Related papers: Tensor Neyman-Pearson Classification: Theory, Algo…

Tensor-based representations are being increasingly used to represent complex data types such as imaging data, due to their appealing properties such as dimension reduction and the preservation of spatial information. Recently, there is a…

We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…

Most state-of-the-art neural network potentials do not account for molecular attributes other than atomic numbers and positions, which limits its range of applicability by design. In this work, we demonstrate the importance of including…

This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order $p \ge 3:$ when the effective ranks of the covariances of the component…

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…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

A common issue for classification in scientific research and industry is the existence of imbalanced classes. When sample sizes of different classes are imbalanced in training data, naively implementing a classification method often leads…

Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…

A scheme for detection of abnormality in molecular nano-networks is proposed. This is motivated by the fact that early diagnosis, classification and detection of diseases such as cancer play a crucial role in their successful treatment. The…

We develop a new approach to estimate the uncertainty due to missing higher orders in perturbative predictions (the perturbative "theory uncertainty"), which overcomes many inherent limitations of the currently prevalent methods based on…

In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data…

We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…

Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the…

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 chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r…

Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

Artificial intelligence (AI) has brought tremendous impacts on biomedical sciences from academic researches to clinical applications, such as in biomarkers' detection and diagnosis, optimization of treatment, and identification of new…