Title: Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting,
Abstract: We present an algorithm to identify sparse dependence structure in continuous
and non-Gaussian probability distributions, given a corresponding set of data.
The conditional independence structure of an arbitrary distribution can be
represented as an undirected graph (or Markov random field), but most
algorithms for learning this structure are restricted to the discrete or
Gaussian cases. Our new approach allows for more realistic and accurate
descriptions of the distribution in question, and in turn better estimates of
its sparse Markov structure. Sparsity in the graph is of interest as it can
accelerate inference, improve sampling methods, and reveal important
dependencies between variables. The algorithm relies on exploiting the
connection between the sparsity of the graph and the sparsity of transport
maps, which deterministically couple one probability measure to another.