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Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…

Score Distillation Sampling (SDS) has been pivotal for leveraging pre-trained diffusion models in downstream tasks such as inverse problems, but it faces two major challenges: $(i)$ mode collapse and $(ii)$ latent space inversion, which…

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding…

In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…

We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is…

This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…

Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…

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…

We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…

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 consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train…

A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…

Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under…

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…