# Support Vector Machines for Regression

“The Support Vector method can also be applied to the case of regression, maintaining all the main features that characterise the maximal margin algorithm: a non-linear function is learned by a linear learning machine in a kernel-induced feature space while the capacity of the system is controlled by a parameter that does not depend on the dimensionality of the space.”

Cristianini and Shawe-Taylor (2000)

“In SVM the basic idea is to map the data x into a high-dimensional feature space F via a nonlinear mapping ?, and to do linear regression in this space (cf. Boser et al. (1992); Vapnik (1995)).”

M?uller et al.

## Most Cited

- SMOLA, Alex J. and Bernhard SCHÖLKOPF, A Tutorial on Support Vector Regression, 1998. [Cited by 309]
- GUNN, S., Support Vector Machines for Classification and Regression, ISIS Technical Report, 1998. [Cited by 164]
- COLLOBERT, R and S BENGIO, SVMTorch: Support Vector Machines for Large-Scale Regression Problems, Journal of Machine Learning Research, 2001. [Cited by 154]

## Bibliography

- CAO, Lijuan, Support vector machines experts for time series forecasting

“The simulation shows that the SVMs experts achieve significant improvement in the generalization performance in comparison with the single SVMs models. In addition, the SVMs experts also converge faster and use fewer support vectors.”

Cao (2002) - COLLOBERT, R and S BENGIO, SVMTorch: Support Vector Machines for Large-Scale Regression Problems, Journal of Machine Learning Research, 2001. [Cited by 154]
- DENIS, François and Rémi GILLERON, PAC Learning under Helpful Distributions

Denis and Gilleron - DRUCKER, H., CJC BURGES, L KAUFMAN, AJ SMOLA, V Support Vector Regression Machines, NIPS, 1996. [Cited by 95]
- FERNÁNDEZ, Rodrigo, Predicting Time Series with a Local Support Vector Regression Machine
- GAO, J.B., S.R. GUNN and C.J. HARRIS, Mean field method for the support vector machine regression

This paper deals with two subjects. First, we will show how support vector machine (SVM) regression problem can be solved as the maximum a posteriori prediction in the Bayesian framework. The second part describes an approximation technique that is useful in performing calculations for SVMs based on the mean field algorithm which was originally proposed in Statistical Physics of disordered systems. One advantage is that it handle posterior averages for Gaussian process which are not analytically tractable.”

Gao, Gunn and Harris (2002) - GUNN, S., Support Vector Machines for Classification and Regression, ISIS Technical Report, 1998. [Cited by 164]
- HARLAND, Zac, Using Support Vector Machines to Trade Aluminium on the LME.

“This paper describes and evaluates the use of support vector regression to trade the three month Aluminium futures contract on the London Metal Exchange, over the period June 1987 to November 1999. The Support Vector Machine is a machine learning method for classification and regression and is fast replacing neural networks as the tool of choice for prediction and pattern recognition tasks, primarily due to their ability to generalise well on unseen data. The algorithm is founded on ideas derived from statistical learning theory and can be understood intuitively within a geometric framework. In this paper we use support vector regression to develop a number of trading submodels that when combined, result in a final model that exhibits above-average returns on out of sample data, thus providing some evidence that the aluminium futures price is less than efficient. Whether these inefficiencies will continue into the future is unknown.”

Harland - HONG, Dug Hun, Changha HWANG, Support vector fuzzy regression machines

“Support vector machine (SVM) has been very successful in pattern recognition and function estimationproblems. In this paper,we introduce the use of SVM for multivariate fuzzy linear and nonlinear regression models. Using the basic idea underlying SVM for multivariate fuzzy regressions gives computational efficiency of getting solutions.”

Hong and Hwang - MÜLLER, K.-R., et al. Using Support Vector Machines for Time Series Prediction

“Support Vector Machines are used for time series prediction and compared to radial basis function networks. We make use of two different cost functions for Support Vectors: training with (i) an [epsilon] insensitive loss and (ii) Huber’s robust loss function and discuss how to choose the regularization parameters in these models. Two applications are considered: data from (a) a noisy Mackey-Glass system (normal and uniform noise) and (b) the Santa Fe Time Series Competition (set D). In both cases, Support Vector Machines show an excellent performance. In case (b), the Support Vector approach improves the best known result on the benchmark by 29%.”Muller et al. (2000) - MÜLLER, K.-R., et al. Predicting Time Series with Support Vector Machines

Muller et al. (1997) - MOORE, Andrew W., Predicting Real-valued outputs: an introduction to Regression
- MUKHERJEE, Sayan, Edgar OSUNA and Federico GIROSI, Nonlinear Prediction of Chaotic Time Series Using Support Vector Machines

Mukherjee, Osuna and Girosi (1997) - PONTIL, Massimiliano, Ryan RIFKIN and Theodoros EVGENIOU, From Regression to Classification in Support Vector Machines
- PONTIL, Massimiliano, Sayan MUKHERJEE and Federico GIROSI, On the Noise Model of Support Vector Machines Regression
- PONTIL, Massimiliano, Sayan MUKHERJEE and Federico GIROSI, On the Noise Model of Support Vector Machine Regression

Pontil, Mukherjee and Girosi (1998) - RAKOTOMAMONJY, Alain and Stéphane CANU, Frame, Reproducing Kernel, Regularization and Learning

Rakotomamonjy and Canu - SCHÖLKOPF, B., et al., Support Vector Regression with Automatic Accuracy Control

Sch olkopf et al. - SMOLA, Alex J. and Bernhard SCHÖLKOPF, A Tutorial on Support Vector Regression

Smola and Scholkopf (1998) [Cited by 309] - TAY, Francis E.H. and L.J. CAO, Modi ed support vector machines in nancial time series forecasting

Tay and Cao (2002) - TAY, Francis E.H. and Lijuan CAO, Application of support vector machines in financial time series forecasting

Tay and Cao (2001) - TRAFALIS, Theodore B. and Huseyin INCE, Support Vector Machine for Regression and Applications to Financial Forecasting

Trafalis and Ince (2000) - VERRI, Alessandro, Support Vector Machines for Regression

- CAO, Lijuan, Support vector machines experts for time series forecasting

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