We wish to congratulate the authors for their innovative contribution, which is bound to inspire much further research. We find latent variable model selection to be a fantastic application of matrix decomposition methods , namely, the superposition of low-rank and sparse elements. Clearly, the methodology introduced in this paper is of potential interest across many disciplines. In the followi...

We propose a new additive decomposition of probability tables that preserves equivalence of the joint distribution while reducing the size of potentials, without extra variables. We formulate the Most Probable Explanation (MPE) problem in belief networks as a Weighted Constraint Satisfaction Problem (WCSP). Our pairwise decomposition allows to replace a cost function with smaller-arity function...

Since recently, there have been an increasing interest in the problem of estimating a high-dimensional matrix K that can be decomposed in a sum of a sparse matrix S∗ (i.e., a matrix having only a small number of nonzero entries) and a low rank matrix L∗. This is motivated by applications in computer vision, video segmentation, computational biology, semantic indexing etc. The main contribution ...

Since recently, there have been an increasing interest in the problem of estimating a high-dimensional matrix K that can be decomposed in a sum of a sparse matrix S∗ (i.e., a matrix having only a small number of nonzero entries) and a low rank matrix L∗. This is motivated by applications in computer vision, video segmentation, computational biology, semantic indexing etc. The main contribution ...

In this paper the optimization of additively decomposed discrete functions is investigated. For these functions genetic algorithms have exhibited a poor performance. First the schema theory of genetic algorithms is reformulated in probability theory terms. A schema deenes the structure of a marginal distribution. Then the conceptual algorithm BEDA is introduced. BEDA uses a Boltzmann distributi...

I want to start by congratulating Professors Chandrasekaran, Parrilo and Willsky for this fine piece of work. Their paper, hereafter referred to as CPW, addresses one of the biggest practical challenges of Gaussian graphical models—how to make inferences for a graphical model in the presence of missing variables. The difficulty comes from the fact that the validity of conditional independence r...

Graphical models provide a rich framework for summarizing the dependencies among variables. The graphical lasso approach attempts to learn the structure of a Gaussian graphical model (GGM) by maximizing the log likelihood of the data, subject to an l1 penalty on the elements of the inverse co-variance matrix. Most algorithms for solving the graphical lasso problem do not scale to a very large n...

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the treereweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work...

We introduce an algorithm for learning sparse, time-varying undirected probabilistic graphical models of Molecular Dynamics (MD) data. Our method computes a maximum a posteriori (MAP) estimate of the topology and parameters of the model (i.e., structure learning) using L1regularization of the negative log-likelihood (aka ‘Graphical Lasso’) to ensure sparsity, and a kernel to ensure smoothly var...

Graphical Games are a succinct representation of multi agent interactions in which each participant interacts with a limited number of other agents. The model resembles Distributed Constraint Optimization Problems (DCOPs) including agents, variables, and values (strategies). However, unlike distributed constraints, local interactions of Graphical Games take the form of small strategic games and...