We consider an Internet of Things network consisting of multiple sensors, each making a private observation and sending information to a fusion center. The fusion center uses the received information to infer a public hypothesis of interest. However, privacy of the network needs to be preserved. We categorize privacy into inference privacy and data privacy. Inference privacy is preventing the fusion center from using its received information to accurately infer another private hypothesis, while data privacy refers to preventing the fusion center from knowing the private observation of each individual sensor. We discuss the relationship between various privacy metrics proposed in the literature, and show that inference and data privacy are in general not equivalent. We then propose a nonparametric optimization framework, which incorporates both inference and data privacy metrics, to design privacy mappings for the sensors without prior knowledge of the sensor observations' distribution. Simulation results demonstrate that our proposed approach allows the fusion center to accurately infer the public hypothesis while making it difficult to infer the private hypothesis and keeping the mutual information between the information sent by each sensor and its private observation low.