## A Latent Mixed Membership Model for Relational Data (2005)

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Venue: | IN LINKKDD ’05: PROCEEDINGS OF THE 3RD INTERNATIONAL WORKSHOP ON LINK DISCOVERY |

Citations: | 16 - 5 self |

### BibTeX

@INPROCEEDINGS{Airoldi05alatent,

author = {Edoardo Airoldi and David Blei and Eric Xing and Stephen Fienberg},

title = {A Latent Mixed Membership Model for Relational Data},

booktitle = {IN LINKKDD ’05: PROCEEDINGS OF THE 3RD INTERNATIONAL WORKSHOP ON LINK DISCOVERY},

year = {2005},

pages = {82--89},

publisher = {}

}

### OpenURL

### Abstract

... data analysis and machine learning. In this paper we propose a Bayesian model that uses a hierarchy of probabilistic assumptions about the way objects interact with one another in order to learn latent groups, their typical interaction patterns, and the degree of membership of objects to groups. Our model explains the data using a small set of parameters that can be reliably estimated with an e#cient inference algorithm. In our approach, the set of probabilistic assumptions may be tailored to a specific application domain in order to incorporate intuitions and/or semantics of interest. We demonstrate our methods on simulated data and we successfully apply our model to a data set of protein-to-protein interactions.

### Citations

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Citation Context ... for analyzing patters of interaction between data. Mixed membership models for soft classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text =-=[2]-=-, text and references [4, 7], text and images [1], multiple disability measures [6, 15], and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naiv... |

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Citation Context ...a. Mixed membership models for soft classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images =-=[1]-=-, multiple disability measures [6, 15], and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian fram... |

510 | Distance metric learning with application to clustering with side-information
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Citation Context ... powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images [1], multiple disability measures [6, 15], and genetics information =-=[19, 18, 24]-=-. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian framework involving a latent variable structure; this induces dependencies and in... |

438 | Graphical models, exponential families, and variational inference
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Citation Context ...1|φi,j,1) q(zi,j,2|φi,j,2) “ ” Mult (zi,j,1|φi,j,1)Mult (zi,j,2|φi,j,2) The lower bound for the log likelihood L[γ, φ ; α, η] can be maximized using exponential family arguments and coordinate ascent =-=[22]-=-; this leads to the following updates for the variational parameters (φi,j,1, φi,j,2), for each pair (i, j): φ ∗ i,j,1,g ∝ exp ˘ KX ψ(γi,g) − ψ( γi,g) ¯ × × KY h=1 η r i,j φ i,j,2,h g,h g=1 KY h=1 φ ∗... |

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Functional organization of the yeast proteome by systematic analysis of protein complexes
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Citation Context ...roteins on a proteome-wide scale in yeast. These include the two-hybrid (Y2H) screens and mass spectrometry methods. For example, mass spectrometry is used to identify components of protein complexes =-=[9, 10]-=-. Highthroughput methods, though, may miss complexes that are not present under the given conditions, for example, tagging may disturb complex formation and weakly associated components may dissociate... |

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Citation Context ... powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images [1], multiple disability measures [6, 15], and genetics information =-=[19, 18, 24]-=-. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian framework involving a latent variable structure; this induces dependencies and in... |

354 |
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Citation Context ...roteins on a proteome-wide scale in yeast. These include the two-hybrid (Y2H) screens and mass spectrometry methods. For example, mass spectrometry is used to identify components of protein complexes =-=[9, 10]-=-. Highthroughput methods, though, may miss complexes that are not present under the given conditions, for example, tagging may disturb complex formation and weakly associated components may dissociate... |

283 |
Bayes and Empirical Bayes Methods for Data Analysis
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Citation Context ... . 3.3 Parameter Estimation Using the optimal lower bound L[γ ∗ , φ ∗ ; α, η] as a tractable surrogate for the likelihood we here look for (pseudo) empirical Bayes estimates for the hyper-parameters. =-=[3]-=- Such maximization amounts to maximum likelihood estimation of the Dirichlet parameters α and Bernoulli parameter matrix η using expected sufficient statistics, where the expectation is taken with res... |

193 | Self-tuning spectral clustering
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Citation Context ...splay in Figure 4, where the S/N ratio is roughly 0.5, 0.4 and 0.3 for the both the top and bottom rows, from left to right. In Figure 4 we compare our model to spectral clustering with local scaling =-=[25]-=- that is particularly suited for recovering the structure of the interactions in the case when proteins take part in a single function. Note that spectral clustering (or normalized cuts) minimizes the... |

188 | Logit models and logistic regressions for social networks: I. an introduction to markov graphs andp
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Citation Context ...cific permission and/or a fee. Link-KDD ’05, August 21, 2005, Chicago, Illinois, USA. Copyright 2005 ACM 1-59593-215-1 ... $5.00. Leinhardt, e.g., [12], and later elaborated upon by others, e.g., see =-=[8, 23, 20, 11]-=-. In machine learning, Markov random networks have been used for link prediction [21] and the traditional block models from Statistics have been extended with nonparametric Bayesian priors [13]. In th... |

186 | The missing link: A probabilistic model of document content and hypertext connectivity
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Citation Context ... interaction between data. Mixed membership models for soft classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text [2], text and references =-=[4, 7]-=-, text and images [1], multiple disability measures [6, 15], and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hiera... |

157 | Latent Space Approaches to Social Network Analysis
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Citation Context ...cific permission and/or a fee. Link-KDD ’05, August 21, 2005, Chicago, Illinois, USA. Copyright 2005 ACM 1-59593-215-1 ... $5.00. Leinhardt, e.g., [12], and later elaborated upon by others, e.g., see =-=[8, 23, 20, 11]-=-. In machine learning, Markov random networks have been used for link prediction [21] and the traditional block models from Statistics have been extended with nonparametric Bayesian priors [13]. In th... |

147 | MIPS: analysis and annotation of proteins from whole genomes. Nucleic Acids Res 2004, 32, (Database issue
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Citation Context ..., may miss complexes that are not present under the given conditions, for example, tagging may disturb complex formation and weakly associated components may dissociate and escape detection. The MIPS =-=[16]-=- database was created in 1998 based on evidence derived from a variety of experimental techniques and does not include information from high-throughput datasets. It contains about 8000 protein complex... |

128 | Estimating a Dirichlet distribution
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Citation Context ...i parameter matrix η using expected sufficient statistics, where the expectation is taken with respect to the variational distribution. Finding the MLE of a Dirichlet requires numerical optimization. =-=[17]-=- For each Bernoulli parameter, the ap-Figure 2: Error rates on simulated protein-protein interaction networks, the lower the better, for spectral clustering with local scaling (LSC) versus latent mix... |

108 | Link prediction in relational data
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Citation Context ...2005 ACM 1-59593-215-1 ... $5.00. Leinhardt, e.g., [12], and later elaborated upon by others, e.g., see [8, 23, 20, 11]. In machine learning, Markov random networks have been used for link prediction =-=[21]-=- and the traditional block models from Statistics have been extended with nonparametric Bayesian priors [13]. In this paper, we develop a mixed membership model for analyzing patters of interaction be... |

104 | Markov chain Monte Carlo estimation of exponential random graph models
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Citation Context ...cific permission and/or a fee. Link-KDD ’05, August 21, 2005, Chicago, Illinois, USA. Copyright 2005 ACM 1-59593-215-1 ... $5.00. Leinhardt, e.g., [12], and later elaborated upon by others, e.g., see =-=[8, 23, 20, 11]-=-. In machine learning, Markov random networks have been used for link prediction [21] and the traditional block models from Statistics have been extended with nonparametric Bayesian priors [13]. In th... |

97 |
Kernel-based data fusion and its application to protein function prediction in yeast
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Citation Context ...ion containing 871 proteins, the interactions amongst which were hand-curated. In Table 1 we summarize the main functions of the protein in our sub-collection, where we retained the function names in =-=[14]-=- where possible. Note that, since most proteins participate in more than one function, Table 1 contains more counts (2119) than proteins (871), for an average of ≈ 2.4 functions per protein. Note that... |

86 |
Mixed-membership models of scientific publications. Proceedings of the National Academy of Sciences of the United States of America 101(Suppl
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Citation Context ... interaction between data. Mixed membership models for soft classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text [2], text and references =-=[4, 7]-=-, text and images [1], multiple disability measures [6, 15], and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hiera... |

73 |
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Citation Context ... powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images [1], multiple disability measures [6, 15], and genetics information =-=[19, 18, 24]-=-. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian framework involving a latent variable structure; this induces dependencies and in... |

65 | Prediction of protein function using protein-‐protein interaction data
- Deng, Zhang, et al.
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Citation Context ... arranged around two positive elements of the diagonal. 4.1.5 PPI Prediction Experiment It is reasonable to assume that a collection of PPI may inform us on the functions protein are able to express. =-=[5]-=- In order to get a feel for the prediction error associated with our model, we split the proteins into a training set and a testing set of about the same size. We then slightly modify our model in ord... |

40 | Statistical Analysis of Multiple Sociometric Relations
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- 1985
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40 | Discovering latent classes in relational data
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Citation Context ...23, 20, 11]. In machine learning, Markov random networks have been used for link prediction [21] and the traditional block models from Statistics have been extended with nonparametric Bayesian priors =-=[13]-=-. In this paper, we develop a mixed membership model for analyzing patters of interaction between data. Mixed membership models for soft classification have emerged as a powerful and popular analytica... |

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Statistical Applications Using Fuzzy Sets
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Citation Context ...t classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images [1], multiple disability measures =-=[6, 15]-=-, and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian framework involving a latent variable stru... |

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Sociological Methodology, chapter Local structure in social networks
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Citation Context ...rvers or to redistribute to lists, requires prior specific permission and/or a fee. Link-KDD ’05, August 21, 2005, Chicago, Illinois, USA. Copyright 2005 ACM 1-59593-215-1 ... $5.00. Leinhardt, e.g., =-=[12]-=-, and later elaborated upon by others, e.g., see [8, 23, 20, 11]. In machine learning, Markov random networks have been used for link prediction [21] and the traditional block models from Statistics h... |

1 |
Classification—The Ubiquitous Challenge, chapter Bayesian Mixed Membership Models for Soft Classification
- Erosheva, Fienberg
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Citation Context ...t classification have emerged as a powerful and popular analytical tool for analyzing large databases involving text [2], text and references [4, 7], text and images [1], multiple disability measures =-=[6, 15]-=-, and genetics information [19, 18, 24]. These models use a simple generative model, such as bag-of-words or naive Bayes, embedded in a hierarchical Bayesian framework involving a latent variable stru... |