Privacy-Preserving Logistic Regression Training on Large Datasets

TL;DR

This paper introduces an efficient homomorphic encryption-based algorithm for privacy-preserving logistic regression on large datasets, utilizing a quadratic gradient for faster convergence and demonstrating practical feasibility on real financial data.

Contribution

It proposes a mini-batch homomorphic logistic regression training algorithm using quadratic gradient, improving efficiency for large encrypted datasets.

Findings

Mini-batch algorithm outperforms full-batch in speed.

Practical training on large encrypted datasets demonstrated.

Quadratic gradient accelerates convergence.

Abstract

Privacy-preserving machine learning is one class of cryptographic methods that aim to analyze private and sensitive data while keeping privacy, such as homomorphic logistic regression training over large encrypted data. In this paper, we propose an efficient algorithm for logistic regression training on large encrypted data using Homomorphic Encryption (HE), which is the mini-batch version of recent methods using a faster gradient variant called $\texttt{quadratic gradient}$. It is claimed that $\texttt{quadratic gradient}$ can integrate curve information (Hessian matrix) into the gradient and therefore can effectively accelerate the first-order gradient (descent) algorithms. We also implement the full-batch version of their method when the encrypted dataset is so large that it has to be encrypted in the mini-batch manner. We compare our mini-batch algorithm with our full-batch implementation method on real financial data consisting of 422,108 samples with 200 freatures. %Our experiments show that Nesterov's accelerated gradient (NAG) Given the inefficiency of HEs, our results are inspiring and demonstrate that the logistic regression training on large encrypted dataset is of practical feasibility, marking a significant milestone in our understanding.