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The aggregation problems in learning theory

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Given a finite class F of functions there are three aggregation problems: 1) the problem of Model Selection aggregation: construct a procedure having a risk as close as possible to the best element in F, 2) the problem of Convex aggregation: construct a procedure having a risk as close as possible to the best element in the convex hull of F, 3) the problem of Linear aggregation: construct a procedure having a risk as close as possible to the best element in the linear span of F.

We will prove that empirical risk minimization is optimal for the Convex and Linear aggregation problems but sub-optimal for the Model Selection aggregation problem. Then we will construct an optimal aggregation procedure for the Model Selection aggregation.

This talk is part of the Statistics series.

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