Secure PAC Bayesian Regression via Real Shamir Secret Sharing. (arXiv:2109.11200v1 [cs.LG])

Common approach of machine learning is to generate a model by using huge
amount of 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 obtaining 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 need 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; an inverse method and a
Gaussian elimination method, and compare these methods at the end.