Related papers: Theoretical and Experimental Analyses of Tensor-Ba…
In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…
We propose a framework for training multiple neural networks simultaneously. The parameters from all models are regularised by the tensor trace norm, so that each neural network is encouraged to reuse others' parameters if possible -- this…
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
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…
In this paper, we introduce a unified framework, inspired by classical regularization theory, for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares…
The objective of this study is to develop a good risk model for classifying business delinquency by simultaneously exploring several machine learning based methods including regularization, hyper-parameter optimization, and model ensembling…
Semi-supervised learning is an important and active topic of research in pattern recognition. For classification using linear discriminant analysis specifically, several semi-supervised variants have been proposed. Using any one of these…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
Regularized regression techniques for linear regression have been created the last few ten years to reduce the flaws of ordinary least squares regression with regard to prediction accuracy. In this paper, new methods for using regularized…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
Symbolic regression is a machine learning technique, and it has seen many advancements in recent years, especially in genetic programming approaches (GPSR). Furthermore, it has been known for many years that constant optimization of…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
In recent years, promising statistical modeling approaches to tensor data analysis have been rapidly developed. Traditional multivariate analysis tools, such as multivariate regression and discriminant analysis, are generalized from…