Related papers: Goal-Oriented Low-Rank Tensor Decompositions for N…
Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of…
We propose a new data analysis approach for the efficient post-processing of bundles of finite element data from numerical simulations. The approach is based on the mathematical principles of symmetry. We consider the case where simulations…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
Representation learning is a widely adopted framework for learning in data-scarce environments to obtain a feature extractor or representation from various different yet related tasks. Despite extensive research on representation learning,…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…
In this paper, we propose a novel low-tubal-rank tensor recovery model, which directly constrains the tubal rank prior for effectively removing the mixed Gaussian and sparse noise in hyperspectral images. The constraints of tubal-rank and…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Low-rank factorization is a popular model compression technique that minimizes the error $\delta$ between approximated and original weight matrices. Despite achieving performances close to the original models when $\delta$ is optimized, a…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…