Related papers: Affine-Mapping based Variational Ensemble Kalman F…
This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of…
We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a…
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…
The Kalman filter (KF) is a widely-used algorithm for tracking the latent state of a dynamical system from noisy observations. For systems that are well-described by linear Gaussian state space models, the KF minimizes the mean-squared…
The Kalman filter is an algorithm for the estimation of hidden variables in dynamical systems under linear Gauss-Markov assumptions with widespread applications across different fields. Recently, its Bayesian interpretation has received a…
We propose a neural network model to estimate the current frame from two reference frames, using affine transformation and adaptive spatially-varying filters. The estimated affine transformation allows for using shorter filters compared to…
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…
This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can be derived from the sample average approximation (SAA) of…
The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…
This work introduces an on-the-fly (i.e., online) linear unmixing method which is able to sequentially analyze spectral data acquired on a spectrum-by-spectrum basis. After deriving a sequential counterpart of the conventional linear mixing…
Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior)…
The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to…
Discrete diffusion and flow matching models capture complex, non-additive and non-autoregressive structure in high-dimensional objective landscapes through parallel, iterative refinement. However, their implicit generative nature precludes…
Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian…
Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…
The article develops a hybrid Variational Bayes algorithm that combines the mean-field and fixed-form Variational Bayes methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We…
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…