Variational Inference in Nonconjugate Models

Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily derived and in closed form. However, many models of interest---like the correlated topic model and Bayesian logistic regression---are nonconjuate. In these models, mean-field methods cannot be directly applied and practitioners have had to develop variational algorithms on a case-by-case basis. In this paper, we develop two generic methods for nonconjugate models, Laplace variational inference and delta method variational inference. Our methods have several advantages: they allow for easily derived variational algorithms with a wide class of nonconjugate models; they extend and unify some of the existing algorithms that have been derived for specific models; and they work well on real-world datasets. We studied our methods on the correlated topic model, Bayesian logistic regression, and hierarchical Bayesian logistic regression

Efficient Correlated Topic Modeling with Topic Embedding

Correlated topic modeling has been limited to small model and problem sizes due to their high computational cost and poor scaling. In this paper, we propose a new model which learns compact topic embeddings and captures topic correlations through the closeness between the topic vectors. Our method enables efficient inference in the low-dimensional embedding space, reducing previous cubic or quadratic time complexity to linear w.r.t the topic size. We further speedup variational inference with a fast sampler to exploit sparsity of topic occurrence. Extensive experiments show that our approach is capable of handling model and data scales which are several orders of magnitude larger than existing correlation results, without sacrificing modeling quality by providing competitive or superior performance in document classification and retrieval.Comment: KDD 2017 oral. The first two authors contributed equall

The Discrete Infinite Logistic Normal Distribution

We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed random variables, and study its statistical properties. We consider applications to topic modeling and derive a variational inference algorithm for approximate posterior inference. We study the empirical performance of the DILN topic model on four corpora, comparing performance with the HDP and the correlated topic model (CTM). To deal with large-scale data sets, we also develop an online inference algorithm for DILN and compare with online HDP and online LDA on the Nature magazine, which contains approximately 350,000 articles.Comment: This paper will appear in Bayesian Analysis. A shorter version of this paper appeared at AISTATS 2011, Fort Lauderdale, FL, US