Projects

Research Projects

• Differentially Private Nonparametric Modal Learning with Applications to Regression and Clustering
  with Arnab Auddy · Submitted to the Journal of Machine Learning Research (JMLR)
  Paper
  Abstract

  Existing private methods for estimating density modes mainly recover a single mode, while recovering all modes requires searches from multiple starting locations that can themselves reveal information about individual records. We propose DP-GRAMS, a differentially private algorithm that selects starting locations with a density-aware initialization on a public grid, moves each toward higher estimated density, and groups the endpoints into estimated modes, all within a single privacy budget. We prove that DP-GRAMS satisfies differential privacy and recovers every population mode with high probability, with error bounds that separate statistical error from the cost of privacy and a lower bound showing these rates are nearly optimal. We extend the method to modal regression and clustering and show that it preserves tumor-type separation in cancer gene-expression data.

• Matched-Mode Testing: Two-Sample Inference for the Locations of Density Modes
  with Arnab Auddy · Under review

• Calibrated Nearest-Neighbor Memorization: Exact Inference and Detectability in Generative Models
  with Abhinav Chakraborty and Arnab Auddy · In preparation

• Differentially Private Levenberg–Marquardt
  Course project, STAT 8820: Statistical Inference for Dynamical Systems, The Ohio State University (2025)
  Abstract

  Developed a privacy-preserving nonlinear least-squares method by adapting Levenberg–Marquardt updates to satisfy individual-level differential privacy, and evaluated it on nonlinear dynamical-system benchmarks.