  A sensor network wishes to transmit information to a fusion center to allow
it to detect a public hypothesis, but at the same time prevent it from
inferring a private hypothesis. We propose a multilayer nonlinear processing
procedure at each sensor to distort the sensor's data before it is sent to the
fusion center. In our proposed framework, sensors are grouped into clusters,
and each sensor first applies a nonlinear fusion function on the information it
receives from sensors in the same cluster and in a previous layer. A linear
weighting matrix is then used to distort the information it sends to sensors in
the next layer. We adopt a nonparametric approach and develop a modified mirror
descent algorithm to optimize the weighting matrices so as to ensure that the
regularized empirical risk of detecting the private hypothesis is above a given
privacy threshold, while minimizing the regularized empirical risk of detecting
the public hypothesis. Experiments on empirical datasets demonstrate that our
approach is able to achieve a good trade-off between the error rates of the
public and private hypothesis.
