Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting
This addresses the limitation of existing methods restricted to discrete or Gaussian cases, enabling more accurate modeling for applications in inference and sampling, though it is incremental as it extends prior work to non-Gaussian settings.
The paper tackled the problem of learning sparse probabilistic graphical models for non-Gaussian continuous distributions, resulting in an algorithm that provides more realistic and accurate descriptions and better estimates of sparse Markov structure.
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.