Question

1. Overfitting of polynomial matching: We have shown that the predictor defined in Equation (2.3) leads to overfitting. While this predictor seems to be very unnatural, the goal of this exercise is to show that it can be described as a thresholded polynomial. That is, show that given a training set S {(Xi ,f(x;)))? C (Rd × {0. Î})", there exists a polynomial Ps such that hs(x) = 1 if and only if Ps(x) 〉 0, where hs is as defined in Equation (2.3) It follows that learning the class of all thresholded polynomials using the ERM rule may lead to overfitting. 0 otherwise. (2.3)

Answer 1

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