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SUMMARY: Theory for local optima of nonconvex high-dimensional M-estimator
 s - Po-Ling Loh\, University of Wisconsin - Madison
DTSTART:20180221T140000Z
DTEND:20180221T150000Z
UID:TALK100345@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:We survey a variety of recent results concerning local optima 
 of penalized M-estimators\, designed for high-dimensional regression probl
 ems. The nonconvexity is allowed to arise in either the loss function or t
 he regularizer. Although the overall landscape of the objective function i
 s nonconvex in high dimensions\, we show that both local and global optima
  are statistically consistent under appropriate conditions. Our theory is 
 applicable to settings involving errors-in-variables models and other cont
 aminated data scenarios. We also discuss statistical and optimization theo
 ry for nonconvex M-estimators suited for robust regression in high dimensi
 ons.
LOCATION:MR5 Centre for Mathematical Sciences
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