## Network inference from co-occurrences (2006)

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Citations: | 13 - 1 self |

### BibTeX

@TECHREPORT{Rabbat06networkinference,

author = {Michael G. Rabbat and Mário A. T. Figueiredo and Senior Member and Robert D. Nowak and Senior Member},

title = {Network inference from co-occurrences},

institution = {},

year = {2006}

}

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### Abstract

Abstract—The discovery of networks is a fundamental problem

### Citations

2404 | The Capacity of Wireless Networks
- Gupta, Kumar
- 2000
(Show Context)
Citation Context ... unit square, and two vertices are connected with an edge if the Euclidean distance between them is less than or equal to . This threshold guarantees that the graph is connected with high probability =-=[27]-=-. Groups of nodes are randomly chosen as sources and destinations, transmission paths are generated between each sourcedestination pair according to either a shortest path or random routing model, and... |

2123 |
Social Network Analysis: Methods and Applications
- Wasserman, Faust
- 1994
(Show Context)
Citation Context ...nt genes, proteins, and metabolites in biological systems [13, 19]. The analysis of social networks contributes to a deeper understanding of interactions, dynamics, and the structure of organizations =-=[18, 25]-=-. The analysis of functional connectivity networks in the brain is necessary for the understanding of couplings and interactions between different neuronal colonies [1,23,24]. Obtaining or inferring t... |

1555 | Probability inequalities for sums of bounded random variables
- Hoeffding
- 1963
(Show Context)
Citation Context ...d set �µL = �L i=1 ZiXi �L i=1 Zi . Then with probability greater than 1 − δ, �µL − µ < � 2b2 log 2 δ . (48) L Proof. From the definitions of Zi and Xi, ZiXi ∈ [0, b]. Applying Hoeffding’s inequality =-=[10]-=- yields that for any t > 0, and for any t > 0, Define the event, Et = Pr(Et) ≤ 2e −2Lt2 /b 2 �µL ≤ 1, if t(1+µ) 1−t Pr Pr � L� i=1 � L� i=1 ZiXi − Lµ ≥ Lt Zi − L ≤ −Lt � � ≤ e −2Lt2 /b 2 , (49) ≤ e −2... |

1151 |
Bayesian Theory
- Bernardo, Smith
- 1994
(Show Context)
Citation Context ... for π and for each row of A, |S| � P [π|u] ∝ i=1 π ui−1 i and P [A|v] ∝ |S| |S| � � i=1 j=1 A vi,j−1 i,j , (19) where the parameters ui and vi,j should be non-negative in order to have proper priors =-=[2]-=-. The larger ui is relative to the other ui ′, i′ �= i, the greater our prior belief that state i is an initial state rather than the others. Similarly, the larger vi,j relative to other vi,j ′ for j′... |

1009 | Monte Carlo Statistical Methods
- Robert, Casella
- 2004
(Show Context)
Citation Context ...would sample permutations directly from the posterior P [r|x, A, π]; however, this would require determining its value for all N! permutations. Instead, we employ importance sampling (IS) (see, e.g., =-=[15, 22]-=-, for an introduction to IS): we sample L permutations, r 1 , . . . , r L , from a distribution R[r|x, A, π], from which it is easier to sample than P [r|x, A, π], then apply a corrective re-weighting... |

950 | Learning Bayesian networks: The combination of knowledge and statistical data
- Heckerman, Geiger, et al.
- 1994
(Show Context)
Citation Context ...bly from that of learning the structure of a directed graphical model or Bayesian network, a graph where nodes correspond to random variables and edges indicate conditional independence relationships =-=[8, 9]-=-. A typical aim of graphical modelling is to find a graph corresponding to a factorization of a high-dimensional distribution which predicts the observations well. In turn, these probabilistic models ... |

442 |
Monte Carlo strategies in scientific computing
- Liu
- 2001
(Show Context)
Citation Context ...would sample permutations directly from the posterior P [r|x, A, π]; however, this would require determining its value for all N! permutations. Instead, we employ importance sampling (IS) (see, e.g., =-=[15, 22]-=-, for an introduction to IS): we sample L permutations, r 1 , . . . , r L , from a distribution R[r|x, A, π], from which it is easier to sample than P [r|x, A, π], then apply a corrective re-weighting... |

351 |
On the convergence properties of the EM algorithm
- Wu
- 1983
(Show Context)
Citation Context ... marks the marginal log likelihood computed using a transition matrix estimated from correctly ordered paths. 23 (c)s5 Monotonicity and Convergence Well-known convergence results due to Wu and Boyles =-=[4, 27]-=- guarantee convergence of our EM algorithm when the exact E-step is used. Let θ k = � A k , π k� denote parameter estimates calculated at the kth EM iteration using the exact EM expressions. By choosi... |

300 | Unsupervised learning for finite mixture models
- Figueiredo, Jain
- 2002
(Show Context)
Citation Context ...o go to one (or a few) of the states. We can push even more aggressively for a sparse solution by choosing negative parameters for the Dirichlet distributions (which will become improper), as done in =-=[7]-=- for Gaussian 15smixtures. When negative Dirichlet parameters are allowed, the M-step updates become π t+1 i A k+1 i,j = = � ui + � |S| � ui + i=1 � vi,j + T� � |S| � vi,j + j=1 Nm� m=1 t ′ =1 T� Nm� ... |

232 |
The Structure and Dynamics of Networks
- Newman, Barabási, et al.
- 2006
(Show Context)
Citation Context ...nt genes, proteins, and metabolites in biological systems [13, 19]. The analysis of social networks contributes to a deeper understanding of interactions, dynamics, and the structure of organizations =-=[18, 25]-=-. The analysis of functional connectivity networks in the brain is necessary for the understanding of couplings and interactions between different neuronal colonies [1,23,24]. Obtaining or inferring t... |

187 |
A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms
- Wei, Tanner
- 1990
(Show Context)
Citation Context ...lo approximate versions of the E-step, which avoid the combinatorial nature of its exact version. The Monte Carlo EM (MCEM) algorithm, based on an MC version of the E-step, was originally proposed in =-=[26]-=-, and used ever since by many authors (recent work can be found in [3, 11] and references therein). To lighten the notation in this section, we drop the superscripts from (A k , π k ), using simply (A... |

119 | Multiple-Source Internet Tomography
- Rabbat, Coates, et al.
- 2006
(Show Context)
Citation Context ...ains of communication systems, biology, sociology, and cognitive science. The analysis of communication networks enables a better understanding of routing, transmission patterns, and information flow =-=[6, 21]-=-. The analysis of biological networks provides insight into the functional roles played by different genes, proteins, and metabolites in biological systems [13, 19]. The analysis of social networks co... |

107 | Organization, development and function of complex brain networks
- Sporns, Chialvo, et al.
- 2004
(Show Context)
Citation Context ...structure of organizations [18, 25]. The analysis of functional connectivity networks in the brain is necessary for the understanding of couplings and interactions between different neuronal colonies =-=[1,23,24]-=-. Obtaining or inferring the structure of networks from experimental data precedes any such analysis and is thus a basic and fundamental task, critical to many applications. Unfortunately, measurement... |

59 |
On the convergence of the EM algorithm
- Boyles
- 1983
(Show Context)
Citation Context ... marks the marginal log likelihood computed using a transition matrix estimated from correctly ordered paths. 23 (c)s5 Monotonicity and Convergence Well-known convergence results due to Wu and Boyles =-=[4, 27]-=- guarantee convergence of our EM algorithm when the exact E-step is used. Let θ k = � A k , π k� denote parameter estimates calculated at the kth EM iteration using the exact EM expressions. By choosi... |

55 |
Systems biology: properties of reconstructed networks
- Palsson
- 2006
(Show Context)
Citation Context ...ssion patterns, and information flow [6, 21]. The analysis of biological networks provides insight into the functional roles played by different genes, proteins, and metabolites in biological systems =-=[13, 19]-=-. The analysis of social networks contributes to a deeper understanding of interactions, dynamics, and the structure of organizations [18, 25]. The analysis of functional connectivity networks in the ... |

50 | Koller.: Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks
- Teyssier
- 2005
(Show Context)
Citation Context ...to the observations: that co-occurring vertices must lie along a path in the network. We note that, although the Bayesian network paradigm does not directly fit our problem setup, Teyssier and Koller =-=[15]-=- describe an approach to Bayesian network structure learning, which is similar to the network inference algorithm presented in this paper. In [15], rather than searching over all Bayesian network stru... |

26 |
Being Bayesian about Bayesian network structure: A Bayesian approach to structure discovery
- Friedman, Koller
- 2003
(Show Context)
Citation Context ...bly from that of learning the structure of a directed graphical model or Bayesian network, a graph where nodes correspond to random variables and edges indicate conditional independence relationships =-=[8, 9]-=-. A typical aim of graphical modelling is to find a graph corresponding to a factorization of a high-dimensional distribution which predicts the observations well. In turn, these probabilistic models ... |

23 | Tononi: Classes of network connectivity and dynamics
- Sporns, G
(Show Context)
Citation Context ...structure of organizations [18, 25]. The analysis of functional connectivity networks in the brain is necessary for the understanding of couplings and interactions between different neuronal colonies =-=[1,23,24]-=-. Obtaining or inferring the structure of networks from experimental data precedes any such analysis and is thus a basic and fundamental task, critical to many applications. Unfortunately, measurement... |

21 |
Convergence of the Monte Carlo expectation maximization for curved exponential families
- Fort, Moulines
- 2003
(Show Context)
Citation Context ...riterion be satisfied on multiple successive iterations since the criterion may be met prematurely due to poor Monte Carlo approximations. Fort and Moulines consider asymptotic convergence of MCEM in =-=[19]-=-. In particular, they prove consistency of the MCEM for curved exponential families using various forms of the ergodic theorem for Markov chains under the assumption that the number of Monte Carlo sam... |

18 |
A computational approach for ordering signal transduction pathway components from genomics and proteomics Data
- Liu, Zhao
- 2004
(Show Context)
Citation Context ...pathways [28]. However, microarray data only reflects order information at a very coarse, unreliable level. Developing computational techniques for inferring pathway orders is an active research area =-=[16]-=-. Co-occurrence or transactional data also appears in the context of social networks, e.g., by considering which academic papers are co-cited by another paper, which web pages are linked to or from an... |

15 | A survey of monte carlo algorithms for maximizing the likelihood of a two-stage hierarchical model
- Booth, Hobert, et al.
- 2001
(Show Context)
Citation Context ...ture of its exact version. The Monte Carlo EM (MCEM) algorithm, based on an MC version of the E-step, was originally proposed in [26], and used ever since by many authors (recent work can be found in =-=[3, 11]-=- and references therein). To lighten the notation in this section, we drop the superscripts from (A k , π k ), using simply (A, π) as the current parameter estimates. Moreover, we focus on a particula... |

14 | R and Swaroop A. Network constrained clustering for gene microarray data, Bioinformatics
- Zhu, AO, et al.
- 2005
(Show Context)
Citation Context ...xperiments are expensive and timeconsuming. High-throughput measurement techniques such as microarrays have successfully been used to identify the components of different signal transduction pathways =-=[28]-=-. However, microarray data only reflects order information at a very coarse, unreliable level. Developing computational techniques for inferring pathway orders is an active research area [16]. Co-occu... |

11 | cGraph: A Fast Graphbased Method for Link Analysis and Queries
- Kubica, Moore, et al.
- 2003
(Show Context)
Citation Context ...der of occurrence. Researchers in this area have considered the problems of reconstructing networks from co-occurrence data and of using the inferred network to predict potential future cooccurrences =-=[14]-=-. Functional magnetic resonance imaging (fMRI) provides a mechanism for measuring activity in the brain with high spatial resolution. By observing which regions of the brain co-activate while a patien... |

10 | Ascent-Based Monte Carlo EM
- Caffo, Jank, et al.
- 2005
(Show Context)
Citation Context ... algorithm when sufficiently many importance samples are used. 31In the recent literature researchers have considered the question of how many importance samples must be used in a Monte Carlo E-step =-=[3, 5, 9]-=-. These studies seek a balance between monotonicity and efficiency. We would like to use enough samples to guarantee that monotonicity holds with sufficiently high probability while not using unnecess... |

6 |
Understanding the Topology of a Telephone Network via Internally Sensed Network Tomography
- Rabbat, Treichler, et al.
- 2005
(Show Context)
Citation Context ...ains of communication systems, biology, sociology, and cognitive science. The analysis of communication networks enables a better understanding of routing, transmission patterns, and information flow =-=[6, 21]-=-. The analysis of biological networks provides insight into the functional roles played by different genes, proteins, and metabolites in biological systems [13, 19]. The analysis of social networks co... |

5 |
Ascent-Based Monte Carlo EM
- Cao, Jank, et al.
- 2005
(Show Context)
Citation Context ...s of the EM algorithm used in this example start from the same initialization. Recently, researchers have considered the question of how many importance samples should be used in a Monte Carlo E-step =-=[3, 5, 11]-=-. The goal is to balance monotonicity and computational efficiency by using enough samples to have a good chance at monotonicity while not using excessively many samples. Booth et al. [3] argue that i... |

4 | Estimation of message source and destination from link intercepts
- Justice, Hero
- 2005
(Show Context)
Citation Context ..., the results they produce are not easily interpreted. Also, these heuristics do not readily lend themselves to incorporating side information. A different approach, introduced by Justice and Hero in =-=[12]-=-, involves averaging over an ensemble of feasible topologies sampled uniformly from the feasible set. In general there is an enormous number of feasible topologies (exponential in the problem dimensio... |

3 |
Stochastic variants of the EM algorithm: Monte Carlo, quasi-Monte Carlo and more
- Jank
- 2005
(Show Context)
Citation Context ...ture of its exact version. The Monte Carlo EM (MCEM) algorithm, based on an MC version of the E-step, was originally proposed in [26], and used ever since by many authors (recent work can be found in =-=[3, 11]-=- and references therein). To lighten the notation in this section, we drop the superscripts from (A k , π k ), using simply (A, π) as the current parameter estimates. Moreover, we focus on a particula... |

3 |
Online methods for network endpoint localization,” April 2007, submitted to
- Justice, Hero
(Show Context)
Citation Context ... destination of the traffic. In fact, one could partition the co-occurrence data into source-dependent (or destination-dependent) subsets and learn different Markov models for each subset (see, e.g., =-=[28]-=-). However, if two or more sources (respectively, destinations) have similar routes, then one could potentially obtain a better overall estimate by pooling observations from the sources. We are curren... |