Related papers: Bayesian Inverse Problems with Heterogeneous Varia…
We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…
Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this…
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…
In this paper we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive con- traction rates for the…
Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…
We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
We consider the linear inverse problem of estimating an unknown signal $f$ from noisy measurements on $Kf$ where the linear operator $K$ admits a wavelet-vaguelette decomposition (WVD). We formulate the problem in the Gaussian sequence…
The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
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…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
We develop a fully intrinsic Bayesian framework for nonparametric regression on the unit sphere based on isotropic Gaussian field priors and the harmonic structure induced by the Laplace-Beltrami operator. Under uniform random design, the…
The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator $Q$ depends not only on the scale but also on location. In this case, the rates…