相关论文: Spectral gap-based deterministic tensor completion

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

We investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank. In order to find the deterministic necessary…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…

We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…

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…

Tensor data, or multi-dimensional arrays, is a data format popular in multiple fields such as social network analysis, recommender systems, and brain imaging. It is not uncommon to observe tensor data containing missing values, and tensor…

The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…

In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…

In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…

This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples.…

We study the problem of low-rank tensor factorization in the presence of missing data. We ask the following question: how many sampled entries do we need, to efficiently and exactly reconstruct a tensor with a low-rank orthogonal…

We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Matrix completion is often applied to data with entries missing not at random (MNAR). For example, consider a recommendation system where users tend to only reveal ratings for items they like. In this case, a matrix completion method that…

We explore applying a tensor completion approach to complete the DrugMatrix toxicogenomics dataset. Our hypothesis is that by preserving the 3-dimensional structure of the data, which comprises tissue, treatment, and transcriptomic…

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative…