Data Confidentiality in Machine Learning: Exploring Multivariate Regression and Its Application on Encrypted Medical Data

In this work, we present a concise literature review on the application of multivariate regression using gradient descent. We employed gradient descent, which provides an optimal approach for minimizing the cost function in a regression model for error estimation, and further modelled a multivariate regression algorithm to perform regression analysis over encrypted data. To encrypt the dataset, we modified the original integer homomorphic encryption scheme into a new scheme for dataset encryption to achieve an efficient and secure data encryption and decryption operation. Since homomorphic operations do not support division, we devised a division-free gradient descent multivariate regression over cost-effective VHE encrypted training samples with high regression accuracy. We conducted simulations to compare least-squares and gradient descent with and without division. We also proved the applicability of machine learning for modeling encrypted datasets based on breast cancer datasets, with the focus on determining breast cancer potential patients. In our system, encrypted datasets should not interrupt the learning task, nor should the learning task reveal sensitive information to unauthorized users.