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 explains the learning process from a statistical point of view.

VC theory is also referred to as statistical learning theory by Vapnik and his close colleagues.

VC theory covers 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?

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

References

• The Nature of Statistical Learning Theory, Vladimir Vapnik, Springer-Verlag, (1999), ISBN 0387987800
• Statistical Learning Theory, Vladimir Vapnik, Wiley-Interscience, (1998), ISBN 0471030031