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Hui Zou, University of Minnesota

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"Another Look at DWD: Thrifty Algorithm and Bayes Risk Consistency in RKHS"
12 November 2015 from 4:00 PM to 5:00 PM
201 Thomas
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Hui ZouDistance weighted discrimination (DWD) is a margin-based classifier with an

interesting geometric motivation. DWD was originally proposed as a superior

alternative to the support vector machine (SVM), however DWD is yet to be

popular compared with the SVM. The main reasons are twofold. First, the

state-of-the-art algorithm for solving DWD is based on the second-order-cone

programming (SOCP), while the SVM is a quadratic programming problem

which is much more efficient to solve. Second, the current statistical theory

of DWD mainly focuses on the linear DWD for the

high-dimension-low-sample-size setting and data-piling, while the learning

theory for the SVM mainly focuses on the Bayes risk consistency of the

kernel SVM. In fact, the Bayes risk consistency of DWD is presented as an

open problem in the original DWD paper. In this work, we advance the

current understanding of DWD from both computational and theoretical

perspectives. We propose a novel efficient algorithm for solving DWD, and

our algorithm can be several hundred times faster than the existing

state-of-the-art algorithm based on the SOCP. In addition, our algorithm can

handle the generalized DWD, while the SOCP algorithm only works well for a

special DWD but not the generalized DWD. Furthermore, we consider a

natural kernel DWD in a reproducing kernel Hilbert space and then establish

the Bayes risk consistency of the kernel DWD. We compare DWD and the

SVM on several benchmark data sets and show that the two have

comparable classification accuracy, but DWD equipped with our new

algorithm can be much faster to compute than the SVM.

This is joint work with my student Boxiang Wang.


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