Related papers: Variational Bayesian Inference of Line Spectra
The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…
Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
The article develops a hybrid Variational Bayes algorithm that combines the mean-field and fixed-form Variational Bayes methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We…
Recent studies have explored the use of deep generative models of speech spectra based of variational autoencoders (VAEs), combined with unsupervised noise models, to perform speech enhancement. These studies developed iterative algorithms…
Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
We derive and present explicit algorithms to facilitate streamlined computing for variational inference for models containing higher level random effects. Existing literature, such as Lee and Wand (2016), is such that streamlined…
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive…
We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These…
Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their…
Despite their theoretical appealingness, Bayesian neural networks (BNNs) are left behind in real-world adoption, mainly due to persistent concerns on their scalability, accessibility, and reliability. In this work, we develop the…
Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…
Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…