基于量子退火的期望最大化算法松弛
Relaxation of the EM Algorithm via Quantum Annealing
摘要：
期望最大化算法是一种获得最大似然估计的新的数值方法，常用于实际计算。然而，许多极大似然估计问题是非凸的，并且已知期望最大化算法由于陷入局部最优而不能给出最优估计。为了解决这一难题，我们在传统的期望最大化算法中引入量子涨落的数学机制，提出了一种确定性量子退火期望最大化算法，因为量子涨落会引起隧道效应，有望缓解极大似然估计问题中非凸优化问题的困难.我们证明了一个定理，保证其收敛性，并给出数值实验，以验证其效率。
英文摘要：
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.
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