# An optimal unrestricted learning procedure

• Shahar Mendelson (Technion - Israel Institute of Technology; Australian National University)
• Friday 19 January 2018, 11:00-11:45
• Seminar Room 1, Newton Institute.

STSW01 - Theoretical and algorithmic underpinnings of Big Data

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 $E((\hat{f}(X)-Y)2|D) \leq \inf_{f \in F} E(f(X)-Y)2+r2$ with probability at least $1-2\exp(-cN \min\{1,r2/\sigma2\})$,
where $\sigma 2=\inf_{f \in F} E(f(X)-Y)^2$.

This talk is part of the Isaac Newton Institute Seminar Series series.