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CATEGORIES:Statistics
SUMMARY:Constrained low-rank matrix estimation - Lenka Zde
borova (IPhT)
DTSTART;TZID=Europe/London:20170512T160000
DTEND;TZID=Europe/London:20170512T170000
UID:TALK71960AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71960
DESCRIPTION:Low-rank matrix factorization is one of the basic
methods used in data analysis for unsupervised lea
rning of relevant features and other types of dime
nsionality reduction. We present a framework to st
udy the constrained low-rank matrix estimation for
a general prior on the factors\, and a general ou
tput channel through which the matrix is observed.
We draw a parallel with the study of vector-spin
glass models - presenting a unifying way to study
a number of inference and learning problems consid
ered previously in separate works. We consider a p
robabilistic model of constrained low-rank matrix
estimation where the factors are drawn uniformly a
t random. This is closely related to the popular s
piked covariance model that is used to model for i
nstance sparse PCA. We present a generic methodolo
gy coming from statistical physics that leads to a
closed formula for the minimum-mean-squared error
achievable in this model. We also present the cor
responding approximate message passing algorithms
and locate a region of parameters for which this a
lgorithms achieves the optimal performance. We dis
cuss intuition on computational hardness of the co
mplementary region. Our analysis also provides re
sults and insight on performance of commonly used
spectral algorithms.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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