# Encrypted accelerated least squares regression

arXiv: https://arxiv.org/abs/1703.00839 · HTML: https://mlsanity.com/paper/1703.00839/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2017.

## Built on by (most cited first, 2 of 2)

- [Deploying Convolutional Networks on Untrusted Platforms Using 2D Holographic Reduced Representations](https://mlsanity.com/paper/2206.05893/) (2022)
- [Encrypted Linear Contextual Bandit](https://mlsanity.com/paper/2103.09927/) (2021)

## Abstract (arXiv)

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.