□= □=Ĥ9 Distributional Stability Degrades Gracefully Under CompositionĬompose( D) For □ = 1 to □: Let choose an □-DP □ □ based on □ 1 ,…, □ □−1. Important: Don’t need to understand anything about □. No metric on □.Ĥ8 Distributional Stability Yields Robustness to PostprocessingĪn “Information Processing” inequality: Theorem: If □: □ □ →□ is (□,□)-differentially private, and □:□→ □ ′ is an arbitrary algorithm, then □∘□ : □ □ → □ ′ is (□,□)-differentially private. □: □ □ →□ is (□,□)-differentially private if for every pair of neighboring datasets □,□′, and outcome □: Pr □ □ ∈□ ≤ □ □ Pr □ □ ′ ∈□ +□ Crucial: Stability on the distribution. Question: Can we do better with a different statistical estimator?Ĥ6 Differential Privacy Īlice Bob Xavier Chris Donna Ernie Algorithm Pr Ĥ7 A stability condition on the output distribution: Bagging methods can have similar effect as majority attack.Ĥ5 Can we do better with a different statistical estimator? Is this a real concern? Can get 1% improvement every few hundred queries. Output hypothesis □ □ ≔majority( □ 1 □ 1 □ ,…, □ □ □ □ □ ) Claim: With high probability, □ has training error 1 2 −□ □/□Ĥ4 Bagging methods can have similar effect as Let me manage your money, and I’ll continue giving you my stock prediction tips in exchange for a small cut! BANK ACCOUNT NUMBER PLS!!ġ3 Hmm… The chance he was right 10 times in a row if he was just randomly guessing is only ≈ □0 set □ □ =1 if □ □ >0, □ □ =−1 otherwise. I’m tired of giving out this great advice for free. ![]() SHAK is going down.Ĥ From: Date: 3/1/15 Subject: Gr8 investment tip!!! Down again.ĥ From: Date: 3/2/15 Subject: Gr8 investment tip!!! Up!Ħ From: Date: 3/3/15 Subject: Gr8 investment tip!!! Down.ħ From: Date: 3/4/15 Subject: Gr8 investment tip!!! Up!Ĩ From: Date: 3/5/15 Subject: Gr8 investment tip!!! Up!ĩ From: Date: 3/6/15 Subject: Gr8 investment tip!!! Up!ġ0 From: Date: 3/7/15 Subject: Gr8 investment tip!!! Down.ġ1 From: Date: 3/8/15 Subject: Gr8 investment tip!!! Down.ġ2 From: Date: 3/8/15 Subject: Gr8 investment opportunity!!! Hi there. Presentation on theme: "Rigorous Data Dredging Theory and Tools for Adaptive Data Analysis."- Presentation transcript:ġ Rigorous Data Dredging Theory and Tools for Adaptive Data Analysis.Ģ From: Date: 2/27/15 Subject: Gr8 investment tip!!! Hi! You don’t know me, but here is a tip! Go long on SHAK – it will go up today.ģ From: Date: 2/28/15 Subject: Gr8 investment tip!!! Hi again! Go short today.
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