相关论文: Optimality of Operator-Like Wavelets for Represent…

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

Predictions of nuclear models guide the design of nuclear facilities to ensure their safe and efficient operation. Because nuclear models often do not perfectly reproduce available experimental data, decisions based on their predictions may…

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…

An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…

Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in {\mathbb R}^p$…

This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…

In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and…

Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…

Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these…

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…

This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the…

In distributed-parameter inverse problems in computational mechanics, spatially varying fields are inferred from noisy, indirect, and heterogeneous observations. The relevant identifiability question concerns which spatial perturbation…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion…

We adress the problem of Laplace deconvolution with random noise in a regression framework. The time set is not considered to be fixed, but grows with the number of observation points. Moreover, the convolution kernel is unknown, and…