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arXiv · 2502.09534

Fast Tensor Completion via Approximate Richardson Iteration

Mehrdad Ghadiri·Matthew Fahrbach·Yunbum Kook·Ali Jadbabaie
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Abstract

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker, and tensor-train decompositions). However, such algebraic structure is often lost in TC regression problems, making direct extensions unclear. This work proposes a novel lifting method for approximately solving TC regression problems using structured TD regression algorithms as blackbox subroutines, enabling sublinear-time methods. We analyze the convergence rate of our approximate Richardson iteration-based algorithm, and our empirical study shows that it can be 100x faster than direct methods for CP completion on real-world tensors.

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Mehrdad Ghadiri, Matthew Fahrbach, Yunbum Kook, Ali Jadbabaie. 2025-08-12. Fast Tensor Completion via Approximate Richardson Iteration. https://arxiv.org/abs/2502.09534

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