Constrained Markov Bayesian Polynomial for Efficient Dialogue State Tracking

Dialogue state tracking (DST) is a process to estimate the distribution of the dialogue states at each dialogue turn given the interaction history. Although data-driven statistical approaches are of most interest, there have been attempts of using rule-based methods for DST, due to their simplicity, efficiency and portability. However, the performance of these methods are usually not competitive to data-driven tracking approaches and it is not possible to improve the DST performance when training data are available. In this paper, a novel hybrid framework, constrained Markov Bayesian polynomial (CMBP), is proposed to formulate rule-based DST in a general way and allow data-driven rule generation. Here, a DST rule is defined as a polynomial function of a set of probabilities satisfying certain linear constraints. Prior knowledge is encoded in these constraints. Under reasonable assumptions, CMBP optimization can be converted to a constrained integer linear programming problem. The integer coefficient CMBP model is further extended to CMBP with real coefficients by applying grid search. CMBP was evaluated on the data corpora of the first, the second, and the third Dialog State Tracking Challenge (DSTC-1/2/3). Experiments showed that CMBP has good generalization ability and can significantly outperform both traditional rule-based approaches and data-driven statistical approaches with similar feature set. Compared with the state-of-the-art statistical DST approaches with much richer features, CMBP is also competitive.