Related papers: Unscented Kalman Inversion: Efficient Gaussian App…
Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…
We formulate the discrete-time inverse optimal control problem of inferring unknown parameters in the objective function of an optimal control problem from measurements of optimal states and controls as a nonlinear filtering problem. This…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…
The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Multi-object tracking (MOT) is an essential technique for navigation in autonomous driving. In tracking-by-detection systems, biases, false positives, and misses, which are referred to as outliers, are inevitable due to complex traffic…
Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
For linear inverse problems with Gaussian priors and Gaussian observation noise, the posterior is Gaussian, with mean and covariance determined by the conditioning formula. Using the Feldman-Hajek theorem, we analyse the prior-to-posterior…
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In…
We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…
Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…