Related papers: Transform-based particle filtering for elliptic Ba…

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…

Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable methods of MCMC are computationally expensive.…

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…

We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and…

Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the…

Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…

Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…

Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

We show that it is feasible to carry out exact Bayesian inference for non-Gaussian state space models using an adaptive Metropolis Hastings sampling scheme with the likelihood approximated by the particle filter. Furthermore, an adapyive…

Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…

This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…

In this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian statistical framework with a preconditioned Markov…

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…

We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…