Nonparametric Bayesian Methods for Machine Learning
Romain Jean Thibaux and Michael Jordan
Probabilistic models have become the central tool, and the common theme, of disciplines involving large real-world data such as speech recognition, robotics, computational biology, or data mining. They describe the probabilitistic relationship between a number of continuous or discrete variables, allowing one to infer the value of one variable given observations of the others. Nonparametric Bayesian methods extend these models by defining probabilities over infinite objects such as measures or functions, thereby gaining tremendous flexibility.
Our work consists of defining novel distributions over infinite objects, and deriving algorithms for inference. Our contributions include a Markov chain Monte Carlo sampler for the Dirichlet process, and the construction of a hierarchical Beta process and associated algorithm.