# A tutorial on support vector regression

```@article{Smola2004ATO,
title={A tutorial on support vector regression},
author={Alex Smola and Bernhard Sch{\"o}lkopf},
journal={Statistics and Computing},
year={2004},
volume={14},
pages={199-222}
}```
• Published 1 August 2004
• Computer Science
• Statistics and Computing
In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.
9,840 Citations

### Support Vector Selection for Regression Machines

• Computer Science
• 2009
The orthogonal least-squares method is adopted to evaluate the support vectors based on their error reduction ratios and a simpler model is obtained which helps avoid the over-fitting problem.

### A general formulation for support vector machines

• Computer Science
Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02.
• 2002
This paper derives a general formulation of support vector machines for classification and regression respectively as a patch of L/sub 1/ and L/ sub 2/ soft margin loss functions for classifier and soft insensitive loss function is introduced as the generalization of popular loss function for regression.

### Complex support vector regression

• Computer Science, Mathematics
2012 3rd International Workshop on Cognitive Information Processing (CIP)
• 2012
This work employs the recently presented Wirtinger's calculus on complex RKHS to compute the Lagrangian and derive the dual problem, and proves that this approach is equivalent with solving two real SVR problems exploiting a specific real kernel.

### Computing the Solution Path for the Regularized Support Vector Regression

• Computer Science, Mathematics
NIPS
• 2005
An algorithm is derived that computes the entire solution path of the support vector regression, with the same computational cost as fitting one SVR model, which allows convenient selection of the regularization parameter.

### Efficient Computation and Model Selection for the Support Vector Regression

• Mathematics
Neural Computation
• 2007
An algorithm is derived that computes the entire solution path of the support vector regression (SVR) and an unbiased estimate for the degrees of freedom of the SVR model is proposed, which allows convenient selection of the regularization parameter.

### Inference for Support Vector Regression under ℓ1 Regularization

• Mathematics, Computer Science
• 2021
This work provides large-sample distribution theory for support vector regression with l1-norm along with error bars for the SVR regression coefficients and proposes an alternative large- sample inference method based on the inversion of a novel test statistic that displays competitive power properties and does not depend on the choice of a tuning parameter.

### A Note on Least Squares Support Vector Machines

• Computer Science, Mathematics
• 2007
An improved conjugate gradient scheme is proposed for solving the optimization problems in LS-SVM, and an improved SMO algorithm is put forward for the general unconstrained quadratic programming problems which is the case of LS- SVM without the bias term.

### Optimal Selection of the Regression Kernel Matrix with Semidefinite Programming

• Computer Science
• 2004
Preliminary experimental results are presented for which the optimal kernel matrix for support vector machine regression is retrieved.

## References

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This tutorial gives an overview of the basic ideas underlying Support Vector machines for regression and function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.

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• Computer Science
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This paper connects this method to projected gradient methods and provides theoretical proofs for a version of decomposition methods and shows that this convergence proof is valid for general decomposition Methods if their working set selection meets a simple requirement.