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CATEGORIES:Statistics
SUMMARY:Distribution-free inference for regression: discre
te\, continuous\, and in between - Rina Foygel Bar
ber\, University of Chicago
DTSTART;TZID=Europe/London:20210528T160000
DTEND;TZID=Europe/London:20210528T170000
UID:TALK159748AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/159748
DESCRIPTION:In data analysis problems where we are not able to
rely on distributional assumptions\, what types o
f inference guarantees can still be obtained? Man
y popular methods\, such as holdout methods\, cros
s-validation methods\, and conformal prediction\,
are able to provide distribution-free guarantees f
or predictive inference\, but the problem of provi
ding inference for the underlying regression funct
ion (for example\, inference on the conditional me
anE[Y|X]) is more challenging. If X takes only a s
mall number of possible values\, then inference on
E[Y|X] is trivial to achieve. At the other extrem
e\, if the features X are continuously distributed
\, we show that any confidence interval for E[Y|X]
must have non-vanishing width\, even as sample si
ze tends to infinity - this is true regardless of
smoothness properties or other desirable features
of the underlying distribution. In between these t
wo extremes\, we find several distinct regimes - i
n particular\, it is possible for distribution-fre
e confidence intervals to have vanishing width if
and only if the effective support size of the dist
ribution ofXis smaller than the square of the samp
le size.\n\nThis work is joint with Yonghoon Lee.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/95871364531?pwd
=aFZaV0loSWt6QmRDbm5ONWNjTTBjZz09
CONTACT:Dr Sergio Bacallado
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