dimension reduction - Yale University

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16 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

45 εμφανίσεις

Yale University


Yale School of

Public Health

Yale
School of Medicine

60 College Street

New Haven, CT


B I O S T A T I S T I C S

S E M I N A R



On hyperplane alignment
for linear

and nonlinear sufficient


dimension reduction




Bing Li
, Ph.D.

Professor

Department of
S
tatistics

Penn State
University





Tuesday, Novem
ber
9
, 20
1
0

4:15 P.M.

LEPH
115

60 COLLEGE ST.



ABSTRACT



We introduce a Hyperplane Alignment (HA) approach that can be used for both linear and
nonlinear suffici
ent dimension reduction. The basic idea is to divide the response variables
into slices and use a modified form of support vector machine to find the optimal hyperplanes
that separate them. These optimal hyperplanes are then
aligned by

the principal compon
ents
of their normal vectors. It is proved that the aligned normal vectors provide an unbiased, root
n
-
consistent, and asymptotically normal estimator of the sufficient dimension reduction space.
The method is then generalized to nonlinear sufficien
t dimen
sion reduction using the
reproducing kernel Hilbert space. In that context, th
e aligned normal vectors become
functions and it is proved that they are unbiased in the sense that they are functions of the true
nonlinear sufficient predictors. We compare HA
with other sufficient dimension reduction
methods by simulation and in real data analysis, and through both comparisons firmly
establish its practical advantages.


Authors:

Bing Li, Andreas Artemiou and Lexin Li