Optimal Distribution Mapping for Inference Privacy

Information sanitization to protect an underlying label from being inferred through a data stream is investigated in this work. The problem is posed as an optimal mapping from an underlying distribution that reveals a class/label for the data to a target distribution with minimum distortion. The optimal sanitization operation are transformed to convex optimization problems corresponding to the domain of the source and target distributions. In particular, when one of the distributions is discrete, a parallel is drawn to a biased quantization method and an efficient sub-gradient method is proposed to derive the optimal transformation. The method is extended to a real time scenario when multiple source distributions are to be mapped to a fixed target distribution without prior knowledge of the label of the streaming data, in order to defeat any hypothesis test between the labels. It is shown that even when the source label is unknown to the sanitizer, optimal distortion is possible with perfect privacy.