Related papers: Tensor Polynomial Additive Model

This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…

The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Understanding the classifications of deep neural networks, e.g. used in safety-critical situations, is becoming increasingly important. While recent models can locally explain a single decision, to provide a faithful global explanation…

Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…

In recent years, machine learning and AI have been introduced in many industrial fields. In fields such as finance, medicine, and autonomous driving, where the inference results of a model may have serious consequences, high…

Raman mapping technique has been used to perform in-line quality inspections of nanomanufacturing processes. In such an application, massive high-dimensional Raman mapping data with mixed effects is generated. In general, fixed effects and…

The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…

Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale…

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…

Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of…

We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…

In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited…

Conventional machine learning methods are predominantly designed to predict outcomes based on a single data type. However, practical applications may encompass data of diverse types, such as text, images, and audio. We introduce…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…