# The Nature of Statistical Learning Theory

@inproceedings{Vapnik2000TheNO, title={The Nature of Statistical Learning Theory}, author={Vladimir Naumovich Vapnik}, booktitle={Statistics for Engineering and Information Science}, year={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 learning algorithms what is important in learning theory?.Â

## 39,505 Citations

### Introduction to Statistical Learning Theory

- Computer ScienceAdvanced Lectures on Machine Learning
- 2003

This tutorial introduces the techniques that are used to obtain results in the form of so-called error bounds in statistical learning theory.

### The key theorem of learning theory about examples corrupted by noise

- Computer ScienceProceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826)
- 2004

This work gives the key theorem when the outputs are corrupted by noise, i.e. noise-free case, and investigates the conditions for consistency of the learning processes based on the empirical risk minimization induction principle.

### The bounds of learning processes on possibility space

- Computer Science2005 International Conference on Machine Learning and Cybernetics
- 2005

The bounds of the learning processes on possibility space are discussed, the rate of relative uniform convergence is estimated, and the relation between the rates of convergence and the capacity of a set of function is pointed out.

### Foundations of Statistical Learning and Model Selection

- Biology
- 2015

What the reader should know to understand this chapter \(\bullet \) Basic notions of machine learning. \(\bullet \) Notions of calculus. \(\bullet \) Chapter 5.

### Bounds on the rate of uniform convergence of learning processes with equality-expect noise samples on quasi-probability space

- Computer Science2009 International Conference on Machine Learning and Cybernetics
- 2009

The bounds on the rate of uniform convergence of learning processes when samples are corrupted by equality-expect noise on quasi-probability space are dealt with.

### Online Methods in Learning Theory

- Computer Science
- 2004

Predictive error bounds for the Bayes mixture and MDL with respect to a countable model class are presented and how assertions and improvements might be obtained for active learning are discussed.

### Qualitative Robustness of Bootstrap Approximations for Kernel Based Methods

- Mathematics
- 2013

The finite sample distribution of many nonparametric methods from statistical learning theory is unknown because the distribution P from which the data were generated is unknown and because thereâ€¦

### Statistical learning theory

- Computer Science
- 1998

Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.

### Statistical Learning Theory

- Computer Science
- 2007

Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.

### Learning Theory and Support Vector Machines - a primer

- Computer ScienceArXiv
- 2019

A brief introduction to the fundamentals of statistical learning theory, in particular the difference between empirical and structural risk minimization, including one of its most prominent implementations, i.e. the Support Vector Machine.

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