Aggregation via empirical risk minimization |
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Authors: | Guillaume Lecué Shahar Mendelson |
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Institution: | 1. Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT, 0200, Australia 2. Department of Mathematics, Technion, I.I.T, Haifa, 32000, Israel
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Abstract: | Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hull of a well chosen, empirically determined subset of F is an optimal aggregation method. |
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