Adaptive Sketching for Fast and Convergent Canonical Polyadic Decomposition

Jul 12, 2020



This work considers the canonical polyadic decomposition (CPD) of tensors using proximally regularized sketched alternating least squares algorithms. First, it establishes a sublinear rate of convergence for proximally regularized sketched CPD algorithms under two natural conditions that are known to be satisfied by many popular forms of sketching. Second, it demonstrates that the iterative nature of CPD algorithms can be exploited algorithmically to choose more performant sketching rates. This is accomplished by introducing CPD-MWU, a proximally-regularized sketched alternating least squares algorithm that adaptively selects the sketching rate at each iteration. On both synthetic and real data we observe that for noisy tensors CPD-MWU produces decompositions of comparable accuracy to the standard CPD decomposition in less time, often half the time; for ill-conditioned tensors, given the same time budget, CPD-MWU produces decompositions with an order-of-magnitude lower relative error. For a representative real- world dataset CPD-MWU produces residual errors on average 20


About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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