dissertationLatent structures play a vital role in many data analysis tasks. By providing compact yet expressive representations, such structures can offer useful insights into the complex and high-dimensional datasets encountered in domains such as computational biology, computer vision, natural language processing, etc. Specifying the right complexity of these latent structures for a given problem is an important modeling decision. Instead of using models with an a priori fixed complexity, it is desirable to have models that can adapt their complexity as the data warrant. Nonparametric Bayesian models are motivated precisely based on this desideratum by offering a flexible modeling paradigm for data without limiting the model-complexity a priori. The flexibility comes from the model's ability to adjust its complexity adaptively with data. This dissertation is about nonparametric Bayesian learning of two specific types of latent structures: (1) low-dimensional latent features underlying high-dimensional observed data where the latent features could exhibit interdependencies, and (2) latent task structures that capture how a set of learning tasks relate with each other, a notion critical in the paradigm of Multitask Learning where the goal is to solve multiple learning tasks jointly in order to borrow information across similar tasks. Another focus of this dissertation is on designing efficient approximate inference algorithms for nonparametric Bayesian models. Specifically, for the nonparametric Bayesian latent feature model where the goal is to infer the binary-valued latent feature assignment matrix for a given set of observations, the dissertation proposes two approximate inference methods. The first one is a search-based algorithm to find the maximum-a-posteriori (MAP) solution for the latent feature assignment matrix. The second one is a sequential Monte-Carlo-based approximate inference algorithm that allows processing the data oneexample- at-a-time while being space-efficient in terms of the storage required to represent the posterior distribution of the latent feature assignment matrix
