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Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
In mixture modeling and clustering applications, the number of components and clusters is often not known. A stick-breaking mixture model, such as the Dirichlet process mixture model, is an appealing construction that assumes infinitely…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
We introduce a family of multiscale stick-breaking mixture models for Bayesian nonparametric density estimation. The Bayesian nonparametric literature is dominated by single scale methods, exception made for P\`olya trees and allied…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
Identifying pure components in mixtures is a common yet challenging problem. The associated unmixing process requires the pure components, also known as endmembers, to be sufficiently spectrally distinct. Even with this requirement met,…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
Substances such as chemical compounds are invisible to human eyes, they are usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified by visual inspection, the spectra of…
Flow cytometry (FCM) is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…
Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…
Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical…
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
Averaging predictions from multiple competing inferential models frequently outperforms predictions from any single model, providing that models are optimally weighted to maximize predictive performance. This is particularly the case in…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Evaluating whether data streams are drawn from the same distribution is at the heart of various machine learning problems. This is particularly relevant for data generated by dynamical systems since such systems are essential for many…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…