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Award ID contains: 2005746

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  1. ; ; (, conference on learning theory)
    We develop a non-asymptotic framework for hypothesis testing in nonparametric regression where the true regression function belongs to a Sobolev space. Our statistical guarantees are exact in thesense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax rate optimality in the asymptotic sense. An important consequence of this non-asymptotic theory is a new and practically useful formula for selecting the optimal smoothing parameter in the testing statistic. Extensions of our results to general reproducing kernel Hilbert spaces and non-Gaussian error regression are also discussed. 
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    Accepted Manuscript Full Text Available
  2. ; ; (, Journal of machine learning research)
    We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models. Specifically, nonparametric Bayesian inferences are separately performed on each subset randomly split from a massive dataset, and then the obtained local results are aggregated into global counterparts. This aggregation step is explicit without involving any additional computation cost. By a careful partition, we show that our aggregated inference results obtain an oracle rule in the sense that they are equivalent to those obtained directly from the entire data (which are computationally prohibitive). For example, an aggregated credible ball achieves desirable credibility level and also frequentist coverage while possessing the same radius as the oracle ball. 
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    Accepted Manuscript Full Text Available
  3. ; ; (, Electronic journal of statistics)
    Full Text Available