FL-GRM:Gamma Regression Algorithm Based on Federated Learning

Abstract

People commonly hypothesize that an independent variable follows a Gamma distribution in many areas,including hydrology,meteorology and insurance claim.Under the Gamma distribution assumption,Gamma regression model enables an outstanding fitting effect,compared with multivariate linear-regression model.Previous studies may be able to obtain a Gamma regression model trained only on a public dataset.However,when the datasets are provided by multiple parties,how to seek to address the problem of data privacy by training Gamma regression model without exchanging the data itself? A secure multi-party federated Gamma regression algorithm has been applied to this area.Firstly,the log-likelihood function is derived with the iterative method.Secondly,the link function is determined according to the fact,and the gradient updating strategy is constructed by the loss function.Finally,the parameters with homomorphic encryption are updated,then the training is completed.The model is tested on two public datasets,and the results show that under the premise of privacy protection our method can effectively use the value of multi-party data to generate Gamma regression model.The fitting performance of our method is better than that of Gamma regression model implements in a single part,and is close to the result yielded by centralized data learning model.

Keywords

• federated learning|gamma regression|homomorphic encryption|privacy protection|secure multi-party computation