Support Vector Machines with Beta-Mixing Input Sequences

This note mainly focuses on a theoretical analysis of support vector machines with beta-mixing input sequences. The explicit bounds are derived on the rate at which the empirical means converge to their true values when the underlying process is beta-mixing. The uniform convergence approach is used to estimate the convergence rates of the support vector machine algorithms with beta-mixing inputs.

[1]  A. Dembo,et al.  A note on uniform laws of averages for dependent processes , 1993 .

[2]  A. A. Mullin,et al.  Principles of neurodynamics , 1962 .

[3]  V. Vapnik.  Estimation of Dependences Based on Empirical Data , 2006 .

[4]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[5]  Ding-Xuan Zhou,et al.  Learning Theory: From Regression to Classification , 2006 .

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

[7]  Mathukumalli Vidyasagar,et al.  Learning and Generalization: With Applications to Neural Networks , 2002 .

[8]  Tong Zhang.  Statistical behavior and consistency of classification methods based on convex risk minimization , 2003 .

[9]  Yiming Ying,et al.  Support Vector Machine Soft Margin Classifiers: Error Analysis , 2004, J. Mach. Learn. Res..

[10]  Yi Lin,et al.  Support Vector Machines and the Bayes Rule in Classification , 2002, Data Mining and Knowledge Discovery.

[11]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[12]  Ingo Steinwart,et al.  Support Vector Machines are Universally Consistent , 2002, J. Complex..

[13]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[14]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[15]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .

[16]  Felipe Cucker,et al.  On the mathematical foundations of learning , 2001 .

[17]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[18]  Bin Yu.  RATES OF CONVERGENCE FOR EMPIRICAL PROCESSES OF STATIONARY MIXING SEQUENCES , 1994 .

[19]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[20]  M. Vidyasagar,et al.  Rates of uniform convergence of empirical means with mixing processes , 2002 .

[21]  中澤 真,et al.  Devroye, L., Gyorfi, L. and Lugosi, G. : A Probabilistic Theory of Pattern Recognition, Springer (1996). , 1997 .

[22]  Christopher J. C. Burges,et al.  A Tutorial on Support Vector Machines for Pattern Recognition , 1998, Data Mining and Knowledge Discovery.

[23]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .