  We learn the structure of a Markov Network between two groups of random
variables from joint observations. Since modelling and learning the full MN
structure may be hard, learning the links between two groups directly may be a
preferable option. We introduce a novel concept called the \emph{partitioned
ratio} whose factorization directly associates with the Markovian properties of
random variables across two groups. A simple one-shot convex optimization
procedure is proposed for learning the \emph{sparse} factorizations of the
partitioned ratio and it is theoretically guaranteed to recover the correct
inter-group structure under mild conditions. The performance of the proposed
method is experimentally compared with the state of the art MN structure
learning methods using ROC curves. Real applications on analyzing
bipartisanship in US congress and pairwise DNA/time-series alignments are also
reported.
