Alpha-EM gives fast hidden Markov model estimation: Derivation and evaluation of alpha-HMM

A fast learning algorithm for Hidden Markov Models is derived starting from convex divergence optimization. This method utilizes the alpha-logarithm as a surrogate function for the traditional logarithm to process the likelihood ratio. This enables the utilization of a stronger curvature than the logarithm. This paper's method includes the ordinary Baum-Welch re-estimation algorithm as a proper subset. The presented algorithm shows fast learning by utilizing time-shifted information during the progress of iterations. The computational complexity of this algorithm, which directly affects the CPU time, remains almost the same as the logarithmic one since only stored results are utilized for the speedup. Software implementation and speed are examined in the test data. The results showed that the presented method is creditable.