Mirror averaging with sparsity priors

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 based on any prior distribution. This oracle inequality is applied in the context of sparse coding for different problems of statistics and machine learning such as regression, density estimation and binary classification.