Everything about Statistical Learning totally explained
Vapnik-Chervonenkis theory (also known as
VC theory) was developed during 1960-1990 by
Vladimir Vapnik and
Alexey Chervonenkis. The theory is a form of
computational learning theory, which attempts to explain the learning process from a statistical point of view.
VC theory is related to
statistical learning theory and to
empirical processes.
Richard M. Dudley and
Vladimir Vapnik himself, among others, apply VC-theory to
empirical processes.
VC theory covers at least four parts (as explained in
The Nature of Statistical Learning Theory):
- Theory of consistency of learning processes
- What are (necessary and sufficient) conditions for consistency of a learning process based on the empirical risk minimization principle ?
- Nonasymptotic theory of the rate of convergence of learning processes
- How fast is the rate of convergence of the learning process?
- Theory of controlling the generalization ability of learning processes
- How can one control the rate of convergence (the generalization ability) of the learning process?
- Theory of constructing learning machines
- How can one construct algorithms that can control the generalization ability?
In addition, VC theory and
VC dimension are instrumental in the theory of
empirical processes, in the case of processes indexed by VC classes.
The last part of VC theory introduced a well-known learning algorithm: the
support vector machine.
VC theory contains important concepts such as the
VC dimension and
structural risk minimization. This theory is related to mathematical subjects such as:
reproducing kernel Hilbert spaces
regularization networks
kernels
empirical processesFurther Information
Get more info on 'Statistical Learning'.
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