Question: PROBLEM 4.2: Suppose that our input space X' = Re and consider the hypothesis set d H = h: h(x) = sign Cixi for some

PROBLEM 4.2: Suppose that our input space X' = Re and consider the hypothesis set d H = h: h(x) = sign Cixi for some co, . . . Ca E Re i=0 In words, H is the set of classifiers obtained by evaluating some polynomial of degree d and com- paring the result to a threshold. Prove that the VC dimension of H is exactly d + 1 by showing that 1. There are d + 1 points which are shattered by 7. [Hint: Root placement.] 2. There are no d + 2 points which are shattered by H

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