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CATEGORIES:Statistics
SUMMARY:A precise high-dimensional asymptotic theory for A
daboost - Pragya Sur (Harvard University)
DTSTART;TZID=Europe/London:20210122T160000
DTEND;TZID=Europe/London:20210122T170000
UID:TALK153538AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/153538
DESCRIPTION:This talk will introduce a precise high-dimensiona
l asymptotic theory for AdaBoost on separable data
\, taking both statistical and computational persp
ectives. We will consider the common modern settin
g where the number of features p and the sample si
ze n are both large and comparable\, and in partic
ular\, look at scenarios where the data is separab
le in an asymptotic sense. Under a class of statis
tical models\, we will provide an (asymptotically)
exact analysis of the generalization error of Ada
Boost\, when the algorithm interpolates the traini
ng data and maximizes an empirical L1 margin. On t
he computational front\, we provide a sharp analys
is of the stopping time when boosting approximatel
y maximizes the empirical L1 margin. Our theory pr
ovides several insights into properties of Boostin
g\; for instance\, the larger the dimensionality r
atio p/n\, the faster the optimization reaches int
erpolation. At the heart of our theory lies an in-
depth study of the maximum L1-margin\, which can b
e accurately described by a new system of non-line
ar equations\; we analyze this margin and the prop
erties of this system\, using Gaussian comparison
techniques and a novel uniform deviation argument.
Time permitting\, I will present a new class of b
oosting algorithms that correspond to Lq geometry\
, for q>1\, together with results on their high-di
mensional generalization and optimization behavior
. \n\nThis is based on joint work with Tengyuan Li
ang.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/92821218455?pwd
=aHFOZWw5bzVReUNYR2d5OWc1Tk15Zz09
CONTACT:Dr Sergio Bacallado
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