Regression estimation with support vector learning machines

1 Support Vector Learning Machines (SVLM) have become an emerging technique which has proven successful in many traditionally neural network dominated applications. This is also the case for Regression Estimation (RE). In particular we are able to construct spline approximations of given data independently from the number of input-dimensions regarding complexity during training and with only linear complexity for reconstruction-compared to exponential complexity in conventional methods.

[1]  Adam W. Bojanczyk,et al.  On the stability of the Bareiss and related Toeplitz factorization algorithms , 2010, SIAM J. Matrix Anal. Appl..

[2]  Bernhard Schölkopf,et al.  Extracting Support Data for a Given Task , 1995, KDD.

[3]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[4]  I. J. Schoenberg.  Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions , 1988 .

[5]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[6]  Roy E. Marsten,et al.  On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming , 1992, SIAM J. Optim..

[7]  Isabelle Guyon,et al.  Automatic Capacity Tuning of Very Large VC-Dimension Classifiers , 1992, NIPS.

[8]  R. Fletcher.  Practical Methods of Optimization , 1988 .

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

[10]  G. Walter.  Wavelets and other orthogonal systems with applications , 1994 .

[11]  Arne Hole.  Vapnik-Chervonenkis Generalization Bounds for Real Valued Neural Networks , 1996, Neural Computation.

[12]  Dr. M. G. Worster.  Methods of Mathematical Physics , 1947, Nature.

[13]  Gerardo Toraldo,et al.  On the Solution of Large Quadratic Programming Problems with Bound Constraints , 1991, SIAM J. Optim..

[14]  Solla,et al.  Learning in linear neural networks: The validity of the annealed approximation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[15]  H. Akaike.  A new look at the statistical model identification , 1974 .

[16]  M. Aizerman,et al.  Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[17]  Alexander J. Smola,et al.  Support Vector Method for Function Approximation, Regression Estimation and Signal Processing , 1996, NIPS.

[18]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[19]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[20]  L. Ljung,et al.  Overtraining, Regularization, and Searching for Minimum in Neural Networks , 1992 .

[21]  Christopher M. Bishop,et al.  Current address: Microsoft Research, , 2022 .

[22]  Young K. Truong,et al.  Polynomial splines and their tensor products in extended linearmodeling , 1997 .

[23]  James R. Bunch,et al.  Stability of Methods for Solving Toeplitz Systems of Equations , 1985 .

[24]  A. Timan.  Theory of Approximation of Functions of a Real Variable , 1994 .

[25]  Shun-ichi Amari,et al.  Network information criterion-determining the number of hidden units for an artificial neural network model , 1994, IEEE Trans. Neural Networks.

[26]  Michael Unser,et al.  Fast B-spline Transforms for Continuous Image Representation and Interpolation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  J. Bunch,et al.  Some stable methods for calculating inertia and solving symmetric linear systems , 1977 .

[28]  Marek Karpinski,et al.  Polynomial bounds for VC dimension of sigmoidal neural networks , 1995, STOC '95.

[29]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[30]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[31]  Noboru Murata,et al.  An Integral Representation of Functions Using Three-layered Networks and Their Approximation Bounds , 1996, Neural Networks.

[32]  F. Hoog.  A new algorithm for solving Toeplitz systems of equations , 1987 .