Encrypted Training Using Logistic Regression with Different Polynomial Approximations of the Sigmoid Function

This chapter delves into the critical issue of data privacy and security in machine learning, particularly when dealing with sensitive information in unencrypted form. It explores various privacy-preserving techniques, including blockchain technology, federated learning, differential privacy, and homomorphic encryption, with a focus on the latter due to its flexibility and suitability for real-world applications. The text presents a framework that combines fully homomorphic encryption (FHE) with machine learning to ensure data remains encrypted and secure throughout the analysis process. A key challenge addressed is the incompatibility of the sigmoid activation function with FHE operations, leading to the exploration of various polynomial approximations of the sigmoid function. The experiments conducted on diverse datasets, including medical, historical, and geological fields, reveal distinct patterns of behavior and highlight the importance of dataset characteristics. The results demonstrate that polynomial approximations can achieve accuracy comparable to plaintext models, validating the feasibility of privacy-preserving machine learning. The text also discusses the computational overhead involved and suggests that scaling to larger datasets is feasible with high-performance computing systems or GPU-based configurations. Overall, this chapter provides a comprehensive overview of the current state and future potential of privacy-preserving machine learning, offering valuable insights for professionals in the field.