Complexity Dimensions and Learnability

In machine learning theory, problem classes are distinguished because of di erences in complexity. In 6 , a stochastic model of learning from examples was introduced. This PAClearning model PAC = probably approximately correct re ects di erences in complexity of concept classes, i.e. very complex classes are not e ciently PAC-learnable. Blumer et al. 1 found, that e cient PAC-learnability depends on the size of the Vapnik Chervonenkis dimension  7  of a class. In Section 2 we will discuss this dimension and give an algorithm to compute it, in order to provide the reader with the intuitive idea behind it. In 3 a new, equivalent dimension is de ned for well-ordered classes. These well-ordered classes happen to satisfy a general condition, that is su cient for the possible construction of a number of equivalent dimensions. We will give this condition, as well as a generalized notion of an equivalent dimension. Also, a relatively e cient algorithm for the calculation of one such dimen...

• Type: Conference
• Year: 1993
• Where: ECML
• Authors: Shan-Hwei Nienhuys-Cheng, Mark Polman
• Keywords: Di Erences, ECML 1993, Equivalent Dimension, Machine Learning, Well-ordered Classes