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In the near-field region of an extremely large-scale multiple-input multiple-output (XL MIMO) system, channel reconstruction is typically addressed through sparse parameter estimation based on compressed sensing (CS) algorithms after…
This paper generalizes the Maurer--Pontil framework of finite-dimensional lossy coding schemes to the setting where a high-dimensional random vector is mapped to an element of a compact set of latent representations in a lower-dimensional…
We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…
We introduce the transport-and-pack(TAP) problem, a frequently encountered instance of real-world packing, and develop a neural optimization solution based on reinforcement learning. Given an initial spatial configuration of boxes, we seek…
Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…
Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…
The Brenier optimal map and the Knothe-Rosenblatt rearrangement are two instances of a transport map, that is to say a map sending one measure onto another. The main interest of the former is that it solves the Monge-Kantorovich optimal…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Despite technological advancements, the significance of interdisciplinary subjects like complex networks has grown. Exploring communication within these networks is crucial, with traffic becoming a key concern due to the expanding…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…