Weibull partition models with applications to hidden semi-Markov models

We develop the Weibull partition model (WPM), which defines a novel nonparametric stochastic process over distributions of partitions of sequential data, aiming at directly modeling the boundaries of segments comprising the sequence. The Weibull partition model employs a Dirichlet process mixture with a Weibull kernel. Weibull distributions having a closed-form cumulative density function plays an important role in the construction of the Weibull partition model. As an application of our model, we propose the hidden semi-Markov model based on the Weibull partition model (WPM-HSMM), along with the corresponding recursive sampling algorithm. The WPM-HSMM can be used to solve the problem of low accuracy of inference for hidden states, caused by the holding times of hidden states having a complicated distribution. In our experiments, we show that the WPM-HSMM rapidly mixes and achieves very competitive results compared to the state-of-the-art algorithms. Apart from the application to hidden Markov models, the WPM can also be found useful in any problem, where explicitly modeling segment boundaries is needed.