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This paper presents a novel approach to binary classification using dynamic logistic ensemble models. The proposed method addresses the challenges posed by datasets containing inherent internal clusters that lack explicit feature-based…

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…

We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive…

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…

This survey paper is written with the intention of giving a mathematical introduction to filtering techniques for intermittent data assimilation, and to survey some recent advances in the field. The paper is divided into three parts. The…

We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any…

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…

Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…

Bayesian multinomial logistic regression provides a principled, interpretable approach to multiclass classification, but posterior sampling becomes increasingly expensive as the model dimension grows. Prior work has studied scalability in…

Bayesian optimisation is a sample efficient method for finding a global optimum of expensive black-box objective functions. Historic datasets from related problems can be exploited to help improve performance of Bayesian optimisation by…

Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitating approximate methods. Though widely used, these methods…

Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been to augment the underlying physics of the governing equations with data driven Bayesian statistical…

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…

A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…