  The remarkable development of deep learning in medicine and healthcare domain
presents obvious privacy issues, when deep neural networks are built on users'
personal and highly sensitive data, e.g., clinical records, user profiles,
biomedical images, etc. However, only a few scientific studies on preserving
privacy in deep learning have been conducted. In this paper, we focus on
developing a private convolutional deep belief network (pCDBN), which
essentially is a convolutional deep belief network (CDBN) under differential
privacy. Our main idea of enforcing epsilon-differential privacy is to leverage
the functional mechanism to perturb the energy-based objective functions of
traditional CDBNs, rather than their results. One key contribution of this work
is that we propose the use of Chebyshev expansion to derive the approximate
polynomial representation of objective functions. Our theoretical analysis
shows that we can further derive the sensitivity and error bounds of the
approximate polynomial representation. As a result, preserving differential
privacy in CDBNs is feasible. We applied our model in a health social network,
i.e., YesiWell data, and in a handwriting digit dataset, i.e., MNIST data, for
human behavior prediction, human behavior classification, and handwriting digit
recognition tasks. Theoretical analysis and rigorous experimental evaluations
show that the pCDBN is highly effective. It significantly outperforms existing
solutions.
