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Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…
We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data…
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…
The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which…
The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…
The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering…
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral…
The ensemble Kalman inversion (EKI) is a particle based method which has been introduced as the application of the ensemble Kalman filter to inverse problems. In practice it has been widely used as derivative-free optimization method in…
Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…
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…
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively…
We revisit the problem of model-based object recognition for intensity images and attempt to address some of the shortcomings of existing Bayesian methods, such as unsuitable priors and the treatment of residuals with a non-robust error…