Related papers: Spectral algorithms for tensor completion
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
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…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix…
In this article, a Probability Mass Function (PMF) estimation method which tames the curse of dimensionality is proposed. This method, called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D, has for principle to partially…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a…
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in…
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows…
We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…
In this paper, we consider the network latency estimation, which has been an important metric for network performance. However, a large scale of network latency estimation requires a lot of computing time. Therefore, we propose a new method…
Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the…
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…
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…