We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. 1 1

The Indian buffet process (IBP) is a Bayesian nonparametric distribution whereby objects are modelled using an unbounded number of latent features. In this paper we derive a stick-breaking representation for the IBP. Based on this new representation, we develop slice samplers for the IBP that are efficient, easy to implement and are more generally applicable than the currently available Gibbs sampler. This representation, along with the work of Thibaux and Jordan [17], also illuminates interesting theoretical connections between the IBP, Chinese restaurant processes, Beta processes and Dirichlet processes. 1

The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a three-parameter generalization of the IBP exhibiting power-law behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the stable-beta process and deriving the IBP corresponding to it. We find interesting relationships between the stable-beta process and the Pitman-Yor process (another stochastic process used in Bayesian nonparametric models with interesting power-law properties). We derive a stick-breaking construction for the stable-beta process, and find that our power-law IBP is a good model for word occurrences in document corpora. 1

We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models, and model validation with DP and Polya tree extensions of parametric models. 1

We present and derive a new stick-breaking construction of the beta process. The construction is closely related to a special case of the stick-breaking construction of the Dirichlet process (Sethuraman, 1994) applied to the beta distribution. We derive an inference procedure that relies on Monte Carlo integration to reduce the number of parameters to be inferred, and present results on synthetic data, the MNIST handwritten digits data set and a time-evolving gene expression data set. 1.

We present model-based inference for proteomic peak identification and quantification from mass spectroscopy data, focusing on nonparametric Bayesian models. Using experimental data generated from MALDI-TOF mass spectroscopy (Matrix Assisted Laser Desorption Ionization Time of Flight) we model observed intensities in spectra with a hierarchical nonparametric model for expected intensity as a function of time-of-flight. We express the unknown intensity function as a sum of kernel functions, a natural choice of basis functions for modelling spectral peaks. We discuss how to place prior distributions on the unknown functions using Lévy random fields and describe posterior inference via a reversible jump Markov chain Monte Carlo algorithm.