  We consider an approximation scheme for multivariate information assuming
that synergistic information only appearing in higher order joint distributions
is suppressed, which may hold in large classes of systems. Our approximation
scheme gives a practical way to evaluate information among random variables and
is expected to be applied to feature selection in machine learning. The
truncation order of our approximation scheme is given by the order of synergy.
In the classification of information, we use the partial information
decomposition of the original one. The resulting multivariate information is
expected to be reasonable if higher order synergy is suppressed in the system.
In addition, it is calculable in relatively easy way if the truncation order is
not so large. We also perform numerical experiments to check the validity of
our approximation scheme.
