基于同态加密的多分类Logistic回归模型

Multinomial Logistic Regression Model Based on Homomorphic Encryption

随着计算能力的发展,机器学习得到了广泛的应用,数据的安全问题也成为一个重要问题.同态加密技术可以在不泄露明文信息的情况下,对密文进行运算并在解密后得到与在明文上执行相应运算一致的结果.因此,同态加密是一种可行的有潜力的数据安全外包解决方案.为了解决现实生活中出现的多分类问题,本文基于Cheon等提出的HEAAN同态加密方案,提出了一种能有效保护数据隐私的多分类Logistic回归模型,采用"一对其余"的拆解策略,通过训练多个分类器,将二分类Logistic回归模型推广到多分类.数据持有者可以将数据加密后发送给服务器,服务器使用多分类Logistic回归模型对加密数据进行训练,并将结果传回数据持有者,数据持有者解密结果后可以用来对多分类数据进行预测,整个过程中不会有隐私被泄露.本文通过对UCI的Dermatology和Iris数据集进行了实验,测试模型的性能.Dermatology数据集包含358条样本, 34个特征属性,分为6个类别,训练时间约为36.70分钟,准确率达到77.18%,与明文计算的准确率一致.实验验证了本文的模型在效率和准确率方面的可行性.

With the development of computing power, machine learning has been widely used,and data security has also become an important issue. Homomorphic encryption technology can operate ciphertexts without revealing the information about the plaintexts and get the same results as corresponding operations on the plaintexts. Therefore, homomorphic encryption is a feasible and potential solution for secure data outsourcing. In order to solve the multi-classification problem in real life, this paper proposes an effective multinomial logistic regression model to protect data privacy based on HEAAN homomorphic encryption scheme proposed by Cheon et al. This paper uses the "one vs rest" disassembly strategy to extend binary logistic regression to multinomial logistic regression by training multiple classifiers. Data holders can encrypt the data and send it to the server. The server trains the encrypted data using the multinomial logistic regression model, and sends the results back to the data holders. The data holders can use the decrypted results to predict the multi-class data.This paper tests the performance of the model by experimenting with the Dermatology and Iris dataset from UCI. Dermatology dataset consists of 358 samples, 34 features and 6 classes. The training time was about 36.70 minutes. The accuracy rate achieves 77.18% which is consistent with the accuracy rate of plaintext calculation. The experiments can verify the feasibility of model in this paper in terms of efficiency and accuracy.