  Undirected probabilistic graphical models represent the conditional
dependencies, or Markov properties, of a collection of random variables.
Knowing the sparsity of such a graphical model is valuable for modeling
multivariate distributions and for efficiently performing inference. While the
problem of learning graph structure from data has been studied extensively for
certain parametric families of distributions, most existing methods fail to
consistently recover the graph structure for non-Gaussian data. Here we propose
an algorithm for learning the Markov structure of continuous and non-Gaussian
distributions. To characterize conditional independence, we introduce a score
based on integrated Hessian information from the joint log-density, and we
prove that this score upper bounds the conditional mutual information for a
general class of distributions. To compute the score, our algorithm SING
estimates the density using a deterministic coupling, induced by a triangular
transport map, and iteratively exploits sparse structure in the map to reveal
sparsity in the graph. For certain non-Gaussian datasets, we show that our
algorithm recovers the graph structure even with a biased approximation to the
density. Among other examples, we apply SING to learn the dependencies between
the states of a chaotic dynamical system with local interactions.
