Related papers: Perspectives on locally weighted ensemble Kalman m…

Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…

Ensemble Kalman inversion (EKI) is a technique for the numerical solution of inverse problems. A great advantage of the EKI's ensemble approach is that derivatives are not required in its implementation. But theoretically speaking, EKI's…

The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving…

In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…

In this paper, the ensemble consider Kalman filter is proposed to mitigate the negative effects of uncertain parameters in nonlinear dynamic and measurement models. The ensemble Kalman filter can avoid using the Jacobian matrices and reduce…

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 propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…

The propensity score is widely used for causal inference in observational studies, but common parametric estimators can produce biased and inefficient effect estimates when model assumptions are violated. Nonparametric approaches reduce…

In recent years, several ensemble-based filtering methods have been proposed and studied. The main challenge in such procedures is the updating of a prior ensemble to a posterior ensemble at every step of the filtering recursions. In the…

Inertial measurement units are widely used in different fields to estimate the attitude. Many algorithms have been proposed to improve estimation performance. However, most of them still suffer from 1) inaccurate initial estimation, 2)…

This paper is focused on the optimization approach to the solution of inverse problems. We introduce a stochastic dynamical system in which the parameter-to-data map is embedded, with the goal of employing techniques from nonlinear Kalman…

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

The Ensemble Kalman Filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control--to--observable identification problems. In applications it may be required to enforce the solution to satisfy…

Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear…

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…

Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may…

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…

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an…