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 sensor network structure, where each sensor first applies a nonlinear fusion function on the information it receives from sensors in a previous layer, and then a linear weighting matrix to distort the information it sends to sensors in the next layer. We adopt a nonparametric approach and develop an 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. Simulations on a synthetic dataset and an empirical experiment demonstrate that our approach is able to achieve a better trade-off between the error rates of the public and private hypothesis than using only linear precoding to achieve information privacy.