相关论文: Measure flow path recovery in Bayes Hilbert spaces
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…
In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…
Estimating the direction of ambient fluid flow is key for many flying or swimming animals and robots, but can only be accomplished through indirect measurements and active control. Recent work with tethered flying insects indicates that…
We develop a \emph{flow-matching framework} for transporting probability measures under control-affine dynamics and for steering systems to points or target sets. Starting from the continuity equation associated with the control affine…
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator…
We consider the problem of sample-based feedback-based motion planning from bearing (direction-only) measurements. We build on our previous work that defines a cell decomposition of the environment using RRT*, and finds an output feedback…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
This paper extends path integral control (PIC) to partially observed systems by formulating the problem in Gaussian belief space. PIC relies on the diffusion being proportional to the control channel -- the so-called matching condition --…
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…
Globally rising demand for transportation by rail is pushing existing infrastructure to its capacity limits, necessitating the development of accurate, robust, and high-frequency positioning systems to ensure safe and efficient train…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…
Acousto-electric tomography (AET) is a hybrid imaging modality that combines electrical impedance tomography with focused ultrasound perturbations to obtain interior power density measurements, which provide additional information that can…
Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In this paper, we analyze the recovery…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…