Related papers: Analyzing Tensor Power Method Dynamics in Overcomp…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

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…

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…

We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor…

We consider the tensor completion problem of predicting the missing entries of a tensor. The commonly used CP model has a triple product form, but an alternate family of quadratic models, which are the sum of pairwise products instead of a…

As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified…

In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

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…

In this paper we study the training dynamics for gradient flow on over-parametrized tensor decomposition problems. Empirically, such training process often first fits larger components and then discovers smaller components, which is similar…

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on…

The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…

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.…

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…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…