Locally Private Statistical Inference: Communication, Samples, and Shared Randomness
summary
Claims tight sample bounds for locally private inference: distribution learning needs about K^2/(ε^2 α^2) samples under LDP private‑coin (centralized is K/α^2), testing (goodness‑of‑fit) rises from centralized ~√K/α^2 to K/(ε^2 α^2) with public coins and to K^{3/2}/(ε^2 α^2) without them. Tools: randomized response loses a 1/K factor for pairwise tests, a Hadamard‑style response restores optimal rates and fast decoding, and lower bounds use a chi‑square fluctuation/PSD‑matrix framework that captures public vs private coin tradeoffs.
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chapters (9)
- 0:00Introduction to the topic
- 1:31Statistical inference basics
- 4:52Distributed privacy framework
- 7:57Privacy and protocol types
- 11:20Distribution learning methods
- 18:00Hadamard response and results
- 27:03Distribution testing models
- 33:02Lower bounds and proofs
- 41:33Summary and conclusions
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