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SUMMARY:Distribution-free inference for regression: discrete\, continuous\
 , and in between - Rina Foygel Barber\, University of Chicago
DTSTART:20210528T150000Z
DTEND:20210528T160000Z
UID:TALK159748@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:In data analysis problems where we are not able to rely on dis
 tributional assumptions\, what types of inference guarantees can still be 
 obtained?  Many popular methods\, such as holdout methods\, cross-validati
 on methods\, and conformal prediction\, are able to provide distribution-f
 ree guarantees for predictive inference\, but the problem of providing inf
 erence for the underlying regression function (for example\, inference on 
 the conditional meanE[Y|X]) is more challenging. If X takes only a small n
 umber of possible values\, then inference on E[Y|X] is trivial to achieve.
  At the other extreme\, if the features X are continuously distributed\, w
 e show that any confidence interval for E[Y|X] must have non-vanishing wid
 th\, even as sample size tends to infinity - this is true regardless of sm
 oothness properties or other desirable features of the underlying distribu
 tion. In between these two extremes\, we find several distinct regimes - i
 n particular\, it is possible for distribution-free confidence intervals t
 o have vanishing width if and only if the effective support size of the di
 stribution ofXis smaller than the square of the sample size.\n\nThis work 
 is joint with Yonghoon Lee.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/95871364531?pwd=aFZaV0loSWt6Qm
 RDbm5ONWNjTTBjZz09
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