  We consider a decentralized detection network whose aim is to infer a public
hypothesis of interest. However, the raw sensor observations also allow the
fusion center to infer private hypotheses that we wish to protect. We consider
the case where there are an uncountable number of private hypotheses belonging
to an uncertainty set, and develop local privacy mappings at every sensor so
that the sanitized sensor information minimizes the Bayes error of detecting
the public hypothesis at the fusion center, while achieving information privacy
for all private hypotheses. We introduce the concept of a most favorable
hypothesis (MFH) and show how to find a MFH in the set of private hypotheses.
By protecting the information privacy of the MFH, information privacy for every
other private hypothesis is also achieved. We provide an iterative algorithm to
find the optimal local privacy mappings, and derive some theoretical properties
of these privacy mappings. Simulation results demonstrate that our proposed
approach allows the fusion center to infer the public hypothesis with low error
while protecting information privacy of all the private hypotheses.
