Multi-Frequency Phase Synchronization

Tingran Gao, Zhizhen Zhao
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2132-2141, 2019.

Abstract

We propose a novel formulation for phase synchronization—the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons—as a nonconvex optimization problem that enforces consistency among the pairwise comparisons in multiple frequency channels. Inspired by harmonic retrieval in signal processing, we develop a simple yet efficient two-stage algorithm that leverages the multi-frequency information. We demonstrate in theory and practice that the proposed algorithm significantly outperforms state-of-the-art phase synchronization algorithms, at a mild computational costs incurred by using the extra frequency channels. We also extend our algorithmic framework to general synchronization problems over compact Lie groups.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-gao19f, title = {Multi-Frequency Phase Synchronization}, author = {Gao, Tingran and Zhao, Zhizhen}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {2132--2141}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/gao19f/gao19f.pdf}, url = {https://proceedings.mlr.press/v97/gao19f.html}, abstract = {We propose a novel formulation for phase synchronization—the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons—as a nonconvex optimization problem that enforces consistency among the pairwise comparisons in multiple frequency channels. Inspired by harmonic retrieval in signal processing, we develop a simple yet efficient two-stage algorithm that leverages the multi-frequency information. We demonstrate in theory and practice that the proposed algorithm significantly outperforms state-of-the-art phase synchronization algorithms, at a mild computational costs incurred by using the extra frequency channels. We also extend our algorithmic framework to general synchronization problems over compact Lie groups.} }
Endnote
%0 Conference Paper %T Multi-Frequency Phase Synchronization %A Tingran Gao %A Zhizhen Zhao %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-gao19f %I PMLR %P 2132--2141 %U https://proceedings.mlr.press/v97/gao19f.html %V 97 %X We propose a novel formulation for phase synchronization—the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons—as a nonconvex optimization problem that enforces consistency among the pairwise comparisons in multiple frequency channels. Inspired by harmonic retrieval in signal processing, we develop a simple yet efficient two-stage algorithm that leverages the multi-frequency information. We demonstrate in theory and practice that the proposed algorithm significantly outperforms state-of-the-art phase synchronization algorithms, at a mild computational costs incurred by using the extra frequency channels. We also extend our algorithmic framework to general synchronization problems over compact Lie groups.
APA
Gao, T. & Zhao, Z.. (2019). Multi-Frequency Phase Synchronization. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:2132-2141 Available from https://proceedings.mlr.press/v97/gao19f.html.

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