An efficient viterbi algorithm on DBNs

DBNs (Dynamic Bayesian Networks) [1] are powerful tool in modeling time-series data, and have been used in speech recognition recently [2,3,4]. The “decoding” task in speech recognition means to find the viterbi path [5](in graphical model community, “viterbi path” has the same meaning as MPE “Most Probable Explanation”) for a given acoustic observations. In this paper we describe a new algorithm utilizes a new data structure “backpointer”, which is produced in the “marginalization” procedure in probability inference. With these backpointers, the viterbi path can be found in a simple backtracking. We first introduce the concept of backpointer and backtracking; then give the algorithm to compute the viterbi path for DBNs based on backpointer and backtracking. We prove that the new algorithm is correct, faster and more memory saving comparison with old algorithm. Several experiments are conducted to demonstrate the effectiveness of the algorithm on several well known DBNs. We also test the algorithm on a real world DBN model that can recognize continuous digit numbers.