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

Area of Science:

• Machine Learning
• Statistical Modeling
• Data Privacy

Background:

• Federated Learning (FL) enables collaborative model training across decentralized data sources while preserving privacy.
• A key challenge in FL is ensuring the federated model's performance matches a centrally trained global model.
• Research on FL for functional regression models, which analyze functional data, is limited.

Purpose of the Study:

• To develop an efficient and privacy-preserving federated learning algorithm for function-on-function regression.
• To address the challenge of achieving comparable performance in federated models without data sharing.

Main Methods:

• Development of the federated Gradient Boosting with Least Squares Approximation (fed-GB-LSA) algorithm.
• Leveraging Gradient Boosting for sparse feature selection in functional regression.
• Utilizing Least Squares Approximation for efficient, one-shot federated learning.

Main Results:

• The fed-GB-LSA algorithm enables efficient, privacy-preserving federated learning for function-on-function regression.
• The method allows for sparse selection of functional and non-functional features.
• Theoretical guarantees for federated model performance are provided without cross-server data sharing.

Conclusions:

• The proposed fed-GB-LSA is the first algorithm for federated learning of function-on-function regression.
• It offers communication and statistical efficiency, validated through simulations and a real-world application in Obstructive Sleep Apnea telemonitoring.