Related papers: Multilevel adaptive sparse Leja approximations for…

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…

The integrated nested Laplace approximations (INLA) method has become a widely utilized tool for researchers and practitioners seeking to perform approximate Bayesian inference across various fields of application. To address the growing…

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large…

A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…

This work is a follow-up to our previous contribution ("Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)", SIAM J. Numer. Anal., 2018), and contains further…

The \emph{deterministic} sparse grid method, also known as Smolyak's method, is a well-established and widely used tool to tackle multivariate approximation problems, and there is a vast literature on it. Much less is known about…

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…

It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods…