Table of Contents
What is shattering in machine learning?
Shattering. Definition: A set S of examples is shattered by a set of functions. H if for every partition of the examples in S into positive and. negative examples there is a function in H that gives exactly. these labels to the examples.
What is the VC dimension of neural networks?
For an ordinary neural network, the VC dimension is roughly equal to the number of weights. Let’s start with the representation of a learning problem. Let’s assume we are looking at a classification task with 2 labels – “+” and “-“.
How do you read VC dimensions?
The VC dimension of is the largest number of distinct points, placed at positions of your choosing, such that every possible labeling of the points can be feasibly classified with zero training error. The VC dimension is therefore one method of describing how complex a model is.
What is Vapnik Chervonenkis dimension how is it calculated?
The VC dimension of a class H is defined as the size of the largest set A that H can shatter. H shatters a set A if for every subset B of A, there exists an element h in H such that B is equal to the intersection of h with A.
What does VC dimension illustrate?
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. A much simpler alternative is to threshold a linear function.
What is the VC dimension of the class of circle in a 4 dimensional plane?
The VC dimension is the maximum number of points that can be shattered. {(5,2), (5,4), (5,6)} cannot be shattered by circles, but {(5,2), (5,4), (6,6)} can be shattered by circles, so the VC dimension is at least 3. Proving that it is exactly 3 is harder. There is a technical point here related to Qnan’s answer.
What do you mean by VC dimension?
The VC dimension of a classifier is defined by Vapnik and Chervonenkis to be the cardinality (size) of the largest set of points that the classification algorithm can shatter [1].
What is the VC dimension of a convex classifier?
Any subset of the points are the vertices of a convex polygon. Clearly that polygon will not contain any of the points not in the subset. This shows that we can shatter arbitrarily large sets, so the VC-dimension is infinite.
What is the purpose of VC dimension?
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.
Why is VC dimension important?
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.
What is shatter in VC dimension?
Shattering a set of points In order to have a VC dimension of at least N, a classifier must be able to shatter a single configuration of N points. For a configuration of N points, there are 2^N possible assignments of positive or negative, so the classifier must be able to properly separate the points in each of these.
What is the VC dimension of circles?
2 Answers. The VC dimension is the maximum number of points that can be shattered. {(5,2), (5,4), (5,6)} cannot be shattered by circles, but {(5,2), (5,4), (6,6)} can be shattered by circles, so the VC dimension is at least 3.