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DTSTAMP:20261016T164516Z
DESCRIPTION:Title: To split or not to split that is the question: From cros
 s validation to debiased machine learning.\n\n\n	Abstract:\n\n\nData splitt
 ing is an ubiquitous method in statistics with examples ranging from cross
  validation to cross-fitting. However\, despite its prevalence\, theoretic
 al guidance regarding its use is still lacking. In this talk we will explo
 re two examples and establish an asymptotic theory for it. In the first pa
 rt of this talk\, we study the cross-validation method\, a ubiquitous meth
 od for risk estimation\, and establish its asymptotic properties for a lar
 ge class of models and with an arbitrary number of folds. Under stability 
 conditions\, we establish a central limit theorem and Berry-Esseen bounds 
 for the cross-validated risk\, which enable us to compute asymptotically a
 ccurate confidence intervals. Using our results\, we study the statistical
  speed-up offered by cross validation compared to a train-test split proce
 dure. We reveal some surprising behavior of the cross-validated risk and e
 stablish the statistically optimal choice for the number of folds. In the 
 second part of this talk\, we study the role of cross fitting in the gener
 alized method of moments with moments that also depend on some auxiliary f
 unctions. Recent lines of work show how one can use generic machine learni
 ng estimators for these auxiliary problems\, while maintaining asymptotic 
 normality and root-n consistency of the target parameter of interest. The 
 literature typically requires that these auxiliary problems are fitted on 
 a separate sample or in a cross-fitting manner. We show that when these au
 xiliary estimation algorithms satisfy natural leave-one-out stability prop
 erties\, then sample splitting is not required. This allows for sample re-
 use\, which can be beneficial in moderately sized sample regimes.\n\n\n	Spe
 aker\n\n\nMorgane Austern is an Assistant Professor of Statistics at Harva
 rd University. She obtained her PhD in statistics from Columbia University
 \, working with Peter Orbanz and Arian Maleki on limit theorems for depend
 ent and structured data. After that\, she was a postdoctoral researcher at
  Microsoft Research New England. Broadly\, she interested in developing pr
 obability tools for modern machine learning and in establishing the proper
 ties of learning algorithms in structured and dependent data contexts. Her
  current work is motivated by generalization and concentration bounds\, st
 able matching problems and random matrix theory.\n\n\n	\n		\n			https://mcgill.z
 oom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09\n\n			Meeting ID: 8
 34 3668 6293\n\n			Passcode: 12345\n		\n	\n\n\n \n
DTSTART:20230113T203000Z
DTEND:20230113T213000Z
SUMMARY:Morgane Austern (Harvard University)
URL:https://www.mcgill.ca/mathstat/channels/event/morgane-austern-harvard-u
 niversity-344874
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