Maximum Likelihood Estimation
نویسنده
چکیده
1 Summary of Lecture 12 In the last lecture we derived a risk (MSE) bound for regression problems; i.e., select an f ∈ F so that E[(f(X)− Y )]− E[(f∗(X)− Y )] is small, where f∗(x) = E[Y |X = x]. The result is summarized below. Theorem 1 (Complexity Regularization with Squared Error Loss) Let X = R, Y = [−b/2, b/2], {Xi, Yi}i=1 iid, PXY unknown, F = {collection of candidate functions}, f : R → Y, R(f) = E[(f(X)− Y )]. Let c(f), f ∈ F , be positive numbers satisfying ∑ f∈F 2 −c(f) ≤ 1, and select a function from F according to
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