Encrypted accelerated least squares regression

Esperança, P.M.; Aslett, L.J.M.; Holmes, C.C.; Singh, Aarti; Zhu, Jerry

Abstract

Information that is stored in an encrypted format is, by definition, usually not amenable to statistical analysis or machine learning methods. In this paper we present detailed analysis of coordinate and accelerated gradient descent algorithms which are capable of fitting least squares and penalised ridge regression models, using data encrypted under a fully homomorphic encryption scheme. Gradient descent is shown to dominate in terms of encrypted computational speed, and theoretical results are proven to give parameter bounds which ensure correctness of decryption. The characteristics of encrypted computation are empirically shown to favour a non-standard acceleration technique. This demonstrates the possibility of approximating conventional statistical regression methods using encrypted data without compromising privacy.

Citation

Esperança, P., Aslett, L., Holmes, C., Singh, A., & Zhu, J. (2017). Encrypted accelerated least squares regression. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54 (334-343)

• Conference Name: The 20th International Conference on Artificial Intelligence and Statistics
• Conference Location: Fort Lauderdale, Florida
• Acceptance Date: Jan 25, 2017
• Online Publication Date: Apr 20, 2017
• Publication Date: Jan 1, 2017
• Deposit Date: Apr 24, 2017
• Publicly Available Date: May 4, 2017
• Volume: 54
• Pages: 334-343
• Series Title: Proceedings of machine learning research
• Series ISSN: 2640-3498
• Book Title: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54.
• Publisher URL: http://proceedings.mlr.press/v54/esperanca17a/esperanca17a.pdf