Related papers: Function Approximation via The Subsampled Poincar\…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
Subsampling is an effective approach to alleviate the computational burden associated with large-scale datasets. Nevertheless, existing subsampling estimators incur a substantial loss in estimation efficiency compared to estimators based on…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
In this paper, we consider Poincar\'e inequalities for non euclidean metrics on $\mathbb{R}^d$. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for…
The performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space is analyzed. Support recovery is formulated as a multiple-hypothesis testing problem. Both upper and lower…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
Under Poincar\'e-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three…
We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather than…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
Traditional measures of smoothness often fail to provide accurate $L_p$-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…