An Information Bottleneck Approach to Secrecy-Preserving Gaussian Mixture Classification

The information bottleneck (IB) approach, initially introduced by [1] to assess the compression-relevance tradeoff for a remote source coding problem in communication, quickly gains popularity recently in its application to modern machine learning (ML). Unlike the use of most - if not all - IB in the literature, either for the analysis of, say deep neural networks, or as an optimization objective, in this paper, we propose to address the secrecy issue in ML, by considering the fundamental model of Gaussian mixture classification. We derive, for the first time, closed-form achievable bounds for the IB problem under the above setting, and provide precise characterization of the underlying performance-secrecy tradeoff. Experiments on both synthetic and real-world data are performed to confirm the satisfactory performance of the proposed scheme.