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Dirichlet Process Mixtures (DPMs) are a popular class of statistical models to perform density estimation and clustering. However, when the data available have a distribution evolving over time, such models are inadequate. We introduce here…
Copula-based methods provide a flexible approach to build missing data imputation models of multivariate data of mixed types. However, the choice of copula function is an open question. We consider a Bayesian nonparametric approach by using…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
Despite the proliferation of generative models, achieving fast sampling during inference without compromising sample diversity and quality remains challenging. Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver…
Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a common problem for data taking values in a…
We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…
Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas of statistics, including spatial statistics, statistical learning and telecommunications networks. They are models for repulsive (or…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
The development of parsimonious models for reliable inference and prediction of responses in high-dimensional regression settings is often challenging due to relatively small sample sizes and the presence of complex interaction patterns…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…