Video segmentation requires the partitioning of a series of images into groups that are both spatially coherent and smooth along the time axis. We formulate segmentation as a Bayesian clustering problem. Context information is propagated over time by a conjugate structure. The level of segment resolution is controlled by a Dirichlet process prior. Our contributions include a conjugate nonparame...

We derive a PAC-Bayesian generalization bound for density estimation. Similar to the PAC-Bayesian generalization bound for classification, the result has the appealingly simple form of a tradeoff between empirical performance and the KL-divergence of the posterior from the prior. Moreover, the PACBayesian generalization bound for classification can be derived as a special case of the bound for ...

Many current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about specific models for spatial clustering. The proposed methodology incorporates ideas from image analysis, from Bayesian mod...

Is it possible to crowdsource categorization? Amongst the challenges: (a) each worker has only a partial view of the data, (b) different workers may have different clustering criteria and may produce different numbers of categories, (c) the underlying category structure may be hierarchical. We propose a Bayesian model of how workers may approach clustering and show how one may infer clusters / ...

A model-based clustering method is proposed for clustering individuals on the basis of measurements taken over time. Data variability is taken into account through non-linear hierarchical models leading to a mixture of hierarchical models. We study both frequentist and Bayesian estimation procedures. From a classical viewpoint, we discuss maximum likelihood estimation of this family of models t...

In this study we suggest a Bayesian approach to fuzzy clustering analysis – the Bayesian fuzzy regression. Bayesian Posterior Odds analysis is employed to select the correct number of clusters for the fuzzy regression analysis. In this study, we use a natural conjugate prior for the parameters, and we find that the Bayesian Posterior Odds provide a very powerful tool for choosing the number of ...

In this paper we present a hierarchical model of linear regression functions in the context of multi–task learning. The parameters of the linear model are coupled by a Dirichlet Process (DP) prior, which implies a clustering of related functions for different tasks. To make approximate Bayesian inference under this model we apply the Bayesian Hierarchical Clustering (BHC) algorithm. The experim...

Current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about speciic models for spatial clustering. The proposed methodology incorporates ideas from image analysis , from Bayesian model av...

Is it possible to crowdsource categorization? Amongst the challenges: (a) each worker has only a partial view of the data, (b) different workers may have different clustering criteria and may produce different numbers of categories, (c) the underlying category structure may be hierarchical. We propose a Bayesian model of how workers may approach clustering and show how one may infer clusters / ...

Is it possible to crowdsource categorization? Amongst the challenges: (a) each worker has only a partial view of the data, (b) different workers may have different clustering criteria and may produce different numbers of categories, (c) the underlying category structure may be hierarchical. We propose a Bayesian model of how workers may approach clustering and show how one may infer clusters / ...