Related papers: Wasserstein bounds for non-linear Gaussian filters
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
In a variety of problems, the number and state of multiple moving targets are unknown and are subject to be inferred from their measurements obtained by a sensor with limited sensing ability. This type of problems is raised in a variety of…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
Filtering is a widely used methodology for the incorporation of observed data into time-evolving systems. It provides an online approach to state estimation inverse problems when data is acquired sequentially. The Kalman filter plays a…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in…
In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of…
We study the possibility of defining a distance on the whole space of measures, with the property that the distance between two measures having the same mass is the Wasserstein distance, up to a scaling factor. We prove that, under very…
Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms,…
We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems. If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity. To…
Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and…
Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…
We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space ${\Bbb R}^n$.…
Wasserstein distances are widely used in modern data analysis but pose significant computational and statistical challenges in high dimensions. The sliced Wasserstein distance alleviates these challenges by leveraging one-dimensional…
We estimate the rate of convergence for the Kantorovich (or Wasserstein) distance between empirical measures of i.i.d. random variables associated with the Laguerre model of order $\alpha$ on $(0,\infty)^N$ and their common law, which is…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…