Daichi Mochihashi, Eiichiro Sumita
We present a nonparametric Bayesian method of estimating variable order Markov processes up to a theoretically inﬁnite order. By extending a stick-breaking prior, which is usually deﬁned on a unit interval, “vertically” to the trees of inﬁnite depth associated with a hierarchical Chinese restaurant process, our model directly infers the hidden orders of Markov dependencies from which each symbol originated. Experiments on character and word sequences in natural language showed that the model has a comparative performance with an exponentially large full-order model, while computationally much efﬁcient in both time and space. We expect that this basic model will also extend to the variable order hierarchical clustering of general data.