相关论文: Bias Correction in Saupe Tensor Estimation

We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…

Higher order singular value decomposition (HOSVD) is an important tool for analyzing big data in multilinear algebra and machine learning. In this paper, we present two quantum algorithms for HOSVD. Our methods allow one to decompose a…

The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the…

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…

Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…

Face recognition and identification is a very important application in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement.…

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical…

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…

We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

In this paper, we investigate the properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by the infinite-dimensional Wiener process and Poisson random…

Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…

This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor…

We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…

This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and…

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…

With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…

Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated singular values occur,…