  In an Internet of Things network, multiple sensors send information to a
fusion center for it to infer a public hypothesis of interest. However, the
same sensor information may be used by the fusion center to make inferences of
a private nature that the sensors wish to protect. To model this, we adopt a
decentralized hypothesis testing framework with binary public and private
hypotheses. Each sensor makes a private observation and utilizes a local sensor
decision rule or privacy mapping to summarize that observation independently of
the other sensors. The local decision made by a sensor is then sent to the
fusion center. Without assuming knowledge of the joint distribution of the
sensor observations and hypotheses, we adopt a nonparametric learning approach
to design local privacy mappings. We introduce the concept of an empirical
normalized risk, which provides a theoretical guarantee for the network to
achieve information privacy for the private hypothesis with high probability
when the number of training samples is large. We develop iterative optimization
algorithms to determine an appropriate privacy threshold and the best sensor
privacy mappings, and show that they converge. Finally, we extend our approach
to the case of a private multiple hypothesis. Numerical results on both
synthetic and real data sets suggest that our proposed approach yields low
error rates for inferring the public hypothesis, but high error rates for
detecting the private hypothesis.
