  We consider the problem of interaction neighborhood estimation from the
partial observation of a finite number of realizations of a random field. We
introduce a model selection rule to choose estimators of conditional
probabilities among natural candidates. Our main result is an oracle inequality
satisfied by the resulting estimator. We use then this selection rule in a
two-step procedure to evaluate the interacting neighborhoods. The selection
rule selects a small prior set of possible interacting points and a cutting
step remove from this prior set the irrelevant points. We also prove that the
Ising models satisfy the assumptions of the main theorems, without restrictions
on the temperature, on the structure of the interacting graph or on the range
of the interactions. It provides therefore a large class of applications for
our results. We give a computationally efficient procedure in these models. We
finally show the practical efficiency of our approach in a simulation study.
