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SUMMARY:Nonlinear Models for Matrix Completion - Rebecca Willett (Universi
 ty of Wisconsin-Madison)
DTSTART:20180117T110000Z
DTEND:20180117T114500Z
UID:TALK97723@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The past decade of research on matrix completion has shown it 
 is possible to leverage linear dependencies to impute missing values in a 
 low-rank matrix. However\, the corresponding assumption that the data lies
  in or near a low-dimensional linear subspace is not always met in practic
 e. Extending matrix completion theory and algorithms to exploit low-dimens
 ional nonlinear structure in data will allow missing data imputation in a 
 far richer class of problems. In this talk\, I will describe several model
 s of low-dimensional nonlinear structure and how these models can be used 
 for matrix completion. In particular\, we will explore matrix completion i
 n the context of three different nonlinear models: single index models\, i
 n which a latent subspace model is transformed by a nonlinear mapping\; un
 ions of subspaces\, in which data points lie in or near one of several sub
 spaces\; and nonlinear algebraic varieties\, a polynomial generalization o
 f classical linear subspaces. In these settings\, we will explore novel an
 d efficient algorithms for imputing missing values and new bounds on the a
 mount of missing data that can be accurately imputed. The proposed algorit
 hms are able to recover synthetically generated data up to predicted sampl
 e complexity bounds and outperform standard low-rank matrix completion in 
 experiments with real recommender system and motion capture data.
LOCATION:Seminar Room 1\, Newton Institute
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