Threshold-based dynamic annealing for multi-thread DAEM and its extreme

The EM algorithm is an efficient algorithm to obtain the ML estimate for incomplete data, but has the local optimality problem. The deterministic annealing EM (DAEM) algorithm was once proposed to solve the problem, but it not guaranteed to obtain the global optimum since it employs a single token search. Then multi-thread DAEM (m-DAEM) algorithm was proposed by incorporating a search framework of multiple tokens, giving further improvement of solution quality with a heavy computing cost. This paper proposes another variant of m-DAEM, called ε-DAEM, by introducing threshold-based dynamic annealing where the Hessian information is made good use of. Given the adequate ε, the ε-DAEM shows excellent performance. Moreover, its extreme case where ε → ∞, called the multi-thread EM, also shows rather excellent performance.