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Does data interpolation contradict statistical optimality?

Presented by: 
Alexandre Tsybakov CREST: Centre de Recherche en Économie et Statistique
Friday 29th June 2018 - 09:00 to 09:45
INI Seminar Room 1
We exhibit estimators that interpolate the data, and yet achieve optimal rates of convergence for the problems of nonparametric regression and prediction with square loss. This curious observation goes against the usual intuition that a good statistical procedure should forego the exact fit to data in favor of a more smooth representation. A motivation for this work is the recent focus within the machine learning community on the out-of-sample performance of neural networks. These flexible models are typically trained to fit the data exactly (either in their sign or in the actual value), and yet they have good prediction behaviour. This talk is based on joint work with Misha Belkin and Sasha Rakhlin.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons