Related papers: A Bayesian approach to learning mixtures of nonpar…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…
The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…
We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…
In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of $p$-values under the null hypothesis and the other component $f$ is…
Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
The conventional use of the Generalized Extreme Value (GEV) distribution to model block maxima may be inappropriate when extremes are actually structured into multiple heterogeneous groups. In this work, we propose a novel approach for…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…
As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being…
We consider nonparametric Bayesian estimation of a probability density $p$ based on a random sample of size $n$ from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the…
The use of hierarchical mixture priors with shared atoms has recently flourished in the Bayesian literature for partially exchangeable data. Leveraging on nested levels of mixtures, these models allow the estimation of a two-layered data…
Feature and trait allocation models are fundamental objects in Bayesian nonparametrics and play a prominent role in several applications. Existing approaches, however, typically assume full exchangeability of the data, which may be…
We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite…
Finite mixtures are a cornerstone of Bayesian modelling, and it is well-known that sampling from the resulting posterior distribution can be a hard task. In particular, popular reversible Markov chain Monte Carlo schemes are often slow to…
We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…
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.…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
In this dissertation, we develop nonparametric Bayesian models for biomedical data analysis. In particular, we focus on inference for tumor heterogeneity and inference for missing data. First, we present a Bayesian feature allocation model…