Related papers: Canonical Tensor Decomposition for Knowledge Base …

This paper explores the finiteness of the solution set of the polynomial complementarity problem (PCP). To achieve this goal, we introduce two new classes of structured tensor tuples, namely the nondegenerate tensor tuple and the strong…

Performance tuning, software/hardware co-design, and job scheduling are among the many tasks that rely on models to predict application performance. We propose and evaluate low-rank tensor decomposition for modeling application performance.…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…

This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…

Higher-order tensors are well-suited for representing multi-dimensional data, such as images and videos, which typically characterize low-rank structures. Low-rank tensor decomposition has become essential in machine learning and computer…

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC…

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Answering complex questions is a time-consuming activity for humans that requires reasoning and integration of information. Recent work on reading comprehension made headway in answering simple questions, but tackling complex questions is…

The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions…

Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions (CPD) are widely applied to analyze high order tensors. Existing CPD methods use alternating least square (ALS) iterations and hence need to unfold tensors to each of the $N$…

The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. However, it is well known that the low rank CPD approximation…

One of the key problems in tensor completion is the number of uniformly random sample entries required for recovery guarantee. The main aim of this paper is to study $n_1 \times n_2 \times n_3$ third-order tensor completion based on…

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does…

We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix completion techniques for a small number of slices along with…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

The safe integration of machine learning modules in decision-making processes hinges on their ability to quantify uncertainty. A popular technique to achieve this goal is conformal prediction (CP), which transforms an arbitrary base…

We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…