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

TL;DR

This paper introduces new algorithms and high-performance Python implementations for tensor completion on sparse tensors, enabling efficient parallel processing with generalized loss functions and novel multi-tensor primitives.

Contribution

It extends the Cyclops library with new multi-tensor primitives and algorithms for tensor completion, optimized for sparse tensors and generalized loss functions.

Findings

Multi-tensor routines outperform pairwise contraction in efficiency.

New primitives demonstrate high performance on supercomputers.

Tensor completion methods scale to billion-scale sparse tensors.

Abstract

Tensor computations are increasingly prevalent numerical techniques in data science, but pose unique challenges for high-performance implementation. We provide novel algorithms and systems infrastructure which enable efficient parallel implementation of algorithms for tensor completion with generalized loss functions. Specifically, we consider alternating minimization, coordinate minimization, and a quasi-Newton (generalized Gauss-Newton) method. By extending the Cyclops library, we implement all of these methods in high-level Python syntax. To make possible tensor completion for very sparse tensors, we introduce new multi-tensor primitives, for which we provide specialized parallel implementations. We compare these routines to pairwise contraction of sparse tensors by reduction to hypersparse matrix formats, and find that the multi-tensor routines are more efficient in theoretical cost and execution time in experiments. We provide microbenchmarking results on the Stampede2 supercomputer to demonstrate the efficiency of the new primitives and Cyclops functionality. We then study the performance of the tensor completion methods for a synthetic tensor with 10 billion nonzeros and the Netflix dataset, considering both least squares and Poisson loss functions.