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Tensor computations are increasingly prevalent numerical techniques in datascience, but pose unique challenges for high-performance implementation. Weprovide novel algorithms and systems infrastructure which enable efficientparallel implementation of algorithms for tensor completion with generalizedloss functions. Specifically, we consider alternating minimization, coordinateminimization, and a quasi-Newton (generalized Gauss-Newton) method. Byextending the Cyclops library, we implement all of these methods in high-levelPython syntax. To make possible tensor completion for very sparse tensors, weintroduce new multi-tensor primitives, for which we provide specializedparallel implementations. We compare these routines to pairwise contraction ofsparse tensors by reduction to hypersparse matrix formats, and find that themulti-tensor routines are more efficient in theoretical cost and execution timein experiments. We provide microbenchmarking results on the Stampede2supercomputer to demonstrate the efficiency of the new primitives and Cyclopsfunctionality. We then study the performance of the tensor completion methodsfor a synthetic tensor with 10 billion nonzeros and the Netflix dataset,considering both least squares and Poisson loss functions.

Distributed-Memory Tensor Completion for Generalized Loss Functions in Python using New Sparse Tensor Kernels