Is there any relation between regularization and the VC dimension?

Basically it says that with regularization (augmented error) the VC dimension does not change, so it proposes to use of the effective number of parameters as a good surrogate for the VC dimension.

What the VC dimension is and what is the relation between VC dimension and break point?

Definition [VC Dimension] dVC = k∗ − 1. The VC dimension is the largest N which can be shattered (mH(N)=2N). N ≤ dVC: H could shatter your data (H can shatter some N points). N>dVC: N is a break point for H; H cannot possibly shatter your data.

What is the VC dimension of a finite hypothesis space?

The VC-dimension of a hypothesis space H is the cardinality of the largest set S that can be shattered by H. Fact: If H is finite, then VCdim H log |H|. If the VC-dimension is d, that means there exists a set of d points that can be shattered, but there is no set of d+1 points that can be shattered.

Can VC dimension be infinite?

The VC-dimension of the set of classifiers that output the sign of a sine wave parametrized by a single parameter (the angular frequency of the sine wave) is infinite.

What is the VC-dimension of a finite hypothesis space?

What is the VC-dimension of H?

3
The VC dimension of H here is 3 even though there may be sets of size 3 that it cannot shatter.

What does VC dimension measure?

In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the capacity (complexity, expressive power, richness, or flexibility) of a set of functions that can be learned by a statistical binary classification algorithm.

What is the VC dimension of a neural network?

Not surprisingly, the VC-dimension of a neural network is related to the number of training examples that are needed in order to train N to compute—or approximate—a specific target function h : D → {0, 1}.

How do you prove VC dimension is infinite?

The VC dimension is infinite if for all m, there is a set of m examples shattered by H. Usually, one considers a set of points in “general position” and shows that they can be shattered. This avoids issues like collinear points for a linear classifier.

What is VC dimension how it is used?

What is VC dimension of Perceptron?

The VC dimension of a perceptron is dVC = d + 1.

Why VC dimension is important for machine learning?

VC dimension is useful in formal analysis of learnability, however. This is because VC dimension provides an upper bound on generalization error. So if we have some notion of how many generalization errors are possible, VC dimension gives an indication of how many could be made in any given context.