|| SDP Methods for Sensitivity-Constrained Privacy Funnel and Information Bottleneck Problems
||Yuheng Bu, Tony Wang, Gregory Wornell, MIT, United States|
||D1-S1-T3: Information Bottleneck I
||Monday, 12 July, 22:00 - 22:20
||Monday, 12 July, 22:20 - 22:40
We generalize the information bottleneck (IB) and privacy funnel (PF) problems by introducing the notion of a sensitive attribute, which arises in a growing number of applications. In this generalization, we seek to construct representations of observations that are maximally (or minimally) informative about a target variable, while also satisfying constraints with respect to a variable corresponding to the sensitive attribute. In the Gaussian and discrete settings, we show that by suitably approximating the Kullback-Liebler (KL) divergence defining traditional Shannon mutual information, the generalized IB and PF problems can be formulated as semi-definite programs (SDPs), and thus efficiently solved, which is important in applications of high-dimensional inference. We validate our algorithms on synthetic data and demonstrate their use in imposing fairness in machine learning on real data as an illustrative application.