NDLI: Multi-parametric solution-path algorithm for instance-weighted support vector machines

Content Provider	Springer Nature Link
Author	Karasuyama, Masayuki Harada, Naoyuki Sugiyama, Masashi Takeuchi, Ichiro
Copyright Year	2012
Abstract	An instance-weighted variant of the support vector machine (SVM) has attracted considerable attention recently since they are useful in various machine learning tasks such as non-stationary data analysis, heteroscedastic data modeling, transfer learning, learning to rank, and transduction. An important challenge in these scenarios is to overcome the computational bottleneck—instance weights often change dynamically or adaptively, and thus the weighted SVM solutions must be repeatedly computed. In this paper, we develop an algorithm that can efficiently and exactly update the weighted SVM solutions for arbitrary change of instance weights. Technically, this contribution can be regarded as an extension of the conventional solution-path algorithm for a single regularization parameter to multiple instance-weight parameters. However, this extension gives rise to a significant problem that breakpoints (at which the solution path turns) have to be identified in high-dimensional space. To facilitate this, we introduce a parametric representation of instance weights. We also provide a geometric interpretation in weight space using a notion of critical region: a polyhedron in which the current affine solution remains to be optimal. Then we find breakpoints at intersections of the solution path and boundaries of polyhedrons. Through extensive experiments on various practical applications, we demonstrate the usefulness of the proposed algorithm.
Starting Page	297
Ending Page	330
Page Count	34
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	88
Issue Number	3
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2012-04-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Parametric programming Solution path Weighted support vector machines Computing Methodologies Control, Robotics, Mechatronics Language Translation and Linguistics Artificial Intelligence (incl. Robotics) Simulation and Modeling
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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