40,251 research outputs found

    Mixed membership stochastic blockmodels

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    Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.Comment: 46 pages, 14 figures, 3 table

    Variational approximation for mixtures of linear mixed models

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    Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variational greedy algorithm is developed for model selection and learning of the mixture components. This approach allows an automatic initialization of the algorithm and returns a plausible number of mixture components automatically. In cases of weak identifiability of certain model parameters, we use hierarchical centering to reparametrize the model and show empirically that there is a gain in efficiency by variational algorithms similar to that in MCMC algorithms. Related to this, we prove that the approximate rate of convergence of variational algorithms by Gaussian approximation is equal to that of the corresponding Gibbs sampler which suggests that reparametrizations can lead to improved convergence in variational algorithms as well.Comment: 36 pages, 5 figures, 2 tables, submitted to JCG

    Statistical Indicators of Collective Behavior and Functional Clusters in Gene Networks of Yeast

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    We analyze gene expression time-series data of yeast S. cerevisiae measured along two full cell-cycles. We quantify these data by using q-exponentials, gene expression ranking and a temporal mean-variance analysis. We construct gene interaction networks based on correlation coefficients and study the formation of the corresponding giant components and minimum spanning trees. By coloring genes according to their cell function we find functional clusters in the correlation networks and functional branches in the associated trees. Our results suggest that a percolation point of functional clusters can be identified on these gene expression correlation networks.Comment: 8 pages, 4 figure
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