Differentially Private Block Coordinate Descent for Linear Regression on Vertically Partitioned Data

Abstract

We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

Separated by Degrees: Social Closure by Education Levels Strengthens Contemporary Political Divides

“…Moreover people barely consider politics in social selection when no information about politics is provided, a situation that resembles many instances of real-life relationship formation, suggesting the persistence of politically heterogeneous social networks(Baldassarri & de Jong, 2024). Though this is still a lively debate, most evidence thus far points to an incidental model of social selection, in which nonpolitical considerations drive relationship formation(Minozzi et al, 2020;Balietti et al, 2021).5 Replication materials and code can be found at DeJong and Kamphorst, 2024.…”