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127
Learning Latent Tree Graphical Models
 J. of Machine Learning Research
, 2011
"... We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing me ..."
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Cited by 46 (10 self)
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We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our algorithms can be applied to both discrete and Gaussian random variables and our learned models are such that all the observed and latent variables have the same domain (state space). Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using socalled information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a preprocessing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures such as neighborjoining) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare
Network tomography: identifiability and fourier domain estimation
 Proc. IEEE INFOCOM’07
, 2007
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Network tomography: A review and recent developments
 In Fan and Koul, editors, Frontiers in Statistics
, 2006
"... The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of largescale inverse problems. The first deals with passive tomography where aggregate data ar ..."
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Cited by 23 (7 self)
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The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of largescale inverse problems. The first deals with passive tomography where aggregate data are collected at the individual router/node level and the goal is to recover pathlevel information. The main problem of interest here is the estimation of the origindestination traffic matrix. The second, referred to as active tomography, deals with reconstructing linklevel information from endtoend pathlevel measurements obtained by actively probing the network. The primary application in this case is estimation of qualityofservice parameters such as loss rates and delay distributions. The paper provides a review of the statistical issues and developments in network tomography with an emphasis on active tomography. An application to Internet telephony is used to illustrate the results.
Network delay tomography using flexicast experiments
 B
, 2006
"... Summary. Estimating and monitoring the quality of service of computer and communications networks is a problem of considerable interest. This paper focuses on estimating linklevel delay distributions from endtoend pathlevel data collected using active probing experiments. This is an interesting ..."
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Cited by 18 (4 self)
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Summary. Estimating and monitoring the quality of service of computer and communications networks is a problem of considerable interest. This paper focuses on estimating linklevel delay distributions from endtoend pathlevel data collected using active probing experiments. This is an interesting largescale statistical inverse (deconvolution) problem. We describe a flexible class of probing experiments (flexicast) for data collection and develop conditions under which the linklevel delay distributions are identifiable. Maximum likelihood estimation using the EM algorithm is studied. It does not scale well for large trees, so a faster algorithm based on solving for local MLEs and combining their information is proposed. The usefulness of the methods is illustrated on real VoiceoverIP data collected from the University of North Carolina campus network.
Likelihood based hierarchical clustering
 IEEE Trans. on Signal Processing
, 2004
"... This paper develops a new method for hierarchical clustering. Unlike other existing clustering schemes, our method is based on a generative, treestructured model that represents relationships between the objects to be clustered, rather than directly modeling properties of objects themselves. In cer ..."
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Cited by 15 (5 self)
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This paper develops a new method for hierarchical clustering. Unlike other existing clustering schemes, our method is based on a generative, treestructured model that represents relationships between the objects to be clustered, rather than directly modeling properties of objects themselves. In certain problems, this generative model naturally captures the physical mechanisms responsible for relationships among objects, for example, in certain evolutionary tree problems in genetics and communication network topology identification. The paper examines the networking problem in some detail, to illustrate the new clustering method. More broadly, the generative model may not reflect actual physical mechanisms, but it nonetheless provides a means for dealing with errors in the similarity matrix, simultaneously promoting two desirable features in clustering: intraclass similarity and interclass dissimilarity.
Efficient and Dynamic Routing Topology Inference From EndtoEnd Measurements
"... Inferring the routing topology and link performance from a node to a set of other nodes is an important component in network monitoring and application design. In this paper we propose a general framework for designing topology inference algorithms based on additive metrics. The framework can flexi ..."
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Cited by 14 (0 self)
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Inferring the routing topology and link performance from a node to a set of other nodes is an important component in network monitoring and application design. In this paper we propose a general framework for designing topology inference algorithms based on additive metrics. The framework can flexibly fuse information from multiple measurements to achieve better estimation accuracy. We develop computationally efficient (polynomialtime) topology inference algorithms based on the framework. We prove that the probability of correct topology inference of our algorithms converges to one exponentially fast in the number of probing packets. In particular, for applications where nodes may join or leave frequently such as overlay network construction, applicationlayer multicast, peertopeer file sharing/streaming, we propose a novel sequential topology inference algorithm which significantly reduces the probing overhead and can efficiently handle node dynamics. We demonstrate the effectiveness of the proposed inference algorithms via Internet experiments.
Practical Issues with Using Network Tomography for Fault Diagnosis
"... This article is an editorial note submitted to CCR. It has NOT been peer reviewed. This paper investigates the practical issues in applying network tomography to monitor failures. We outline an approach for selecting paths to monitor, detecting and confirming the existence of a failure, correlating ..."
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Cited by 13 (1 self)
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This article is an editorial note submitted to CCR. It has NOT been peer reviewed. This paper investigates the practical issues in applying network tomography to monitor failures. We outline an approach for selecting paths to monitor, detecting and confirming the existence of a failure, correlating multiple independent observations into a single failure event, and applying existing binary networking tomography algorithms to identify failures. We evaluate the ability of network tomography algorithms to correctly detect and identify failures in a controlled environment on the VINI testbed.
Statistical Inverse Problems in Active Network Tomography
"... Abstract: Active network tomography includes several interesting statistical inverse problems that arise in the context of computer and communication networks. The primary goal in these problems is to recover linklevel information about qualityofservice parameters from aggregate endtoend data m ..."
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Cited by 13 (2 self)
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Abstract: Active network tomography includes several interesting statistical inverse problems that arise in the context of computer and communication networks. The primary goal in these problems is to recover linklevel information about qualityofservice parameters from aggregate endtoend data measured on paths across the network. The estimation and monitoring of these parameters are of considerable interest to network engineers and Internet service providers. This paper provides a review of the inverse problems and recent research on inference for loss rates and delay distributions. Some new results on parametric inference for delay distributions are developed. The results are illustrated using a network application related to Internet telephony. 1. The Inverse Problems Consider a tree T = {V, E} with a set of nodes V and a set of links or edges E. Figure 1 shows two examples: a simple twolayer symmetric binary tree on the left and a more general fourlayer tree on the right. Each member of E is a directed link numbered after the node at its terminus. V includes a root node 0, a set of receiver or destination nodes R and a set of internal nodes I. All transmissions on the tree are initiated at the root node. The internal nodes have a single incoming link and at least two outgoing links (children). The receiver nodes have a single incoming link but no
Network delay inference from additive metrics, Preprint. Available at Arxiv: math.PR/0604367
, 2006
"... We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicastbased delay inference, that is, the problem of reconstructing delay characteristics of a network from endtoend delay measurements on ..."
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Cited by 12 (1 self)
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We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicastbased delay inference, that is, the problem of reconstructing delay characteristics of a network from endtoend delay measurements on network paths. Our inference algorithm is based on additive metric techniques used in phylogenetics. It runs in polynomial time and requires a sample of size only poly(log n). We also show how to recover the topology of the routing tree. 1