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SUMMARY:Boosting in the presence of outliers: adaptive classification with
  non-convex loss functions - Jelena Bradic (UC San Diego)
DTSTART:20151211T160000Z
DTEND:20151211T170000Z
UID:TALK60705@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:This paper examines the role and efficiency of the non-convex 
 loss functions for binary classification problems. In particular\, we inve
 stigate how to design a simple and effective boosting algorithm that is ro
 bust to the outliers in the data. The analysis of the role of a particular
  non-convex loss for prediction accuracy varies depending on the diminishi
 ng tail properties of the gradient of the loss -- the ability of the loss 
 to efficiently adapt to the outlying data\, the local convex properties of
  the loss and the proportion of the contaminated data. In order to use the
 se properties efficiently\, we propose a new family of non-convex losses n
 amed γ-robust losses. Moreover\, we present a new boosting framework\, {\
 \it Arch Boost}\, designed for augmenting the existing work such that its 
 corresponding classification algorithm is significantly more adaptable to 
 the unknown data contamination. Along with the Arch Boosting framework\, t
 he non-convex losses lead to the new class of boosting algorithms\, named 
 adaptive\, robust\, boosting (ARB). Furthermore\, we present theoretical e
 xamples that demonstrate the robustness properties of the proposed algorit
 hms. In particular\, we develop a new breakdown point analysis and a new i
 nfluence function analysis that demonstrate gains in robustness. Moreover\
 , we present new theoretical results\, based only on local curvatures\, wh
 ich may be used to establish statistical and optimization properties of th
 e proposed Arch boosting algorithms with highly non-convex loss functions.
  Extensive numerical calculations are used to illustrate these theoretical
  properties and reveal advantages over the existing boosting methods when 
 data exhibits a number of outliers.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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