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Distributionally Robust Bayesian Nonparametric Regression

[Virtual] Hot Topics: Foundations of Stable, Generalizable and Transferable Statistical Learning March 07, 2022 - March 10, 2022

March 09, 2022 (09:00 AM PST - 09:25 AM PST)
Speaker(s): Jose Blanchet (Stanford University)
Location: SLMath: Online/Virtual
Tags/Keywords
  • Distributional robustness

  • Bayesian nonparametrics

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Distributionally Robust Bayesian Nonparametric Regression

Abstract

A distributionally robust Bayesian nonparametric regression estimator is the solution of a min-max game in which the statistician chooses a regression function of observations (i.e. an element in L2) and the adversary, knowing the statistician's selection, maximizes the mean-squared error incurred over a Wasserstein-type-2 ball around a full nonparametric Bayesian model, which we assume to be Gaussian on a suitable Hilbert space. We study this doubly infinite-dimensional game, show the existence of a Nash equilibrium and its evaluation.

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Distributionally Robust Bayesian Nonparametric Regression

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