Related papers: Distributed-Memory Tensor Completion for Generaliz…

Alternating least squares is the most widely used algorithm for CP tensor decomposition. However, alternating least squares may exhibit slow or no convergence, especially when high accuracy is required. An alternative approach is to regard…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically…

Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…

Sparse tensors are rapidly becoming critical components of modern deep learning workloads. However, developing high-performance sparse operators can be difficult and tedious, and existing vendor libraries cannot satisfy the escalating…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

In this paper, we develop software for decomposing sparse tensors that is portable to and performant on a variety of multicore, manycore, and GPU computing architectures. The result is a single code whose performance matches optimized…

Sparse tensor decomposition and completion are common in numerous applications, ranging from machine learning to computational quantum chemistry. Typically, the main bottleneck in optimization of these models are contractions of a single…

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…

Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP method (GCP) was introduced by Hong and Kolda to allow for flexible choice of the loss…

Sparse tensors appear frequently in distributed deep learning, either as a direct artifact of the deep neural network's gradients, or as a result of an explicit sparsification process. Existing communication primitives are agnostic to the…

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…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse…

Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with…

Sparse tensor operations are increasingly important in diverse applications such as social networks, deep learning, diagnosis, crime, and review analysis. However, a major obstacle in sparse tensor research is the lack of large-scale sparse…