There has been an explosive growth of data-mining models involving latent structure for clustering and classification. While having related objectives these models use different parameterizations and often very different specifications and constraints. Model choice is thus a major methodological issue and a crucial practical one for applications. In this paper, we work from a general formulation of hierarchical Bayesian mixed-membership models in Erosheva [15] and Erosheva, Fienberg, and Lafferty [19] and present several model specifications and variations, both parametric and nonparametric, in the context of the learning the number of latent groups and associated patterns for clustering units. Model choice is an issue within specifications, and becomes a component of the larger issue of model comparison. We elucidate strategies for comparing models and specifications by producing novel analyses of two data sets: (1) a corpus of scientific publications from the Proceedings of the National Academy of Sciences (PNAS) examined earlier by Erosheva, Fienberg, and Lafferty [19] and Griffiths and Steyvers [22]; (2) data on functionally disabled American seniors from the National

Data mining has experienced an explosive growth of models with latent structure for clustering and classification. While having related objectives these models use different parameterizations and often very different specifications and constraints. Model choice is thus a big methodological issue and a crucial practical one for applications. In this paper, we work from a general formulation of hierarchical Bayesian mixed-membership models in Erosheva, Fienberg, and Lafferty (2004) and present several model specifications and variations, both parametric and nonparametric, in the context of the learning the number of latent groups, and associated patterns, for clustering units. Model choice is an issue within specifications, and becomes a component of the larger issue of model comparison. We elucidate strategies for comparing models and specifications by producing novel analyses of the following two data sets: (1) a corpus of scientific publications from the

We consider linear ill-posed inverse problems y = Ax, in which we want to infer many count parameters x from few count observations y, where the matrix A is binary and has some unimodularity property. Such problems are typical in applications such as contingency table analysis and network tomography (on which we present testing results). These properties of A have a geometrical implication for the solution space: It is a convex integer polytope. We develop a novel approach to characterize this polytope in terms of its vertices; by taking advantage of the geometrical intuitions behind the Hermite normal form decomposition of the matrix A, and of a newly defined pivoting operation to travel across vertices. Next, we use this characterization to develop three (exact) polytope samplers for x with emphasis on uniform distributions. We showcase one of these samplers on simulated and real data. 1

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In many applications we are interested in making inference on latent time series from indirect measurements, which are often low-dimensional projections resulting from mixing or aggregation. Positron emission tomography, super-resolution, and network traffic monitoring are some examples. Inference in such settings requires solving a sequence of ill-posed inverse problems, yt = Axt, where the projection mechanism provides information on A. We consider problems in which A specifies mixing on a graph of times series that are bursty and sparse. We develop a multilevel state-space model for mixing times series and an efficient approach to inference. A simple model is used to calibrate regularization parameters that lead to efficient inference in the multilevel state-space model. We apply this method to the problem of estimating point-to-point traffic flows on a network from aggregate measurements. Our solution outperforms existing methods for this problem, and our two-stage approach suggests an efficient inference strategy for multilevel models of multivariate time series. 1