  Inspired by Kalikow-type decompositions, we introduce a new stochastic model
of infinite neuronal networks, for which we establish sharp oracle inequalities
for Lasso methods and restricted eigenvalue properties for the associated Gram
matrix with high probability. These results hold even if the network is only
partially observed. The main argument rely on the fact that concentration
inequalities can easily be derived whenever the transition probabilities of the
underlying process admit a sparse space-time representation.
