相关论文: Ares: Approximate Representations via Efficient Sp…

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…

The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find…

A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…

Deep learning accelerators efficiently train over vast and growing amounts of data, placing a newfound burden on commodity networks and storage devices. A common approach to conserve bandwidth involves resizing or compressing data prior to…

We propose a scheme for multi-layer representation of images. The problem is first treated from an information-theoretic viewpoint where we analyze the behavior of different sources of information under a multi-layer data compression…

This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain.…

Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the…

Piecewise Linear Approximation (PLA) is a well-established tool to reduce the size of the representation of time series by approximating the series by a sequence of line segments while keeping the error introduced by the approximation…

Hypergraphs provide a natural representation for many-to-many relationships in data-intensive applications, yet their scalability is often hindered by high memory consumption. While prior work has improved computational efficiency, reducing…

Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large…

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could…

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…