Adjusted Viterbi Training

We propose modifications of the Viterbi Training (VT) algorithm to estimate emission parameters in Hidden Markov Models (HMM) which are widely used in speech recognition, natural language modeling, image analysis, and bioinformatics. Our goal is to alleviate the inconsistency of VT while controlling the amount of extra computations. Specifically, we modify VT to enable it asymptotically to fix the true values of the parameters as does the EM algorithm. Our approach relies on infinite Viterbi alignment and an associated with it limiting probability distribution. We focus on mixture models, an important special case of HMM, wherein the limiting distribution can be computed exactly and be used in the adjusted VT algorithm. A simulation experiment shows that our central algorithm (VA1) can dramatically improve accuracy without much cost in computation time. We also propose VA2, a more mathematically advanced correction to VT, verify its fast convergence and high accuracy, and intend to elaborate on its computationally feasible implementations in future work.