BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Constrained low-rank matrix estimation - Lenka Zdeborova (IPhT)
DTSTART:20170512T150000Z
DTEND:20170512T160000Z
UID:TALK71960@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:Low-rank matrix factorization is one of the basic methods used
  in data analysis for unsupervised learning of relevant features and other
  types of dimensionality reduction. We present a framework to study the co
 nstrained low-rank matrix estimation for a general prior on the factors\, 
 and a general output channel through which the matrix is observed. We draw
  a parallel with the study of vector-spin glass models - presenting a unif
 ying way to study a number of inference and learning problems considered p
 reviously in separate works. We consider a probabilistic model of constrai
 ned low-rank matrix estimation where the factors are drawn uniformly at ra
 ndom. This is closely related to the popular spiked covariance model that 
 is used to model for instance sparse PCA. We present a generic methodology
  coming from statistical physics that leads to a closed formula for the mi
 nimum-mean-squared error achievable in this model. We also present the cor
 responding approximate message passing algorithms and locate a region of p
 arameters for which this algorithms achieves the optimal performance. We d
 iscuss intuition on computational hardness of the complementary region.  O
 ur analysis also provides results and insight on performance of commonly u
 sed spectral algorithms.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
END:VEVENT
END:VCALENDAR