Bounds of VC – Dimension

The VC dimension provides both upper and lower bounds on the number of training examples required to achieve a given level of accuracy. The upper bound on the number of training examples is logarithmic in the VC dimension, while the lower bound is linear.

The Vapnik-Chervonenkis (VC) dimension is a measure of the capacity of a hypothesis set to fit different data sets. It was introduced by Vladimir Vapnik and Alexey Chervonenkis in the 1970s and has become a fundamental concept in statistical learning theory. The VC dimension is a measure of the complexity of a model, which can help us understand how well it can fit different data sets.

The VC dimension of a hypothesis set H is the largest number of points that can be shattered by H. A hypothesis set H shatters a set of points S if, for every possible labeling of the points in S, there exists a hypothesis in H that correctly classifies the points. In other words, a hypothesis set shatters a set of points if it can fit any possible labeling of those points.