Related papers: Bayesian Model Parameter Learning in Linear Invers…
This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
We study source localization from high dimensional M/EEG data by extending a multiscale method based on Entropic inference devised to increase the spatial resolution of inverse problems. This method is used to construct informative prior…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…