In this paper, a graphical algorithm (GrA) is presented for an investment optimization problem. This algorithm is based on the same Bellman equations as the best known dynamic programming algorithm (DPA) for the problem but the GrA has several advantages in comparison with the DPA. Based on this GrA, a fully-polynomial time approximation scheme is proposed having the best known running time. Th...

The design of future multi-standard systems is very challenging. Flexible architectures exploiting processing commonalities of the different set of standards cohabiting in the device offer promising solutions. This paper presents a graphical approach for the optimization of multi-standard Software Defined Radio (SDR) systems. The potential of our approach for optimizing multi-standard SDR syste...

We introduce a strategy for parallelizing a state-of-the-art sequential search algorithm for optimization on a grid of computers. Based on the AND/OR graph search framework, the procedure exploits the structure of the underlying problem graph. Worker nodes concurrently solve subproblems that are generated by a single master process. Subproblem generation is itself embedded into an AND/OR Branch...

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model i...

1. Introduction. We would like to congratulate the authors for their refreshing contribution to this high-dimensional latent variables graphical model selection problem. The problem of covariance and concentration matrices is fundamentally important in several classical statistical methodolo-gies and many applications. Recently, sparse concentration matrices estimation had received considerable...

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of `1-penalized estimation in the Gaussian framework. Though many of these inverse covariance estimation approaches are demonstrably scalable and have leveraged recent advances in convex optimization, they still depend on...

We consider a Project Investment problem, where a set of projects and an overall budget are given. For each project, a profit function is known which describes the profit obtained if a specific amount is invested in this project. The objective is to determine the amount invested in each project such that the overall budget is not exceeded and the total profit is maximized. For this problem, we ...

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...

We want to congratulate the authors for a thought-provoking and very interesting paper. Sparse modeling of the concentration matrix has enjoyed popularity in recent years. It has been framed as a computationally convenient convex l1-constrained estimation problem in Yuan and Lin (2007) and can be applied readily to higher-dimensional problems. The authors argue— we think correctly—that the spar...

Over the past two decades graphical models have been widely used as powerful tools for compactly representing distributions. On the other hand, kernel methods have been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. Graphical models are a powerful underlying formalis...