Encrypted accelerated least squares regression
This work addresses privacy concerns in data analysis by enabling regression on encrypted data, though it is incremental as it adapts existing methods to encrypted settings.
The paper tackled the problem of performing statistical regression on encrypted data, which is typically not feasible, by developing gradient descent algorithms for least squares and ridge regression under fully homomorphic encryption. The result showed that gradient descent is faster in encrypted computation, with theoretical bounds ensuring correctness and empirical evidence favoring a non-standard acceleration technique.
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.