Nonparametric Bayesian Methods for Extracting Structure from Data

One desirable property of machine learning algorithms is the ability to balance the number of parameters in a model in accordance with the amount of available data. Incorporating nonparametric Bayesian priors into models is one approach of automatically adjusting model capacity to the amount of available data: with small datasets, models are less complex (require storing fewer parameters in memory), whereas with larger datasets, models are implicitly more complex (require storing more parameters in memory). Thus, nonparametric Bayesian priors satisfy frequentist intuitions about model complexity within a fully Bayesian framework. This thesis presents several novel machine learning models and applications that use nonparametric Bayesian priors. We introduce two novel models that use flat, Dirichlet process priors. The first is an infinite mixture of experts model, which builds a fully generative, joint density model of the input and output space. The second is a Bayesian biclustering model, which simultaneously organizes a data matrix into block-constant biclusters. The model capable of efficiently processing very large, sparse matrices, enabling cluster analysis on incomplete data matrices. We introduce binary matrix factorization, a novel matrix factorization model that, in contrast to classic factorization methods, such as singular value decomposition, decomposes a matrix using latent binary matrices. We describe two nonparametric Bayesian priors over tree structures. The first is an infinitely exchangeable generalization of the nested Chinese restaurant process [11] that generates data-vectors at a single node in the tree. The second is a novel, finitely exchangeable prior generates trees by first partitioning data indices into groups and then by randomly assigning groups to a tree. We present two applications of the tree priors: the first automatically learns probabilistic stick-figure models of motion-capture data that recover plausible structure and are robust to missing marker data. The second learns hierarchical allocation models based on the latent Dirichlet allocation topic model for document corpora, where nodes in a topic-tree are latent “super-topics”, and nodes in a document-tree are latent categories. The thesis concludes with a summary of contributions, a discussion of the models and their limitations, and a brief outline of potential future research directions.