BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CREST - ECPv5.1.3//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:CREST
X-ORIGINAL-URL:https://crest.science
X-WR-CALDESC:Events for CREST
BEGIN:VTIMEZONE
TZID:Europe/Helsinki
BEGIN:DAYLIGHT
TZOFFSETFROM:+0200
TZOFFSETTO:+0300
TZNAME:EEST
DTSTART:20210328T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
TZNAME:EET
DTSTART:20211031T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Helsinki:20211201T140000
DTEND;TZID=Europe/Helsinki:20211201T150000
DTSTAMP:20260711T232211
CREATED:20211122T051354Z
LAST-MODIFIED:20211122T051451Z
UID:13148-1638367200-1638370800@crest.science
SUMMARY:Thibault Randrianarisoa (LPSM\, Sorbonne Université) – “On Adaptive Confidence Sets for the Wasserstein Distances”
DESCRIPTION:\nStatistics-Econometrics-Machine Learning Seminar. \nTime: 2:00 pm – 3:00 pm\nDate: 1st of december 2021\nPlace: room 3001 and Online \nThibault Randrianarisoa (LPSM\, Sorbonne Université) – “On Adaptive Confidence Sets for the Wasserstein Distances” \nAbstract : In the density estimation model\, we investigate the problem of constructing adaptive honest confidence sets with radius measured in Wasserstein distance $W_p\,p\geq 1$\, and for densities with unknown regularity measured on a Besov scale. As sampling domains\, we focus on the $d$-dimensional torus $mathbb T^d$\, in which case $1\leq p\leq 2$\, and $\mathbb R^d$\, for which $p=1$. We identify necessary and sufficient conditions for the existence of adaptive confidence sets with diameters of the order of the regularity-dependent $W_p$-minimax estimation rate. Interestingly\, it appears that the possibility of such adaptation of the diameter depends on the dimension of the underlying space. In low dimensions\, $d\leq 4$\, adaptation to any regularity is possible. In higher dimensions\, adaptation is possible if and only if the underlying regularities belong to some interval of width at least $d/(d-4)$. This contrasts with the $L_p$-theory where\, independently of the dimension\, adaptation requires regularities to lie in a small fixed-width window. For configurations allowing these adaptive sets to exist\, we explicitly construct confidence regions via the method of risk estimation\, centred at adaptive estimators. Those are the first results in a statistical approach to adaptive uncertainty quantification with Wasserstein distances. Our analysis and methods extend more globally to weak losses such as Sobolev norm distances with negative smoothness indices. \n             \nSponsors: \n\n\n\nCREST \n\n\n
URL:https://crest.science/event/thibault-randrianarisoa-lpsm-sorbonne-universite-on-adaptive-confidence-sets-for-the-wasserstein-distances/
LOCATION:zoom
END:VEVENT
END:VCALENDAR