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/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20190331T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20191027T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191104T140000
DTEND;TZID=Europe/Paris:20191104T151500
DTSTAMP:20260817T041220
CREATED:20190703T122117Z
LAST-MODIFIED:20190703T122117Z
UID:12295-1572876000-1572880500@crest.science
SUMMARY:Richard SAMWORTH (Université de Cambridge) - "High-dimensional principal component analysis with heterogeneous missingness"
DESCRIPTION:\nThe Statistical Seminar: Every Monday at 2:00 pm.\nTime: 2:00 pm – 3:15 pm\nDate: 4th of November 2019\nPlace: Room 3001.\nRichard SAMWORTH (Université de Cambridge) – “High-dimensional principal component analysis with heterogeneous missingness“ \nAbstract: We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple\, homogeneous missingness settings with a noise level of constant order\, we show that an existing inverse-probability weighted (IPW) estimator of the leading principal components can (nearly) attain the minimax optimal rate of convergence. However\, deeper investigation reveals both that\, particularly in more realistic settings where the missingness mechanism is heterogeneous\, the empirical performance of the IPW estimator can be unsatisfactory\, and moreover that\, in the noiseless case\, it fails to provide exact recovery of the principal components. We therefore introduce a new method for high-dimensional PCA\, called `primePCA’\, that is designed to cope with situations where observations may be missing in a heterogeneous manner. Starting from the IPW estimator\, primePCA iteratively projects the observed entries of the data matrix onto the column space of our current estimate to impute the missing entries\, and then updates our estimate by computing the leading right singular space of the imputed data matrix. It turns out that the interaction between the heterogeneity of missingness and the low-dimensional structure is crucial in determining the feasibility of the problem. This leads us to impose an incoherence condition on the principal components and we prove that in the noiseless case\, the error of primePCA converges to zero at a geometric rate when the signal strength is not too small. An important feature of our theoretical guarantees is that they depend on average\, as opposed to worst-case\, properties of the missingness mechanism. \nOrganizers:\nCristina BUTUCEA\, Alexandre TSYBAKOV\, Julie JOSSE\, Eric MOULINES\, Mathieu ROSENBAUM\nSponsors:\nCREST-CMAP\n \n\n
URL:https://crest.science/event/richard-samworth/
CATEGORIES:Statistics
ATTACH;FMTTYPE=:
END:VEVENT
END:VCALENDAR