Finite Sample Differentially Private Confidence Intervals
summary
Constructs finite-sample differentially private confidence intervals for a Gaussian mean (known and unknown variance) by first estimating a data range estimator via noisy histogram then truncating and releasing a Laplace-noised mean; this removes linear dependence on a user-chosen data bound and yields exact finite-sample coverage (not just asymptotic). Length scales like sigma/√n plus an additive privacy term O(1/(ε n)) (with logarithmic dependence on a parameter bound R), gives ~2× interval length at n≈1,000 in simulations and ≈93% coverage for ε=0.5 in a two-sample example.
AI-written summary · about
chapters (13)
- 0:00Introduction
- 2:55Problem Statement
- 6:00Optimal Interval
- 7:00Laplace
- 8:05Point Estimate
- 11:40Hypothesis Testing
- 12:50Results
- 18:50Issues
- 34:38Further Optimization
- 37:10Difference of Means
- 38:34Basic Idea
- 39:33Framework
- 43:02Summary
related talks
01h 07mStatistical Inference and Privacy, Part I
01h 03mStatistical Inference and Privacy, Part II
47mDifferential Privacy from a Statistical Perspective–Obtaining Valid Inferences...
36mPrivately Learning High-Dimensional Distributions
01h 02mLarge-Scale Private Learning, Part I
01h 00mDifferential Privacy And The Complexity Of Simple Queries
39mVirtual talk by Jonathan Ullman (Northeastern)
30mAccuracy First: Selecting a Differential Privacy Level for Accuracy-Constrained...