Differentially Private Nonparametric Modal Learning with Applications to Regression and Clustering

Arkajyoti Bhattacharjee, Arnab Auddy|July 31, 2026arXiv

Key Takeaway

You can privately estimate where data clusters (density modes) with theoretical guarantees on both privacy and accuracy, achieving near-optimal statistical rates that balance the privacy-utility tradeoff.

Summary

This paper develops methods for finding density modes (peaks in probability distributions) while guaranteeing differential privacy—a mathematical constraint that limits what can be learned about individual data points. The authors propose DP-GRAMS, which uses noisy gradient ascent on a privately estimated score function, and prove it recovers all modes with near-optimal accuracy.

safety evaluation data

Key Terms

differential-privacy density-modes hölder-class mean-shift minimax-lower-bounds