A fast optimization method for large margin estimation of HMMs based on second order cone programming

In this paper, we present a new fast optimization method to solve large margin estimation (LME) of continuous density hiddenMarkov models (CDHMMs) for speech recognition based on second order cone programming (SOCP). SOCP is a class of nonlinear convex optimization problems which can be solved quite efficiently. In this work, we have proposed a new convex relaxation condition under which LME of CDHMMs can be formulated as an SOCP problem. The new LME/SOCP method has been evaluated in a connected digit string recognition task using the TIDIGITS database. Experimental results clearly demonstrate that the LME using SOCP outperforms the previous gradient descent method and can achieve comparable performance as our previously proposed semidefinite programming (SDP) approach. But the SOCP yields much better efficiency in terms of optimization time (about 20-200 times faster) and memory usage when compared with the SDP method.