What are the limitations of the null hypothesis?

Meaning of Union of hypothesis sets

• I have to define the VC dimension for the union of two hypothesis sets (H1 U H2) but I am having problems to visualize the meaning of the union of the hypothesis sets. For example, if H1 is a two dimensional perceptron and H2 is another two dimensional perceptron. What does it mean to have a hypothesis set H that is the union of H1 and H2 in this case. Can I use both H1 and H2 at same time. That is, am I able to use two lines in my classification algorithm.  If H1 contains {h11,h12,h13...h1n} hypothesis and H2 contains {h21,h22,h23,h2n} hypothesis, the union of H1 and H2 contains {h11,h12,h13,h1n,h21,h22,h23,h2n} hypothesis. In the 2d preceptron example, the union H1 U H2 contains more hypothesis but each hypothesis is of the same kind (a line in the plane). I do not see any difference between the union set and H1 and H2.  Need help to understand the meaning of union of hypothesis sets.

• Answer:

  A hypotheses set isn't a single classifier like a two-dimensional perceptron.  Instead, it's a class of classifiers, such as the class of all two-dimensional perceptrons.  For this problem, think of an algorithm that can output either a two-dimensional perceptron or an SVM from its training data.