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Settling Pure Differentially Private Covariance Estimation

NeurIPS 2026 · Federated learning and privacy › Differential privacy · approach: Local-DP and private estimation

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Gives a single efficient pure-DP algorithm for d-dimensional covariance release with Schatten-p error, matched by information-theoretic lower bounds in two sample-size regimes.

Problem

Releasing a d-dimensional covariance matrix under pure differential privacy with error measured in Schatten-p norms (p in [1, infinity]), where optimal error depends on the sample size regime.

Approach

A single efficient algorithm that attains error matching information-theoretic lower bounds across both a large-sample regime (n gtrsim d^2) and a complementary regime, showing qualitatively different behavior between them.

Experimental setup

Metrics: Schatten-p norm error

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