Related papers: High-Dimensional Tensor Discriminant Analysis with…

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…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…

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…

This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed that this problem can be tackled using…

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA is to find mode-specific projections that optimally separate tensor data from…

There has been a great effort to transfer linear discriminant techniques that operate on vector data to high-order data, generally referred to as Multilinear Discriminant Analysis (MDA) techniques. Many existing works focus on maximizing…

As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Supervised learning with missing data aims at building the best prediction of a target output based on partially-observed inputs. Major approaches to address this problem can be decomposed into $(i)$ impute-then-predict strategies, which…

Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…

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…

Matrix completion, the problem of completing missing entries in a data matrix with low dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog, that attempts to impute…

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,…

Tensor completion plays a crucial role in applications such as recommender systems and medical imaging, where data are often highly incomplete. While extensive prior work has addressed tensor completion with data missingness, most assume…

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…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…