Paper:
Blossom Tree Graphical Models
We combine the ideas behind trees and Gaussian graphical models to form a new nonparametric family of graphical models. Our approach is to attach nonparanormal "blossoms", with arbitrary graphs, to a collection of nonparametric trees. The tree edges are chosen to connect variables that most violate joint Gaussianity. The non-tree edges are partitioned into disjoint groups, and assigned to tree nodes using a nonparametric partial correlation statistic. A nonparanormal blossom is then "grown" for each group using established methods based on the graphical lasso. The result is a factorization with respect to the union of the tree branches and blossoms, defining a high-dimensional joint density that can be efficiently estimated and evaluated on test points. Theoretical properties and experiments with simulated and real data demonstrate the effectiveness of blossom trees.

Review:
The paper continues a line of work in graphical models to go beyondGaussian modeling of real-valued attributes. The apparent novelty isthe combination of a previous algorithm for non-parametric forestdensity estimation, which rests on a non-parametric generalization ofthe classical Chow-Liu algorithm for learning tree graphical models, with the standardgraphical LASSO (glasso), resulting on the authors call a "blossom treegraphical model." The paper states a type of statistical-consistency(theoretical) result, and a few experiments.* On Section 3: Can the authors' comment on how much the stated resultsays about *machine learning* properties (i.e., PAC orlarge-deviation, as opposed to data-size-asymptotic bounds)?  Can theauthors say anything at all about the properties of the constant N?What would be an expression of a lower or upper bound, even if exact?Just like the typical asymptotic convergence as the number of samplesgoes to infinity (e.g., CLT), it is hard to know when thelarge-deviation bounds of the kind provided in the paper start beingvalid. Without such information regarding N and the exact numberof samples n, while it may be an interesting and useful statisticalresult, it does not appear very useful to machine learning, IMHO.Hence, I would have Section 3 moved fully to the supplementarymaterial and replace it with more experimental evaluations. For example,I would have moved the sections Supplementary Simulations 1 and 2 intothe main body of the paper. But even then, a slightly more thoroughevaluation would be useful such as experimenting by changing the classor form of the underlying ground-truth density, and the class ofunderlying graphs, whenever applicable, the number of samples, and thenumber of attributes/variables. *  Given the nature of the paper, a reference to the Chow-Liu algorithm, from 1968, seems warranted, even if only in passing. C. K. Chow, and C. N. Liu, "Approximating Discrete ProbabilityDistributions with Dependence Trees," IEEE Transactions of InformationTheory, vol. IT-14, no. 3, May 1968Despite the different statistical setups/models (i.e., discretevs. continuous), and the fact that the work in the submitted papergoes beyond simple trees/forests/blossom representations, it isundeniable that the core of the underlying approach has its roots onChow-Liu's work.* It'd have been nice to see experiments on real-world data such asthose on microarray data that Liu et al (JMLR, 2011) performed. Isthe problem public access to the data? What about other datasets(e.g., fMRI)?* I am curious as the core distinctions among the following work andforest density estimation, which serves as the foundation for the submission?- Marwan Mattar, and Erik Learned-Miller.  Improved generative models forcontinuous image features through tree-structured non-parametricdistributions. UMass Amherst Technical Report 06-57, 10 pages, 2006.- Mihai Datcu, Farid Melgani, Andrea Piardi, and SebastianoB. Serpico, "Multisource Data Classification With Dependence Trees,"IEEE Transactions on Geoscience and Remote Sensing, vol. 40, no. 3,pp. 609-617, March 2002. I am interested in directly ML-relevant, as opposed to statistical,distinctions.* It has been quite a long time since Chow and Liu's work in 1968. Hence,I was originally skeptical that no one had actually tried anything like what theauthors' propose. If it exists, I have not been able to find it. So,while somewhat surprising, I must give the authors their due for thenovelty and originality of their proposed approach... Now, I maychange my mind later, should I find a reference :) ... All kidding aside,even if I find an old reference, it does not take much away from theauthors' originality/novelty, because no one in recent years haveproposed the technique, despite the intense attention to the problemof modeling continuous/real-valued attributes going back a decade, at least!