Related papers: Local and Dimension Adaptive Sparse Grid Interpola…

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…

Super-resolution is an important but difficult problem in image/video processing. If a video sequence or some training set other than the given low-resolution image is available, this kind of extra information can greatly aid in the…

Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting…

In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…

In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…

In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric…

Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…

The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…

Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points.…

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…

Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…

A corpus of recent work has revealed that the learned index can improve query performance while reducing the storage overhead. It potentially offers an opportunity to address the spatial query processing challenges caused by the surge in…