BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Asymptotics of Eigenvectors and Eigenvalues for La
rge Structured Random Matrices - Jinchi Lv (Univer
sity of Southern California)
DTSTART;TZID=Europe/London:20180628T140000
DTEND;TZID=Europe/London:20180628T144500
UID:TALK107491AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/107491
DESCRIPTION:Characterizing the exact asymptotic distributions
of high-dimensional eigenvectors for large structu
red random matrices poses important challenges yet
can provide useful insights into a range of appli
cations. This paper establishes the asymptotic pro
perties of the spiked eigenvectors and eigenvalues
for the generalized Wigner random matrix\, where
the mean matrix is assumed to have a low-rank stru
cture. Under some mild regularity conditions\, we
provide the asymptotic expansions for the spiked e
igenvalues and show that they are asymptotically n
ormal after some normalization. For the spiked eig
envectors\, we provide novel asymptotic expansions
for the general linear combination and further sh
ow that the linear combination is asymptotically n
ormal after some normalization\, where the weight
vector can be an arbitrary unit vector. Simulation
studies verify the validity of our new theoretica
l results. Our family of models encompasses many p
opularly used ones such as the stochastic block mo
dels with or without overlapping communities for n
etwork analysis and the topic models for text anal
ysis\, and our general theory can be exploited for
statistical inference in these large-scale applic
ations. This is a joint work with Jianqing Fan\, Y
ingying Fan and Xiao Han.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
END:VEVENT
END:VCALENDAR