A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Large Scale Kernel Regression via Linear Programming
Machine Learning
Applying the Bayesian Evidence Framework to \nu -Support Vector Regression
EMCL '01 Proceedings of the 12th European Conference on Machine Learning
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
A tutorial on support vector regression
Statistics and Computing
Multiple kernel learning, conic duality, and the SMO algorithm
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A tutorial on ν-support vector machines: Research Articles
Applied Stochastic Models in Business and Industry - Statistical Learning
Neural Computation
Dual /spl nu/-support vector machine with error rate and training size biasing
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 200. on IEEE International Conference - Volume 02
The evidence framework applied to classification networks
Neural Computation
ν-support vector machine as conditional value-at-risk minimization
Proceedings of the 25th international conference on Machine learning
Infinite kernel learning via infinite and semi-infinite programming
Optimization Methods & Software - The International Conference on Engineering Optimization (EngOpt 2008)
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Multiple Kernel Learning Algorithms
The Journal of Machine Learning Research
Measuring financial risk with generalized asymmetric least squares regression
Applied Soft Computing
The evidence framework applied to support vector machines
IEEE Transactions on Neural Networks
Support vector regression based on data shifting
Neurocomputing
Robust ν-support vector machine based on worst-case conditional value-at-risk minimization
Optimization Methods & Software
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Statistical learning theory provides the justification of the @e-insensitive loss in support vector regression, but suggests little guidance on the determination of the critical hyper-parameter @e. Instead of predefining @e, @n-support vector regression automatically selects @e by making the percent of deviations larger than @e be asymptotically equal to @n. In stochastic programming terminology, the goal of @n-support vector regression is to minimize the conditional Value-at-Risk measure of deviations, i.e. the expectation of the larger @n-percent deviations. This paper tackles the determination of the critical hyper-parameter @n in @n-support vector regression when the error term follows a complex distribution. Instead of one singleton @n, the paper assumes @n to be a combination of multiple, finite or infinite, candidate choices. Thus, the cost function becomes a weighted sum of component conditional value-at-risk measures associated with these base @ns. This paper shows that this cost function can be represented with a spectral risk measure and its minimization can be reformulated to a linear programming problem. Experiments on three artificial data sets show that this multiple-@n support vector regression has great advantage over the classical @n-support vector regression when the error terms follow mixed polynomial distributions. Experiments on 10 real-world data sets also clearly demonstrate that this new method can achieve better performance than @e-support vector regression and @n-support vector regression.