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Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov…

In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for approximating intractable distributions. However, its usage is limited in the context of deep latent variable models owing to costly datapoint-wise sampling iterations…

The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand…

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…

Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…

Modern data assimilation schemes typically use the same discrete dynamical model to evolve the state estimate in time also to approximate the evolution, or propagation, of the estimation error covariance. Ensemble-based methods, such as the…

Black-box variational inference (BBVI) with Gaussian mixture families offers a flexible approach for approximating complex posterior distributions without requiring gradients of the target density. However, standard numerical optimization…

Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high…

The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various…

Data assimilation is the task to combine evolution models and observational data in order to produce reliable predictions. In this paper, we focus on ensemble-based recursive data assimilation problems. Our main contribution is a hybrid…

We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…

In this letter we generalise Ensemble Kalman inversion techniques to general Bayesian models where previously they were restricted to additive Gaussian likelihoods - all in the difficult setting where the likelihood can be sampled from, but…

Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…

Control variates have become an increasingly popular variance-reduction technique in Bayesian inference. Many broadly applicable control variates are based on the Langevin-Stein operator, which leverages gradient information from any…

Ensemble modeling has been widely used to solve complex problems as it helps to improve overall performance and generalization. In this paper, we propose a novel TemporalAugmenter approach based on ensemble modeling for augmenting the…

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state…