PAC-Bayesian aggregation of linear estimators
Résumé
We consider the aggregation of linear estimator in regresison with a sub-Gaussian noise assumption. Aggregating estimators using exponential weights depending on their risk performs well in expectation, but sadly not in probability. A way to overcome this issue is considering exponential weights of a penalized risk. In this case, an oracle inequality can be obtained in probability, but is not sharp. Taking into account the estimated function's norm in the penalty offers a sharp inequality.
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