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Completely Random Measures in Bayesian Nonparametrics

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In Bayesian nonparametric modelling, we allow a model to learn an unbounded number of parameters by replacing classical finite-dimensional statistical distributions with infinite-dimensional stochastic processes. Completely random measures are a special class of stochastic processes, which are intuitive, highly interpretable, and useful for statistical applications. While this theory is mathematically deep, in this tutorial we will instead focus on practicalities such as how to sample such objects, providing pointers to more theoretical material when necessary. This tutorial will include an introduction to random measures and their practical uses, Poisson processes and how to sample them, complete randomness, and how to characterise a completely random measure. Finally, we introduce some important completely random measures, such as the Bernoulli process, the Beta process, and the Gamma process, and we will show how they are related to some popular objects used in machine learning, such as the Dirichlet process, Chinese restaurant process and the Indian buffet process.

This talk is part of the Machine Learning Reading Group @ CUED series.

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