相关论文: Tucker tensor factor models: matricization and mod…

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…

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…

Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…

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…

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,…

Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional…

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product…

In this paper, we propose a new algorithm for point cloud denoising based on the tensor Tucker decomposition. We first represent the local surface patches of a noisy point cloud to be matrices by their distances to a reference point, and…

This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…

We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…

Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…

Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…

This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…

Higher-order tensor decompositions have hardly been used in muscle activity analysis despite multichannel electromyography (EMG) datasets naturally occurring as multi-way structures. Here, we seek to demonstrate and discuss the potential of…

Combining tensor network techniques with quantum autoregressive moving average models, we quantify the effects of time-correlated noise on quantum algorithms and predict their performance at scale. As a paradigmatic test case, we examine…