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Abstract:
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Bayesian nonparametric inference is often too expensive for massive datasets to be practically useful. Many current Bayesian computation ideas deal with discovery of a underlying lower dimensional structure. In this context, we propose a new class of algorithms using randomized inference - which show that explicit dimension reduction is often not necessary, depending on the underlying smoothness of the prior processes, we may get away with random projections. We describe a methodology and associated computation that provides an extremely scalable and generic scheme for randomized inference with Bayesian algorithms, with strong theoretical justification. We provide several examples, including in the context of Gaussian process, Bayesian classification and Bayesian random forests, with simulated and real data sets, where we demonstrate the superiority of our approach, not only from an efficiency point of view, but also with respect to increased accuracy of predictions, which are probably due to the increased stability of the resultant inference.
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