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CATEGORIES:Statistics
SUMMARY:Boosting in the presence of outliers: adaptive cla
ssification with non-convex loss functions - Jelen
a Bradic (UC San Diego)
DTSTART;TZID=Europe/London:20151211T160000
DTEND;TZID=Europe/London:20151211T170000
UID:TALK60705AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60705
DESCRIPTION:This paper examines the role and efficiency of the
non-convex loss functions for binary classificati
on problems. In particular\, we investigate how to
design a simple and effective boosting algorithm
that is robust to the outliers in the data. The an
alysis of the role of a particular non-convex loss
for prediction accuracy varies depending on the d
iminishing tail properties of the gradient of the
loss -- the ability of the loss to efficiently ada
pt to the outlying data\, the local convex propert
ies of the loss and the proportion of the contamin
ated data. In order to use these properties effici
ently\, we propose a new family of non-convex loss
es named γ-robust losses. Moreover\, we present a
new boosting framework\, {\\it Arch Boost}\, desig
ned for augmenting the existing work such that its
corresponding classification algorithm is signifi
cantly more adaptable to the unknown data contamin
ation. Along with the Arch Boosting framework\, th
e non-convex losses lead to the new class of boost
ing algorithms\, named adaptive\, robust\, boostin
g (ARB). Furthermore\, we present theoretical exam
ples that demonstrate the robustness properties of
the proposed algorithms. In particular\, we devel
op a new breakdown point analysis and a new influe
nce function analysis that demonstrate gains in ro
bustness. Moreover\, we present new theoretical re
sults\, based only on local curvatures\, which may
be used to establish statistical and optimization
properties of the proposed Arch boosting algorith
ms with highly non-convex loss functions. Extensiv
e numerical calculations are used to illustrate th
ese theoretical properties and reveal advantages o
ver the existing boosting methods when data exhibi
ts a number of outliers.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge.
CONTACT:Quentin Berthet
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