Federated Function-on-function Regression with an Efficient Gradient Boosting Algorithm for Privacy-Preserving...

Federated Learning (FL) is an emerging computing paradigm to collaboratively train Machine Learning (ML) models across multi-source data while preserving privacy. The major challenge of "meaningful" implementation of FL for any ML model is how to guarantee that the federated ML model can achieve comparable performance compared to the global model trained using the combined data. Moreover, there are very limited studies on FL of functional regression models that analyze functional data, a commonly encountered type of data in many fields. This study develops the first-of-its-kind federated Gradient Boosting algorithm with the Least Squares Approximation (fed-GB-LSA) for efficient, privacy-preserving federated learning of the function-on-function regression with several distinct merits: (1) The GB-based algorithm allows the sparse selection of multivariate functional and non-functional features in the function-on-function regression prediction, which is not straightforward in the functional regression; (2) The parameter estimation by the GB algorithm results in separate sub-optimization problems with explicitly analytical solutions for each of the features, providing an efficient estimation algorithm for the function-on-function regression; (3) The LSA-enabled fed-GB provides a "one-shot" approach for FL that is communicationally and statistically efficient, providing theoretical guarantees to the federated model's performance without data sharing across local servers. The proposed fed-GB-LSA is tested in extensive simulation studies by considering real-world challenges such as device heterogeneity and applied in a real-world dataset for privacy-preserving telemonitoring of Obstructive Sleep Apnea (OSA).