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## Inferring Block Structure of Graphical Models in Exponential Families

### Citations

1630 |
Spatial interaction and the statistical analysis of lattice systems (with Discussion
- Besag
- 1974
(Show Context)
Citation Context ... X−a)), (23) where log(Xa!) is the base measure and A(wa, X−a) is log-normalizing constant. Some simple algebra can show that A(wa, X−a) = exp( ∑ b 6=a wabXb) and wab ≤ 0 for all a, b so that A(w) <∞ =-=[8]-=-. Given the conditional distribution, Gibbs sampling is used to generate simulated data for PGMs. We set p = 128 for both GGMs and PGMs. The simulation is conducted for each sample size N , where Siqi... |

1051 | A Fast Iterative ShrinkageThresholding Algorithm for Linear Inverse Problems
- Beck, Teboulle
- 2009
(Show Context)
Citation Context ...he problem (5) is usually a linear model (in GGMs) or a generalized linear model (in Ising or Potts model) with l1 penalty, which can be solved efficiently by methods like iterative soft-thresholding =-=[7]-=-. The advantage of this estimator is that it has both sparsity and consistency [19, 24, 29]. Further it can be easily implemented and parallelized, so it is scalable for very large scale data. For gra... |

734 | High-dimensional graphs and variable selection with the lasso
- Meinshausen, Bühlmann
- 2006
(Show Context)
Citation Context ... specific settings of this structure learning problem. For Gaussian Graphical Models (GGMs), it is well known that conditional independence is encoded in the precision matrix. Neighborhood estimation =-=[19]-=- and log-likelihood maximization with l1 penalty [5, 11, 30] have been developed to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a cons... |

592 | Sparse inverse covariance estimation with the graphical lasso
- Friedman, Hastie, et al.
- 2007
(Show Context)
Citation Context .... For Gaussian Graphical Models (GGMs), it is well known that conditional independence is encoded in the precision matrix. Neighborhood estimation [19] and log-likelihood maximization with l1 penalty =-=[5, 11, 30]-=- have been developed to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a consistent neighborhood estimator is proposed by Ravikumar et al... |

570 | A tutorial on spectral clustering
- Luxburg
(Show Context)
Citation Context ...e more likely to form a pathway or complex to expression a specific function [25]. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering =-=[27, 28]-=- or Mixed-Membership Stochastic Blockmodel (MMSB) [1, 12, 13] to obtain block structure. However, simultaneously inferring the graph and block structure may improve the result in terms of both cluster... |

248 | Model selection and estimation in the Gaussian graphical model. Biometrika 94
- Yuan, Lin
- 2007
(Show Context)
Citation Context .... For Gaussian Graphical Models (GGMs), it is well known that conditional independence is encoded in the precision matrix. Neighborhood estimation [19] and log-likelihood maximization with l1 penalty =-=[5, 11, 30]-=- have been developed to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a consistent neighborhood estimator is proposed by Ravikumar et al... |

166 | A spectral clustering approach to finding communities in graphs
- White, Smyth
(Show Context)
Citation Context ...e more likely to form a pathway or complex to expression a specific function [25]. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering =-=[27, 28]-=- or Mixed-Membership Stochastic Blockmodel (MMSB) [1, 12, 13] to obtain block structure. However, simultaneously inferring the graph and block structure may improve the result in terms of both cluster... |

163 |
Network-based prediction of protein function
- SHARAN, ULITSKY, et al.
- 2007
(Show Context)
Citation Context ... a graph is of special interest for biological networks. For example, in a protein-protein interaction network, proteins are more likely to form a pathway or complex to expression a specific function =-=[25]-=-. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering [27, 28] or Mixed-Membership Stochastic Blockmodel (MMSB) [1, 12, 13] to obtain b... |

131 | Stochastic variational inference.
- Hoffman, Blei, et al.
- 2013
(Show Context)
Citation Context ...e all n2 pairs of local variables (φa→b, φa←b), which is a waste in the first several iterations because the parameters are initialized randomly. Hence we apply stochastic variational inference (SVI) =-=[12, 14]-=- to further speed up computation. In each step of SVI, we use a noisy estimate of gradient from a subsample of nodes for global variables. Proposition 3. Given a pair of nodes (a, b), the estimated gr... |

64 | Convex optimization techniques for fitting sparse Gaussian graphical models.
- Banerjee, Ghaoui, et al.
- 2006
(Show Context)
Citation Context .... For Gaussian Graphical Models (GGMs), it is well known that conditional independence is encoded in the precision matrix. Neighborhood estimation [19] and log-likelihood maximization with l1 penalty =-=[5, 11, 30]-=- have been developed to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a consistent neighborhood estimator is proposed by Ravikumar et al... |

27 |
MicroRNA expression profiling of human metastatic cancers identifies cancer gene targets.
- Baffa, Fassan, et al.
- 2009
(Show Context)
Citation Context ...still several interesting results from a biological perspective. For example, our algorithm identifies 8 overlapping nodes (i.e., miRNAs). Amongst them, it is known that HSA-MIR-146A[23], HSA-MIR-200B=-=[4]-=- and HSA-MIR-200C [4] play a very important role in identifying breast cancer gene targets. In contrast, other models such as GGMs or PGMs cannot identify such targets since only hard clustering is in... |

24 |
Non-coding MicroRNAs hsa-let-7g and hsamiR-181b are associated with chemoresponse to S-1 in colon cancer. Cancer Genomics Proteomics
- Nakajima, Hayashi, et al.
- 2006
(Show Context)
Citation Context ...ogical experimental results. For example, in the purple cluster, the non-coding miRNAs HSA-LET-7g, MIR-200C, HSAMIR-181B-1 and HSA-MIR181B are all associated with Chemoresponse to S-1 in Colon Cancer =-=[20]-=-. In the red cluster, the HSA-LET-7A family members are a modulator of KLK6 protein expression that is independent of the KLK6 copy number status. Further, the miRNAs which have been identified to hav... |

22 | Scalable inference of overlapping communities.
- Gopalan, Gerrish, et al.
- 2012
(Show Context)
Citation Context ... specific function [25]. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering [27, 28] or Mixed-Membership Stochastic Blockmodel (MMSB) =-=[1, 12, 13]-=- to obtain block structure. However, simultaneously inferring the graph and block structure may improve the result in terms of both cluster accuracy and graph estimation [22, 26], especially when the ... |

19 |
Efficient discovery of overlapping communities in massive networks.
- Gopalan, Blei
- 2013
(Show Context)
Citation Context ... specific function [25]. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering [27, 28] or Mixed-Membership Stochastic Blockmodel (MMSB) =-=[1, 12, 13]-=- to obtain block structure. However, simultaneously inferring the graph and block structure may improve the result in terms of both cluster accuracy and graph estimation [22, 26], especially when the ... |

18 | Sparse gaussian graphical models with unknown block structure.
- Marlin, Murphy
- 2009
(Show Context)
Citation Context ... into structure learning has drawn much attention because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free [9, 16], block structure =-=[3, 17, 22, 26]-=- and other topological constraints [10]. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a protein-protein interaction network,... |

14 | Group sparse priors for covariance estimation.
- Marlin, Schmidt, et al.
- 2009
(Show Context)
Citation Context ... estimation [22, 26], especially when the data is limited. To the best of our knowledge, existing works that focusing on block structure in graphical models are all based on Gaussian graphical models =-=[3, 15, 17, 18, 26]-=- or factor models [22], and can only be used to infer hard clustering and non-overlapping block structure. This paper proposes a generative model that can (1) apply to a graphical model on exponential... |

10 |
Learning scale free networks by reweighted l1 regularization.
- Liu, Ihler
- 2011
(Show Context)
Citation Context ...rporating prior knowledge into structure learning has drawn much attention because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free =-=[9, 16]-=-, block structure [3, 17, 22, 26] and other topological constraints [10]. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a pro... |

8 | A Log-Linear Graphical Model for Inferring Genetic Networks from HighThroughput Sequencing Data.
- Allen, Liu
- 2012
(Show Context)
Citation Context ... apply it to a breast cancer microRNA (miRNA) data set from next generation sequencing data. The data set is obtained from Cancer Genome Atlas (TCGA) [21], and preprocessed according to the method in =-=[2]-=-. The final dataset has 416 variables and 452 samples. An EM Poisson graphical model with = 0.05 is fitted to estimate and cluster the graph at the same time. Note that GGMs cannot be easily applied... |

7 |
Association between hsa-mir-146a genotype and tumor age-of-onset in BRCA1/BRCA2-negative familial breast and ovarian cancer patients
- Pastrello, Polesel, et al.
- 2010
(Show Context)
Citation Context ...ilable, there are still several interesting results from a biological perspective. For example, our algorithm identifies 8 overlapping nodes (i.e., miRNAs). Amongst them, it is known that HSA-MIR-146A=-=[23]-=-, HSA-MIR-200B[4] and HSA-MIR-200C [4] play a very important role in identifying breast cancer gene targets. In contrast, other models such as GGMs or PGMs cannot identify such targets since only hard... |

6 |
E Fienberg, and Eric P Xing. Mixed membership stochastic blockmodels
- Airoldi, Blei, et al.
(Show Context)
Citation Context ... specific function [25]. It is straightforward to estimate the graph first, and then apply a clustering algorithm such as spectral clustering [27, 28] or Mixed-Membership Stochastic Blockmodel (MMSB) =-=[1, 12, 13]-=- to obtain block structure. However, simultaneously inferring the graph and block structure may improve the result in terms of both cluster accuracy and graph estimation [22, 26], especially when the ... |

4 | A Convex Formulation for Learning Scale-Free Networks via Submodular Relaxation,”
- Defazio, Caetano
- 2012
(Show Context)
Citation Context ...rporating prior knowledge into structure learning has drawn much attention because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free =-=[9, 16]-=-, block structure [3, 17, 22, 26] and other topological constraints [10]. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a pro... |

3 |
et al. High-dimensional ising model selection using l1-regularized logistic regression
- Ravikumar, JWainwright, et al.
(Show Context)
Citation Context ...have been developed to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a consistent neighborhood estimator is proposed by Ravikumar et al =-=[24]-=- and Yang et al [29], which apply a logistic regression and a generalAppearing in Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS) 2015, San Diego, ... |

2 |
Topology constraints in graphical models
- Fiori, Musé, et al.
- 2012
(Show Context)
Citation Context ...because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free [9, 16], block structure [3, 17, 22, 26] and other topological constraints =-=[10]-=-. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a protein-protein interaction network, proteins are more likely to form a pat... |

2 |
Genome Atlas Network et al. Comprehensive molecular portraits of human breast tumours
- Cancer
(Show Context)
Citation Context ...eal Data To test the performance of our method, we apply it to a breast cancer microRNA (miRNA) data set from next generation sequencing data. The data set is obtained from Cancer Genome Atlas (TCGA) =-=[21]-=-, and preprocessed according to the method in [2]. The final dataset has 416 variables and 452 samples. An EM Poisson graphical model with = 0.05 is fitted to estimate and cluster the graph at the s... |

2 |
Pradeep Ravikumar, Genevera I Allen, and Zhandong Liu. Conditional random fields via univariate exponential families
- Yang
- 2013
(Show Context)
Citation Context ...to estimate the structure of GGMs. Furthermore, for the Ising, Poisson and other models in exponential families, a consistent neighborhood estimator is proposed by Ravikumar et al [24] and Yang et al =-=[29]-=-, which apply a logistic regression and a generalAppearing in Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS) 2015, San Diego, CA, USA. JMLR: W&CP ... |

1 |
et al. Inferring sparse gaussian graphical models with latent structure
- Ambroise, Chiquet, et al.
(Show Context)
Citation Context ... into structure learning has drawn much attention because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free [9, 16], block structure =-=[3, 17, 22, 26]-=- and other topological constraints [10]. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a protein-protein interaction network,... |

1 |
A Fung, Antoninus Soosaipillai, Jeremy A Squire, and Eleftherios P Diamandis. Copy number and expression alterations of mirnas in the ovarian cancer cell line ovcar-3: Impact on kallikrein 6 protein expression. Clinical chemistry
- Bayani, Kuzmanov, et al.
(Show Context)
Citation Context ...6 copy number status. Further, the miRNAs which have been identified to have no direct relationship with KLK6 copy number status, such as HSA-MIR-296 and HSA-MIR-296, do not apprear in the red cluster=-=[6]-=-. On the other hand, empirical approach fails to detect such information. Inferring Block Structure of Graphical Models in Exponential Families 5 Conclusions We present a generative model that can sim... |

1 | Bayesian estimation of latently-grouped parameters in undirected graphical models
- Liu, Page
- 2013
(Show Context)
Citation Context ... estimation [22, 26], especially when the data is limited. To the best of our knowledge, existing works that focusing on block structure in graphical models are all based on Gaussian graphical models =-=[3, 15, 17, 18, 26]-=- or factor models [22], and can only be used to infer hard clustering and non-overlapping block structure. This paper proposes a generative model that can (1) apply to a graphical model on exponential... |

1 |
A Knowles, and Zoubin Ghahramani. A nonparametric variable clustering model
- Palla, David
- 2012
(Show Context)
Citation Context ... into structure learning has drawn much attention because the graph under estimation in many real-world applications usually has some intrinsic properties, such as scale free [9, 16], block structure =-=[3, 17, 22, 26]-=- and other topological constraints [10]. Amongst those properties, the block structure of a graph is of special interest for biological networks. For example, in a protein-protein interaction network,... |

1 | Adaptive variable clustering in gaussian graphical models
- Sun, Zhu, et al.
- 2014
(Show Context)
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