Quantum Annealing for Gaussian Mixture Models,
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.