Mirror averaging with sparsity priors

Understand

We consider the problem of aggregating the elements of a possibly infinite dictionary for building a decision procedure that aims at minimizing a given criterion.

• Along with the dictionary, an independent identically distributed training sample is available, on which the performance of a given procedure can be tested.
• In a fairly general set-up, we establish an oracle inequality for the Mirror Averaging aggregate with any prior distribution.
• By choosing an appropriate prior, we apply this oracle inequality in the context of prediction under sparsity assumption for the problems of regression with random design, density estimation and binary classification.