  We propose a method for recovering the structure of a sparse undirected
graphical model when very few samples are available. The method decides about
the presence or absence of bonds between pairs of variable by considering one
pair at a time and using a closed form formula, analytically derived by
calculating the posterior probability for every possible model explaining a two
body system using Jeffreys prior. The approach does not rely on the
optimisation of any cost functions and consequently is much faster than
existing algorithms. Despite this time and computational advantage, numerical
results show that for several sparse topologies the algorithm is comparable to
the best existing algorithms, and is more accurate in the presence of hidden
variables. We apply this approach to the analysis of US stock market data and
to neural data, in order to show its efficiency in recovering robust
statistical dependencies in real data with non stationary correlations in time
and space.
