On the equivalence of Gaussian HMM and Gaussian HMM-like hidden conditional random fields

In this work we show that Gaussian HMMs (GHMMs) are equivalent to GHMM-like Hidden Conditional Random Fields (HCRFs). Hence, improvements of HCRFs over GHMMs found in literature are not due to a refined acoustic modeling but rather come from the more robust formulation of the underlying optimization problem or spurious local optima. Conventional GHMMs are usually estimated with a criterion on segment level whereas hybrid approaches are based on a formulation of the criterion on frame level. In contrast to CRFs, these approaches do not provide scores or do not support more than two classes in a natural way. In this work we analyze these two classes of criteria and propose a refined frame based criterion, which is shown to be an approximation of the associated criterion on segment level. Experimental results concerning these issues are reported for the German digit string recognition task Sietill and the large vocabulary English European Parliament Plenary Sessions (EPPS) task.