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Hierarchical Bayesian modeling of topics in timestamped documents. IEEE transactions on pattern analysis and machine intelligence
, 2009
"... Abstract—We consider the problem of inferring and modeling topics in a sequence of documents with known publication dates. The documents at a given time are each characterized by a topic and the topics are drawn from a mixture model. The proposed model infers the change in the topic mixture weights ..."
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Abstract—We consider the problem of inferring and modeling topics in a sequence of documents with known publication dates. The documents at a given time are each characterized by a topic and the topics are drawn from a mixture model. The proposed model infers the change in the topic mixture weights as a function of time. The details of this general framework may take different forms, depending on the specifics of the model. For the examples considered here, we examine base measures based on independent multinomialDirichlet measures for representation of topicdependent word counts. The form of the hierarchical model allows efficient variational Bayesian inference, of interest for largescale problems. We demonstrate results and make comparisons to the model when the dynamic character is removed, and also compare to latent Dirichlet allocation (LDA) and Topics over Time (TOT). We consider a
Posterior consistency in conditional distribution estimation
"... Abstract: A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as weak and strong posterior consistency. Estimation of an uncountable collect ..."
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Abstract: A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as weak and strong posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a challenging problem, which differs in some important ways from density and mean regression estimation problems. We first introduce new notions of weak and strong neighborhoods that are applicable to conditional distributions. Focusing on a broad class of priors formulated as predictordependent mixtures of Gaussian kernels, we provide sufficient conditions under which weak and strong posterior consistency hold. This theory is illustrated by showing that the conditions are satisfied for a class of generalized stickbreaking process mixtures in which the stickbreaking lengths are constructed through mapping continuous stochastic processes to the unit interval using a monotone differentiable link function. Probit stickbreaking processes provide a computationally convenient special case. We also provide a set of sufficient conditions to ensure strong and weak posterior consistency using fixedπ dependent Dirichlet process mixtures of
Logistic StickBreaking Process
"... Editor: A logistic stickbreaking process (LSBP) is proposed for nonparametric clustering of general spatially or temporallydependent data, imposing the belief that proximate data are more likely to be clustered together. The sticks in the LSBP are realized via multiple logistic regression functi ..."
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Cited by 10 (5 self)
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Editor: A logistic stickbreaking process (LSBP) is proposed for nonparametric clustering of general spatially or temporallydependent data, imposing the belief that proximate data are more likely to be clustered together. The sticks in the LSBP are realized via multiple logistic regression functions, with shrinkage priors employed to favor contiguous and spatially localized segments. The LSBP is also extended for the simultaneous processing of multiple data sets, yielding a hierarchical logistic stickbreaking process (HLSBP). The model parameters (atoms) within the HLSBP are shared across the multiple learning tasks. Efficient variational Bayesian inference is derived, and comparisons are made to related techniques in the literature. Experimental analysis is performed for audio waveforms and images, and it is demonstrated that for segmentation applications the LSBP yields generally homogeneous segments with sharp boundaries.
Nonparametric Bayes regression and classification through mixtures of product kernels
"... It is routine in many fields to collect data having a variety of measurement scales and supports. For example, in biomedical studies for each patient one may collect functional data on a biomarker over time, gene expression values normalized to lie on a hypersphere to remove artifacts, clinical and ..."
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It is routine in many fields to collect data having a variety of measurement scales and supports. For example, in biomedical studies for each patient one may collect functional data on a biomarker over time, gene expression values normalized to lie on a hypersphere to remove artifacts, clinical and demographic covariates and a health outcome. A common interest focuses on building predictive models, with parametric assumptions seldom supported by prior knowledge. Hence, it is most appropriate to define a prior with large support allowing the conditional distribution of the response given predictors to be unknown and changing flexibly across the predictor space not just in the mean but also in the variance and shape. Building on earlier work on Dirichlet process mixtures, we describe a simple and general strategy for inducing models for conditional distributions through discrete mixtures of product kernel models for joint distributions of predictors and response variables. Computation is straightforward and the approach can easily accommodate combining of widely disparate data types, including vector data in a Euclidean space, categorical observations, functions, images and manifold data.
Bayesian Clustering with Regression
, 2008
"... Summary. We consider clustering with regression, i.e., we develop a probability model for random partitions that is indexed by covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by reporting a weighted average of the responses ..."
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Summary. We consider clustering with regression, i.e., we develop a probability model for random partitions that is indexed by covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by reporting a weighted average of the responses of clusters of earlier patients. The weights should be determined by the similarity of the new patient’s covariate with the covariates of patients in each cluster. We achieve the desired inference by defining a random partition model that includes a regression on covariates. Patients with similar covariates are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. We build on product partition models (PPM). We define an extension of the PPM to include a regression on covariates by including in the cohesion function a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for any combination of continuous, categorical, count and ordinal covariates. 1.
Mixture models with a prior on the number of components. arXiv:1502.06241
, 2015
"... A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonlyused method of inference ..."
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A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonlyused method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in highdimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMs—an exchangeable partition distribution, restaurant process, random measure representation, and stickbreaking representation—and crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including highdimensional gene expression data used to discriminate cancer subtypes.
chromosomal
, 2015
"... Species sampling priors for modeling dependence: an application to the detection of ..."
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Species sampling priors for modeling dependence: an application to the detection of
A Product Partition Model with Regression on
, 2010
"... We propose a probability model for random partitions in the presence of covariates. In other words, we develop a modelbased clustering algorithm that exploits available covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by repo ..."
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We propose a probability model for random partitions in the presence of covariates. In other words, we develop a modelbased clustering algorithm that exploits available covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by reporting a weighted average of the responses of clusters of earlier patients. The weights should be determined by the similarity of the new patient’s covariate with the covariates of patients in each cluster. We achieve the desired inference by defining a random partition model that includes a regression on covariates. Patients with similar covariates are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. We build on product partition models (PPM). We define an extension of the PPM to include a regression on covariates by including in the cohesion function a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for any combination of continuous, categorical, count and ordinal covariates. An implementation of the proposed model as Rpackage is available for download.