As the data-driven decision process becomes dominating for industrial applications, fairness-aware machine learning arouses great attention in various areas. This work proposes fairness penalties learned by neural networks with a simple random sampler of sensitive attributes for non-discriminatory supervised learning. In contrast to many existing works that critically rely on the discreteness of sensitive attributes and response variables, the proposed penalty is able to handle versatile formats of the sensitive attributes, so it is more extensively applicable in practice than many existing algorithms. This penalty enables us to build a computationally efficient group-level in-processing fairness-aware training framework. Empirical evidence shows that our framework enjoys better utility and fairness measures on popular benchmark data sets than competing methods. We also theoretically characterize estimation errors and loss of utility of the proposed neural-penalized risk minimization problem.

This paper is the first to attempt differentially private (DP) topological data analysis (TDA), producing near-optimal private persistence diagrams. We analyze the sensitivity of persistence diagrams in terms of the bottleneck distance, and we show that the commonly used Cech complex has sensitivity that does not decrease as the sample size $n$ increases. This makes it challenging for the persistence diagrams of Cech complexes to be privatized. As an alternative, we show that the persistence diagram obtained by the $L^1$-distance to measure (DTM) has sensitivity $O(1/n)$. Based on the sensitivity analysis, we propose using the exponential mechanism whose utility function is defined in terms of the bottleneck distance of the $L^1$-DTM persistence diagrams. We also derive upper and lower bounds of the accuracy of our privacy mechanism; the obtained bounds indicate that the privacy error of our mechanism is near-optimal. We demonstrate the performance of our privatized persistence diagrams through simulations as well as on a real data set tracking human movement.