Problem 3 (Problem 2.18 in the textbook) (25 pt) The VC dimension of the perceptron hypothesis set corresponds to the number of parameters (wo, wi,... .wa) of the set, and this observation is usually true for other hypothesis sets. However, we will present a counter-example here. Prove that the following hypothesis set for ER has an infinite VC dimension: H =a l ha(z) = (-1)lar] , where a E R} where LAJ is the biggest integer S A (the floor function). This hypothesis has only one parameter a but enjoys an infinite VC dimension. Hint: Consr, .,^v, where n 10" and show how to implement an arbitrary dichotomy , HN-] Problem 3 (Problem 2.18 in the textbook) (25 pt) The VC dimension of the perceptron hypothesis set corresponds to the number of parameters (wo, wi,... .wa) of the set, and this observation is usually true for other hypothesis sets. However, we will present a counter-example here. Prove that the following hypothesis set for ER has an infinite VC dimension: H =a l ha(z) = (-1)lar] , where a E R} where LAJ is the biggest integer S A (the floor function). This hypothesis has only one parameter a but enjoys an infinite VC dimension. Hint: Consr, .,^v, where n 10" and show how to implement an arbitrary dichotomy , HN-]