Encrypted Accelerated Least Squares Regression
Pedro Esperanca, Louis Aslett, Chris Holmes
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.
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.}
}