Decision tree state tying based on penalized Bayesian information criterion

In this paper, an approach of the penalized Bayesian information criterion (pBIC) for decision tree state tying is described. The pBIC is applied to two important applications. First, it is used as a decision tree growing criterion in place of the conventional approach of using a heuristic constant threshold. It is found that original BIC penalty is too low and will not lead to a compact decision tree state tying model. Based on Wolfe's modification to the asymptotic null distribution, it is derived that two times BIC penalty should be used for decision tree state tying based on pBIC. Secondly, pBIC is studied as a model compression criterion for decision tree state tying based acoustic modeling. Experimental results on a large vocabulary (Wall Street Journal) speech recognition task indicate that a compact decision tree could be achieved with almost no loss of the speech recognition performance.