Related papers: A Bayesian View of the Poisson-Dirichlet Process
In this paper we consider the problem of dynamic clustering, where cluster memberships may change over time and clusters may split and merge over time, thus creating new clusters and destroying existing ones. We propose a Bayesian…
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…
There is a rich literature on clustering functional data with applications to time-series modeling, trajectory data, and even spatio-temporal applications. However, existing methods routinely perform global clustering that enforces…
We propose the CliPS procedure when fitting Bayesian mixture models in the context of model-based clustering to identify the cluster distributions while simultaneously assessing the suitability of a cluster solution and validating the…
Dependent Dirichlet processes (DDP) have been widely applied to model data from distributions over collections of measures which are correlated in some way. On the other hand, in recent years, increasing research efforts in machine learning…
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions,…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
Differential Privacy (DP) is a probabilistic framework that protects privacy while preserving data utility. To protect the privacy of the individuals in the dataset, DP requires adding a precise amount of noise to a statistic of interest;…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
To identify novel dynamic patterns of gene expression, we develop a statistical method to cluster noisy measurements of gene expression collected from multiple replicates at multiple time points, with an unknown number of clusters. We…
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance…
The discrepant posterior phenomenon (DPP) is a counter-intuitive phenomenon that can frequently occur in a Bayesian analysis of multivariate parameters. It refers to the phenomenon that a parameter estimate based on a posterior is more…
We investigate the class of $\sigma$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular…
Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
Assigning weights to a large pool of objects is a fundamental task in a wide variety of applications. In this article, we introduce the concept of structured high-dimensional probability simplexes, in which most components are zero or near…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…
Discrete biomarkers derived as cell densities or counts from tissue microarrays and immunostaining are widely used to study immune signatures in relation to survival outcomes in cancer. Although routinely collected, these signatures are not…
The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $\alpha$ and…