Related papers: Tensor Completion with Provable Consistency and Fa…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Efficient resource allocation is one of the main driving forces of human civilizations. Of the many existing approaches to resource allocation, matrix completion is one that is frequently applied. In this paper, we investigate a special…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
The tensor data recovery task has thus attracted much research attention in recent years. Solving such an ill-posed problem generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms…
We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured…
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
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…
We study tensor completion in the agnostic setting. In the classical tensor completion problem, we receive $n$ entries of an unknown rank-$r$ tensor and wish to exactly complete the remaining entries. In agnostic tensor completion, we make…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
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…
In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption…
In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…
Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…
The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…