Pruning hidden Markov models with optimal brain surgeon

A method of pruning hidden Markov models (HMMs) is presented. The main purpose is to find a good HMM topology for a given task with improved generalization capability. As a side effect, the resulting model will also save memory and computation costs. The first goal falls into the active research area of model selection. From the model-theoretic research community, various measures such as Bayesian information criterion, minimum description length, minimum message length have been proposed and used with some success. In this paper, we are considering another approach in which a well-performed HMM, though perhaps oversized, is optimally pruned so that the loss in the model training cost function is minimal. The method is known as optimal brain surgeon (OBS) that has been applied to pruning neural networks (NNs) in the past. In this paper, the OBS algorithm is modified to prune HMMs. While the application of OBS to NNs is a constrained optimization problem with only equality constraints that can be solved by Lagrange multipliers, its application to HMMs requires significant modifications, resulting in a quadratic programming problem with both equality and inequality constraints. The detailed formulation of pruning an HMM with OBS is presented. It was evaluated by two experiments: one simulation using a discrete HMM, and another with continuous density HMMs trained for the TIDIGITS task. It is found that our novel OBS algorithm was able to "re-discover" the true topology of the discrete HMM in the first simulation experiment; in the second speech recognition experiment, up to about 30% of HMM transitions were successfully pruned, and yet the reduced models gave better generalization performance on unseen test data.