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TZID:America/Chicago
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DTSTART:20221106T020000
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DTSTART:20230312T020000
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UID:calendar.25720.field_event_date_2.0@math.wustl.edu
CREATED:20230123T162342Z
DESCRIPTION:Abstract: It has been observed that the statistical properties
of many high-dimensional regression problems empirically exhibit universal
ity with respect to the underlying design matrices. Specifically, design
matrices with very different constructions seem to lead to identical estim
ation performance if they share the same spectrum and have generic singula
r vectors. This general universality phenomenon appears in numerous applic
ations: in random optimization problems arising in statistical physics, i
n statistical inference problems like sparse regression or compressed sens
ing, and in the performance of sketching algorithms in randomized numeric
al linear algebra. In the first part of this talk, I will show how these
empirical observations of universality can be exploited to design and anal
yze information-theoretically optimal spectral estimators for the phase re
trieval problem: a non-linear regression problem that arises in imaging ap
plications like X-ray crystallography. In the second part of the talk, I
will describe recent progress toward a mathematical understanding of this
universality phenomenon. In the context of regularized linear regression w
ith strongly convex penalties, I will describe nearly deterministic condi
tions on the design matrix under which this universality phenomenon occurs
. I will show that these conditions can be easily verified for highly stru
ctured and practically relevant design matrices constructed with limited r
andomness, like randomly subsampled Hadamard transforms and signed incohe
rent tight frames. \n\nHost: Soumendra Lahiri\n\nTea will be served in Cup
ples I, room 200 at 3:45pm.
DTSTART;TZID=America/Chicago:20230125T161500
DTEND;TZID=America/Chicago:20230125T171500
LAST-MODIFIED:20230123T164450Z
SUMMARY:Colloquium: 'Universality in High-dimensional Statistics'
URL;TYPE=URI:https://math.wustl.edu/events/colloquium-universality-high-dim
ensional-statistics
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