Towards Federated Learning by Kernels

Kernelization enhances machine learning algorithms, allowing them to solve nonlinear problems by embedding data into high-dimensional reproducing kernel Hilbert spaces (RKHS). It notably expanded the utility of Support Vector Machines (SVM) from linear to nonlinear classification, making SVM a powerful tool in modern machine learning. This technique, while yielding linear solutions in RKHS, translates them back to nonlinear solutions in the original data space, leveraging the representer theorem for feasible computation. The paper discusses applying kernelization to federated learning–-a collaborative model prioritizing data privacy–-where multiple parties work together without exposing individual data. The approach relies on sharing Gram matrices, representing kernel values, to preserve the confidentiality of original data while enabling collective learning. Compared to traditional multi-party computation (MPC) and homomorphic encryption (HE), our kernelization-based method requires significantly less computational resources, offering a more practical solution for federated learning. However, it's crucial to mathematically evaluate the privacy implications of disclosing Gram matrices to ensure data security. This framework paves the way for efficient, privacy-preserving federated learning.