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DESCRIPTION:Title: On the Minimal Error of Empirical Risk Minimization\n\n
 \n	Abstract:\n\n\nIn recent years\, highly expressive machine learning mode
 ls\, i.e. models that can express rich classes of functions\, are becoming
  more and more commonly used due their success both in regression and clas
 sification tasks\, such models are deep neural nets\, kernel machines and 
 more. From the classical theory statistics point of view (the minimax theo
 ry)\, rich models tend to have a higher minimax rate\, i.e. any estimator 
 must have a high risk (a “worst case scenario” error). Therefore\, it seem
 s that for modern models the classical theory may be too conservative and 
 strict. In this talk\, we consider the most popular procedure for regressi
 on task\, that is Empirical Risk Minimization with squared loss (ERM) and 
 we shall analyze its minimal squared error both in the random and the fixe
 d design settings\, under the assumption of a convex family of functions. 
 Namely\, the minimal squared error that the ERM attains on estimating any 
 function in our class in both settings. In the fixed design setting\, we s
 how that the error is governed by the global complexity of the entire clas
 s. In contrast\, in random design\, the ERM may only adapt to simpler mode
 ls if the local neighborhoods around the regression function are nearly as
  complex as the class itself\, a somewhat counter-intuitive conclusion. We
  provide sharp lower bounds for performance of ERM for both Donsker and no
 n-Donsker classes. This talk is based on joint work with Alexander Rakhlin
 .\n\n\n	Speaker\n\n\nGil Kur is a PhD student MIT. He is currently a visiti
 ng scholar working with Professor Elliot Paquette. His research focuses on
  nonparametric statistics\, high dimensional statistics and convex geometr
 y.\n\n\n	\n		\n			Zoom Link\n\n			Meeting ID: 843 0865 5572\n\n			Passcode: 690084\n		\n
 	\n\n
DTSTART:20210917T193000Z
DTEND:20210917T203000Z
SUMMARY:Gil Kur (MIT)
URL:https://www.mcgill.ca/mathstat/channels/event/gil-kur-mit-333325
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