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SUMMARY:Optimal Estimation in Orthogonally Invariant Generalized Linear Mo
 dels - Dr Yihan Zhang\, University of Bristol 
DTSTART:20260311T140000Z
DTEND:20260311T150000Z
UID:TALK241483@talks.cam.ac.uk
CONTACT:Dr Varun Jog
DESCRIPTION:We consider the problem of parameter estimation from a general
 ized linear model with a random design matrix that is orthogonally invaria
 nt in law. Such a model allows the design to have an arbitrary distributio
 n of singular values and only assumes that its singular vectors are generi
 c. It is a vast generalization of the i.i.d. Gaussian design typically con
 sidered in the theoretical literature\, and is motivated by the fact that 
 real data often have a complex correlation structure so that methods relyi
 ng on i.i.d. assumptions can be highly suboptimal. Building on the paradig
 m of spectrally-initialized iterative optimization\, this paper proposes o
 ptimal spectral estimators and combines them with an approximate message p
 assing (AMP) algorithm\, establishing rigorous performance guarantees for 
 these two algorithmic steps. Both the spectral initialization and the subs
 equent AMP meet existing conjectures on the fundamental limits to estimati
 on -- the former on the optimal sample complexity for efficient weak recov
 ery\, and the latter on the optimal errors. Numerical experiments suggest 
 the effectiveness of our methods and accuracy of our theory beyond orthogo
 nally invariant data.\nBased on joint work with Hong Chang Ji\, Ramji Venk
 ataramanan and Marco Mondelli. 
LOCATION:MR5\, CMS Pavilion A
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