Relaxation of the EM Algorithm via Quantum Annealing
This addresses a key bottleneck in statistical estimation for practitioners, though it appears incremental as it modifies an existing method.
The paper tackles the problem of the EM algorithm getting trapped in local optima in nonconvex maximum likelihood estimation by proposing a deterministic quantum annealing EM algorithm that incorporates quantum fluctuations to induce tunneling effects, showing convergence and efficiency in numerical experiments.
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.