  A crucial assumption in most statistical learning theory is that samples are
independently and identically distributed (i.i.d.). However, for many real
applications, the i.i.d. assumption does not hold. We consider learning
problems in which examples are dependent and their dependency relation is
characterized by a graph. To establish algorithm-dependent generalization
theory for learning with non-i.i.d. data, we first prove novel McDiarmid-type
concentration inequalities for Lipschitz functions of graph-dependent random
variables. We show that concentration relies on the forest complexity of the
graph, which characterizes the strength of the dependency. We demonstrate that
for many types of dependent data, the forest complexity is small and thus
implies good concentration. Based on our new inequalities we are able to build
stability bounds for learning from graph-dependent data.
