Encrypted Accelerated Least Squares Regression

Pedro Esperanca, Louis Aslett, Chris Holmes
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:334-343, 2017.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-esperanca17a, title = {{Encrypted accelerated least squares regression}}, author = {Esperanca, Pedro and Aslett, Louis and Holmes, Chris}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {334--343}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/esperanca17a/esperanca17a.pdf}, url = {https://proceedings.mlr.press/v54/esperanca17a.html}, 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.} }
Endnote
%0 Conference Paper %T Encrypted Accelerated Least Squares Regression %A Pedro Esperanca %A Louis Aslett %A Chris Holmes %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-esperanca17a %I PMLR %P 334--343 %U https://proceedings.mlr.press/v54/esperanca17a.html %V 54 %X 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.
APA
Esperanca, P., Aslett, L. & Holmes, C.. (2017). Encrypted Accelerated Least Squares Regression. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:334-343 Available from https://proceedings.mlr.press/v54/esperanca17a.html.

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