EXTENSION OF DECODING PROBLEM OF HMM BASED ON LP-NORM

The decoding problem of hidden Markov model (HMM) is extended based on the L-p-norm of a vector of the log transition probabilities along the sequence of hidden states. The extended decoding problem coincides with the conventional decoding problem for p = 1, and with the minimax decoding problem for p = infinity. To solve the extended decoding problem, we introduce a family of Viterbi algorithm termed the "L-p-Viterbi algorithm" that continuously interpolates the conventional Viterbi algorithm and the minimax Viterbi algorithm. We also consider the corresponding evaluation and estimation problems. Numerical simulations show that the L-p-Viterbi algorithm with an adequately large value of p has an advantage over the minimax Viterbi algorithm.