基于实数 Shamir 秘密共享的安全 PAC 贝叶斯回归
Secure PAC Bayesian Regression via Real Shamir Secret Sharing
AI总结：
本文针对多方数据隐私保护下的线性回归问题，提出基于实数 Shamir 秘密共享的安全 PAC 贝叶斯回归协议，并给出安全求逆与安全高斯消元两种求解方法，在保护数据隐私的同时实现模型学习。
摘要：
系统辨识与机器学习的一种常见方法是利用训练数据生成模型，以尽可能准确地预测测试数据实例。然而，关于数据隐私的担忧日益增多，但并非总能得到解决。我们提出一种安全协议，用于基于最近提出的实数秘密共享技术学习线性模型。我们以 PAC 贝叶斯界为出发点，从 PAC 贝叶斯界推导出依赖数据和先验的模型参数的闭式形式。为获得模型参数，需要求解一个线性系统。然而，我们考虑的情况是多个参与方持有不同的数据实例，且不愿放弃数据隐私。因此，我们建议使用实数秘密共享和多方计算来共享数据，并在不侵犯数据隐私的前提下安全地求解线性回归。我们提出两种方法：安全求逆方法和安全高斯消元方法，并在最后对这两种方法进行比较。直接在实数上使用秘密共享的好处体现在协议的简洁性和所需通信轮数上。然而，这也带来一个缺点，即份额可能泄露少量信息，但在我们的分析中，我们论证该泄露量很小。
英文摘要：
A common approach of system identification and machine learning is to generate a model by using training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but not always addressed. We present a secure protocol for learning a linear model relying on recently described technique called real number secret sharing. We take as our starting point the PAC Bayesian bounds and deduce a closed form for the model parameters which depends on the data and the prior from the PAC Bayesian bounds. To obtain the model parameters one needs to solve a linear system. However, we consider the situation where several parties hold different data instances and they are not willing to give up the privacy of the data. Hence, we suggest to use real number secret sharing and multiparty computation to share the data and solve the linear regression in a secure way without violating the privacy of data. We suggest two methods; a secure inverse method and a secure Gaussian elimination method, and compare these methods at the end. The benefit of using secret sharing directly on real numbers is reflected in the simplicity of the protocols and the number of rounds needed. However, this comes with the drawback that a share might leak a small amount of information, but in our analysis we argue that the leakage is small.
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