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Neural Information Processing Systems 

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Authors propose a method of estimating a graphical model for continuous data that blends the following three, established ideas: 1) assume the data follows a multivariate Gaussian and estimate using the graphical lasso; 2) do not assume the data follows a multivariate Gaussian and instead use a Gaussian copula, the nonparanormal, to allow arbitrary single variable marginals; or 3) assume a specific tree-structured factorization and model arbitrary bivariate marginals along the tree structure. The proposed method introduces the blossom tree, which is a specific factorization of the model into a collection of densely connected blossom components that are connected by a specific set of tree edges. In particular, each blossom is connected (via a pedicel node) to at most one tree edge. The blossom components are modeled as sparse multivariate Gaussians (or using the non-paranormal copula) and the tree edges are modeled as arbitrary bivariate distributions with single variable marginals that are consistent with the marginal of any blossom pedicel to which they are attached.