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# Ordered Stick-Breaking Prior for Sequential MCMC Inference of Bayesian Nonparametric Models

*Proceedings of the 32nd International Conference on Machine Learning*, PMLR 37:550-559, 2015.

#### Abstract

This paper introduces ordered stick-breaking process (OSBP), where the atoms in a stick-breaking process (SBP) appear in order. The choice of weights on the atoms of OSBP ensure that; (1) probability of adding new atoms exponentially decrease, and (2) OSBP, though non-exchangeable, admit predictive probability functions (PPFs). In a Bayesian nonparametric (BNP) setting, OSBP serves as a natural prior over sequential mini-batches, facilitating exchange of relevant statistical information by sharing the atoms of OSBP. One of the major contributions of this paper is SUMO, an MCMC algorithm, for solving the inference problem arising from applying OSBP to BNP models. SUMO uses the PPFs of OSBP to obtain a Gibbs-sampling based truncation-free algorithm which applies generally to BNP models. For large scale inference problems existing algorithms such as particle filtering (PF) are not practical and variational procedures such as TSVI (Wang & Blei, 2012) are the only alternative. For Dirichlet process mixture model (DPMM), SUMO outperforms TSVI on perplexity by 33% on 3 datasets with million data points, which are beyond the scope of PF, using only 3GB RAM.