  To learn (statistical) dependencies among random variables requires
exponentially large sample size in the number of observed random variables if
any arbitrary joint probability distribution can occur.
  We consider the case that sparse data strongly suggest that the probabilities
can be described by a simple Bayesian network, i.e., by a graph with small
in-degree \Delta. Then this simple law will also explain further data with high
confidence. This is shown by calculating bounds on the VC dimension of the set
of those probability measures that correspond to simple graphs. This allows to
select networks by structural risk minimization and gives reliability bounds on
the error of the estimated joint measure without (in contrast to a previous
paper) any prior assumptions on the set of possible joint measures.
  The complexity for searching the optimal Bayesian networks of in-degree
\Delta increases only polynomially in the number of random varibales for
constant \Delta and the optimal joint measure associated with a given graph can
be found by convex optimization.
