Latent variable models are powerful tools for probabilistic modeling, and have been successfully applied to various domains, such as speech analysis and bioinformatics. However, parameter learning algorithms for latent variable models have predominantly relied on local search heuristics such as expectation maximization (EM). We propose a fast, local-minimum-free spectral algorithm for learning ...

In a recently proposed graphical compression algorithm by Choi and Szpankowski (2009), the following tree arose in the course of the analysis. The root contains n balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability p) or the right subtree (with probability 1− p). A new ...

The sparse inverse covariance estimation problem is commonly solved using an l1-regularizedGaussian maximum likelihood estimator known as “graphical lasso”, but its computational cost becomes prohibitive for large data sets. A recent line of results showed–under mild assumptions–that the graphical lasso estimator can be retrieved by soft-thresholding the sample covariance matrix and solving a m...

The latent tree structure learned by the algorithm by [1] is shown in Figure 1. The blue nodes are hidden nodes and the red nodes are observed. Note how integrating out some of these hidden nodes could lead to very large cliques. Thus it is not surprising why both our spectral method and EM perform better than Chow Liu. The Chow Liu Tree is shown in Figure 1. Note how it is forced to pick some ...

Cooperative decision making is a vision of future network management and control. Distributed connection preemption is an important example where nodes can make intelligent decisions on allocating resources and controlling traffic flows for multi-class service networks. A challenge is that nodal decisions are spatially dependent as traffic flows trespass multiple nodes in a network. Hence the p...

We study a multi-period, multi-item dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing optimal prices while satisfying several important practical business rules. The strength of our work lies in a graphical model reformulation we introduce, which can be used to solve the problem, while providing access to a whole range of ideas from combinato...

The pioneering work of Akers (1978) on graphical representation of Boolean functions using Binary Decision Diagrams (BDDs) offered an attractive and convenient technique for simplification and manipulation of complex Boolean functions. Modification of these BDDs was suggested by Bryant (1986) and since then different types of Decision Diagrams (DDs) have been introduced by researchers (see the ...

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