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Flexible martingale priors for deep hierarchies

By Jacob Steinhardt and Zoubin Ghahramani


We present an infinitely exchangeable prior over discrete tree structures that allows the depth of the tree to grow with the data. We show that the depth of the tree under the prior increases with the amount of data, which distinguishes it from any existing model; we then implement the model for a hierarchical beta process. We also show that deep hierarchical models are in general intimately tied to a process called a martingale, and use Doob’s martingale convergence theorem to demonstrate some unexpected properties of deep hierarchies.

Year: 2012
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