1. The sample complexity of confidence. In lecture we saw that in order to learn a class of VC-dimension d with confidence 1- and error bounded by e, it is sufficient to find 0() (dlog log })) examples. We also saw that 9(d/e) examples were necessary to guarantee an error rate ofe with confidence 1-50 for some constant > 0, In this problem we will extend this lower bound to include a dependence on a representation h that is consistent with when we wish to learn to arbitrarily high confidence 1- (a) Show that for any class of VC-dimension at least 2, ( log examples are necesssary for an algorithm to identify a representation that has error at most e with probability at least 1-5 1. The sample complexity of confidence. In lecture we saw that in order to learn a class of VC-dimension d with confidence 1- and error bounded by e, it is sufficient to find 0() (dlog log })) examples. We also saw that 9(d/e) examples were necessary to guarantee an error rate ofe with confidence 1-50 for some constant > 0, In this problem we will extend this lower bound to include a dependence on a representation h that is consistent with when we wish to learn to arbitrarily high confidence 1- (a) Show that for any class of VC-dimension at least 2, ( log examples are necesssary for an algorithm to identify a representation that has error at most e with probability at least 1-5