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The combinatorial structure of conditionally i.i.d. negative binomial processes directed by a beta process

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If you have a question about this talk, please contact Creighton Heaukulani.

We give a simple constructive characterization of a beta negative binomial process, i.e., a random measure that is conditionally a negative binomial process, given a beta process base measure. Our results build on those for exchangeable sequences of Bernoulli process directed by beta processes developed by Roy (2013), where a beta process is reinterpreted as a continuum of Dirichlet processes, so that a directed sequence of Bernoulli processes is a continuum of Blackwell-MacQueen urn schemes.

We then define a negative binomial Indian buffet process (NB-IBP), which is the discrete-time combinatorial stochastic process underlying exchangeable sequences of negative binomial processes directed by a beta process. In particular, the NB-IBP is an exchangeable sequence of multisets. Similar to the IBP , the NB-IBP induces a distribution over non-negative integer-valued matrices.

Joint work with Daniel M. Roy.

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

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