Statistical Properties and Adaptive Tuning of Support Vector Machines

@article{Lin2002StatisticalPA,
  title={Statistical Properties and Adaptive Tuning of Support Vector Machines},
  author={Yi Lin and Grace Wahba and Hao Zhang and Yoonkyung Lee},
  journal={Machine Learning},
  year={2002},
  volume={48},
  pages={115-136}
}
In this paper we consider the statistical aspects of support vector machines (SVMs) in the classification context, and describe an approach to adaptively tuning the smoothing parameter(s) in the SVMs. The relation between the Bayes rule of classification and the SVMs is discussed, shedding light on why the SVMs work well. This relation also reveals that the misclassification rate of the SVMs is closely related to the generalized comparative Kullback-Leibler distance (GCKL) proposed in Wahba… 

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References

SHOWING 1-10 OF 21 REFERENCES

Support Vector Machines and the Bayes Rule in Classification

  • Yi Lin
  • Computer Science
    Data Mining and Knowledge Discovery
  • 2004
It is shown that the asymptotic target of SVMs are some interesting classification functions that are directly related to the Bayes rule, and helps understand the success of SVM in many classification studies, and makes it easier to compare SVMs and traditional statistical methods.

Advances in kernel methods: support vector learning

Support vector machines for dynamic reconstruction of a chaotic system, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel.

A training algorithm for optimal margin classifiers

A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of the classification functions,

Support-Vector Networks

High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.

Knowledge-based analysis of microarray gene expression data by using support vector machines.

A method of functionally classifying genes by using gene expression data from DNA microarray hybridization experiments, based on the theory of support vector machines (SVMs), to predict functional roles for uncharacterized yeast ORFs based on their expression data is introduced.

Asymptotic Analysis of Penalized Likelihood and Related Estimators

A general approach to the first order asymptotic analysis ofpenalized likelihood and related estimators is described. The method gives expansions for the systematic and random error. Asymptotic

The Nature of Statistical Learning Theory

  • V. Vapnik
  • Computer Science
    Statistics for Engineering and Information Science
  • 2000
Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing

A Sparse Representation for Function Approximation

We derive a new general representation for a function as a linear combination of local correlation kernels at optimal sparse locations (and scales) and characterize its relation to principal

Construction and Assessment of Classification Rules

We may not be able to make you love reading, but construction and assessment of classification rules will lead you to love reading starting from now. Book is the window to open the new world. The

A Tutorial on Support Vector Machines for Pattern Recognition

The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, w...