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CATEGORIES:Information Theory Seminar
SUMMARY:Fundamental limits in structured PCA\, and how to
reach them - Dr Jean Barbier\, International Cente
r for Theoretical Physics (ICTP)
DTSTART;TZID=Europe/London:20230315T140000
DTEND;TZID=Europe/London:20230315T150000
UID:TALK194131AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194131
DESCRIPTION:I will discuss the paradigmatic spiked matrix mode
l of principal components analysis\, where a rank-
one signal is corrupted by additive noise. While t
he noise is typically taken from a Wigner matrix w
ith independent entries\, here the potential actin
g on the eigenvalues has a quadratic plus a quarti
c component. The quartic term induces strong corre
lations between the matrix elements\, which makes
the setting relevant for applications but analytic
ally challenging. Our work provides the first char
acterization of the Bayes-optimal limits for infer
ence in this model with structured noise. If the s
ignal prior is rotational-invariant\, then we show
that a spectral estimator is optimal. In contrast
\, for more general priors\, the existing approxim
ate message passing algorithm (AMP) falls short of
achieving the information-theoretic limits\, and
we provide a justification for this sub-optimality
. Finally\, by generalizing the theory of Thouless
-Anderson-Palmer equations\, we cure the issue by
proposing a novel AMP which matches the theoretica
l limits. Our information-theoretic analysis is ba
sed on the replica method\, a powerful heuristic f
rom statistical mechanics\; instead\, the novel AM
P comes with a rigorous state evolution analysis t
racking its performance in the high-dimensional li
mit. \n
LOCATION:B1.19 (MR19)\, CMS Pavilion B
CONTACT:Prof. Ramji Venkataramanan
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