Extended Robust Support Vector Machine Based on Financial Risk Minimization

Financial risk measures have been used recently in machine learning. For example, -support vector machine (-SVM) minimizes the conditional value at risk (CVaR) of margin distribution. The measure is popular in finance because of the subadditivity property, but it is very sensitive to a few outliers in the tail of the distribution. We propose a new classification method, extended robust SVM (ER-SVM), which minimizes an intermediate risk measure between the CVaR and value at risk (VaR) by expecting that the resulting model becomes less sensitive than -SVM to outliers. We can regard ER-SVM as an extension of robust SVM, which uses a truncated hinge loss. Numerical experiments imply the ER-SVM’s possibility of achieving a better prediction performance with proper parameter setting.

[1]  Akiko Takeda,et al.  ν-support vector machine as conditional value-at-risk minimization , 2008, ICML '08.

[2]  Shie Mannor,et al.  Risk sensitive robust support vector machines , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[3]  Takafumi Kanamori,et al.  A Unified Classification Model Based on Robust Optimization , 2013, Neural Computation.

[4]  Kristin P. Bennett,et al.  Duality and Geometry in SVM Classifiers , 2000, ICML.

[5]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[6]  Jason Weston,et al.  Trading convexity for scalability , 2006, ICML.

[7]  Keinosuke Fukunaga,et al.  Introduction to statistical pattern recognition (2nd ed.) , 1990 .

[8]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[9]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[10]  J. Paul Brooks,et al.  Support Vector Machines with the Ramp Loss and the Hard Margin Loss , 2011, Oper. Res..

[11]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[12]  Michael I. Jordan,et al.  A Robust Minimax Approach to Classification , 2003, J. Mach. Learn. Res..

[13]  Walter Briec,et al.  Minimum Distance to the Complement of a Convex Set: Duality Result , 1997 .

[14]  Bernhard Schölkopf,et al.  Extension of the nu-SVM range for classification , 2003 .

[15]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[16]  Yufeng Liu,et al.  Robust Truncated Hinge Loss Support Vector Machines , 2007 .

[17]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[18]  W. Wong,et al.  On ψ-Learning , 2003 .

[19]  Martha White,et al.  Relaxed Clipping: A Global Training Method for Robust Regression and Classification , 2010, NIPS.

[20]  Helmut Mausser,et al.  ALGORITHMS FOR OPTIMIZATION OF VALUE­ AT-RISK* , 2002 .

[21]  Stan Uryasev,et al.  Value-at-risk support vector machine: stability to outliers , 2013, Journal of Combinatorial Optimization.

[22]  Koby Crammer,et al.  Robust Support Vector Machine Training via Convex Outlier Ablation , 2006, AAAI.

[23]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[24]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[25]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[26]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[27]  David J. Crisp,et al.  A Geometric Interpretation of v-SVM Classifiers , 1999, NIPS.

[28]  David J. Crisp,et al.  A Geometric Interpretation of ?-SVM Classifiers , 1999, NIPS 2000.

[29]  Takafumi Kanamori,et al.  A Unified Robust Classification Model , 2012, ICML.