On the Privacy-preserving Generalized Eigenvalue Problem

Wei-Hong Chen, YU-FENG HUANG, Chen Yu Lee, Hung Yi Chen, Shi-Chun Tsai
Proceedings of the 17th Asian Conference on Machine Learning, PMLR 304:814-829, 2025.

Abstract

Generalized eigenvalues serve as a foundational tool for extracting insights from data and constructing robust statistical learning models, while differential privacy ensures the protection of individual information within these models by minimizing the impact of any single data point. In this work, we propose an $(\\epsilon,\\delta)$-differential privacy algorithm to solve the generalized eigenvalue problem (GEP). Our algorithm gives better classification accuracy over existing methods and has the nearly optimal $\\ell_2$-norm error bounds in both low and high dimensions. Furthermore, our algorithm guarantees convergence to the solution regardless of the initial vector and this improves a previous method that requires a specific procedure to find a proper starting vector. Our experiments confirm the effectiveness of our algorithm in safeguarding privacy while simultaneously boosting classification accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v304-chen25b, title = {On the Privacy-preserving Generalized Eigenvalue Problem}, author = {Chen, Wei-Hong and HUANG, YU-FENG and Lee, Chen Yu and Chen, Hung Yi and Tsai, Shi-Chun}, booktitle = {Proceedings of the 17th Asian Conference on Machine Learning}, pages = {814--829}, year = {2025}, editor = {Lee, Hung-yi and Liu, Tongliang}, volume = {304}, series = {Proceedings of Machine Learning Research}, month = {09--12 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v304/main/assets/chen25b/chen25b.pdf}, url = {https://proceedings.mlr.press/v304/chen25b.html}, abstract = {Generalized eigenvalues serve as a foundational tool for extracting insights from data and constructing robust statistical learning models, while differential privacy ensures the protection of individual information within these models by minimizing the impact of any single data point. In this work, we propose an $(\\epsilon,\\delta)$-differential privacy algorithm to solve the generalized eigenvalue problem (GEP). Our algorithm gives better classification accuracy over existing methods and has the nearly optimal $\\ell_2$-norm error bounds in both low and high dimensions. Furthermore, our algorithm guarantees convergence to the solution regardless of the initial vector and this improves a previous method that requires a specific procedure to find a proper starting vector. Our experiments confirm the effectiveness of our algorithm in safeguarding privacy while simultaneously boosting classification accuracy.} }
Endnote
%0 Conference Paper %T On the Privacy-preserving Generalized Eigenvalue Problem %A Wei-Hong Chen %A YU-FENG HUANG %A Chen Yu Lee %A Hung Yi Chen %A Shi-Chun Tsai %B Proceedings of the 17th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Hung-yi Lee %E Tongliang Liu %F pmlr-v304-chen25b %I PMLR %P 814--829 %U https://proceedings.mlr.press/v304/chen25b.html %V 304 %X Generalized eigenvalues serve as a foundational tool for extracting insights from data and constructing robust statistical learning models, while differential privacy ensures the protection of individual information within these models by minimizing the impact of any single data point. In this work, we propose an $(\\epsilon,\\delta)$-differential privacy algorithm to solve the generalized eigenvalue problem (GEP). Our algorithm gives better classification accuracy over existing methods and has the nearly optimal $\\ell_2$-norm error bounds in both low and high dimensions. Furthermore, our algorithm guarantees convergence to the solution regardless of the initial vector and this improves a previous method that requires a specific procedure to find a proper starting vector. Our experiments confirm the effectiveness of our algorithm in safeguarding privacy while simultaneously boosting classification accuracy.
APA
Chen, W., HUANG, Y., Lee, C.Y., Chen, H.Y. & Tsai, S.. (2025). On the Privacy-preserving Generalized Eigenvalue Problem. Proceedings of the 17th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 304:814-829 Available from https://proceedings.mlr.press/v304/chen25b.html.

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