Related papers: Understanding uncertainty in Bayesian cluster anal…
In this work, we propose a method for tracking multiple extended targets or unresolvable group targets in a clutter environment. Firstly, based on the Random Matrix Model (RMM), the joint state of the target is modeled as the Gamma Gaussian…
In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well…
K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…
Bi-clustering is a useful approach in analyzing biological data when observations come from heterogeneous groups and have a large number of features. We outline a general Bayesian approach in tackling bi-clustering problems in moderate to…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
Deep ensembles can be considered as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as a non-Bayesian technique, arguments supporting its Bayesian footing have been…
Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…
We propose Bayesian model averaging (BMA) as a method for postprocessing the results of model-based clustering. Given a number of competing models, appropriate model summaries are averaged, using the posterior model probabilities, instead…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…
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 Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
When faced with high frequency streams of data, clustering raises theoretical and algorithmic pitfalls. We introduce a new and adaptive online clustering algorithm relying on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent)…