Related papers: Towards Efficient and Accurate Approximation: Tens…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods…
We consider the problem of rank-$1$ low-rank approximation (LRA) in the matrix-vector product model under various Schatten norms: $$ \min_{\|u\|_2=1} \|A (I - u u^\top)\|_{\mathcal{S}_p} , $$ where $\|M\|_{\mathcal{S}_p}$ denotes the…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
In this work, we address the problem of outlier detection for robust motion estimation by using modern sparse-low-rank decompositions, i.e., Robust PCA-like methods, to impose global rank constraints. Robust decompositions have shown to be…
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…
The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the…
Computing low-rank approximations of kernel matrices is an important problem with many applications in scientific computing and data science. We propose methods to efficiently approximate and store low-rank approximations to kernel matrices…
This paper describes and compares some structure preserving techniques for the solution of linear discrete ill-posed problems with the t-product. A new randomized tensor singular value decomposition (R-tSVD) with a t-product is presented…
Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficient sampling strategy for two primary tensor CUR…
The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally…
In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
Effective modeling of heterogeneous subpopulations presents a significant challenge due to variations in individual characteristics and behaviors. This paper proposes a novel approach to address this issue through multi-task learning (MTL)…