基于联邦学习的Gamma回归算法

FL-GRM:Gamma Regression Algorithm Based on Federated Learning

在水文学、气象学以及保险理赔评估等领域中,通常假设因变量服从Gamma分布,相比多元线性回归,在Gamma分布假设下建立起的Gamma回归具有更出色的拟合效果。以往获得Gamma回归模型的方法是将数据集中起来进行训练,当数据是由多方提供时,在不交换数据的情况下训练满足隐私保护的Gamma回归模型成为需要解决的问题。为此,提出了一种多方安全的纵向联邦Gamma回归算法,该算法首先使用迭代法推导出纵向联邦Gamma回归模型的对数似然估计表达式,然后结合工程实际确定模型的连接函数,进而构造损失函数建立参数的梯度更新策略,最后对同态加密后的各方参数进行融合更新,获得联邦学习后的Gamma回归模型。在两种公开数据集上进行性能测试,实验结果表明,所提联邦Gamma回归算法在不交换数据的前提下,可有效利用多方数据的价值生成Gamma回归模型,该模型对数据的拟合效果逼近数据在集中情况下学习到的Gamma回归模型,优于单方独立学习获得的Gamma回归模型。

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.