  Consider a regression model with fixed design and Gaussian noise where the
regression function can potentially be well approximated by a function that
admits a sparse representation in a given dictionary. This paper resorts to
exponential weights to exploit this underlying sparsity by implementing the
principle of sparsity pattern aggregation. This model selection take on sparse
estimation allows us to derive sparsity oracle inequalities in several popular
frameworks, including ordinary sparsity, fused sparsity and group sparsity. One
striking aspect of these theoretical results is that they hold under no
condition in the dictionary. Moreover, we describe an efficient implementation
of the sparsity pattern aggregation principle that compares favorably to
state-of-the-art procedures on some basic numerical examples.
