Abstract

The question of prediction is of central importance in Statistical Learning Theory. The optimal tradeoff between accuracy and confidence and the identity of a procedure that attains that optimal tradeoff have been studied extensively over the years.

In this talk I present some of ideas used in the recent solution of this problem: a procedure $\hat{f}$ that attains the best possible accuracy/confidence tradeoff for a triplet $(F,X,Y)$ consisting of an arbitrary class $F$, an unknown distribution $X$ and an unknown target $Y$.

Specifically, I explain why under minimal assumptions on $(F,X,Y)$, there is a natural critical level $r^{$ that depends on the triplet and the sample size $N$, such that for any accuracy parameter $r>r}$, one has $E((\hat{f}(X)-Y)^{2|D) \leq \inf_{f \in F} E(f(X)-Y)}2+r^{2$ with probability at least $1-2\exp(-cN \min\{1,r}2/\sigma^{2\})$,
where $\sigma}2=\inf_{f \in F} E(f(X)-Y)^2$.