Aliakbarpour, MaryamSilver, RoseSteinke, ThomasUllman, Jonathan2024-07-252024-07-252024Aliakbarpour, M., Silver, R., Steinke, T., & Ullman, J. (2024). Differentially Private Medians and Interior Points for Non-Pathological Data. DROPS-IDN/v2/Document/10.4230/LIPIcs.ITCS.2024.3. 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). https://doi.org/10.4230/LIPIcs.ITCS.2024.3https://hdl.handle.net/1911/117535We construct sample-efficient differentially private estimators for the approximate-median and interior-point problems, that can be applied to arbitrary input distributions over ℝ satisfying very mild statistical assumptions. Our results stand in contrast to the surprising negative result of Bun et al. (FOCS 2015), which showed that private estimators with finite sample complexity cannot produce interior points on arbitrary distributions.engExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Journal articleLIPIcsITCS20243https://doi.org/10.4230/LIPIcs.ITCS.2024.3