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Preserving Positivity (and other Constraints?) in Released Microdata

Preserving Positivity (and other Constraints?) in Released Microdata. Alan Karr 12/2/05. Problem. O = original microdata Constrained to satisfy o ij >= 0 for all data records i and (some or all) attributes j Want masked data release M that Satisfies same positivity constraints

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Preserving Positivity (and other Constraints?) in Released Microdata

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  1. Preserving Positivity(and other Constraints?) in Released Microdata Alan Karr 12/2/05

  2. Problem • O = original microdata • Constrained to satisfy oij >= 0 for all data records i and (some or all) attributes j • Want masked data release M that • Satisfies same positivity constraints • Has high utility • Has low disclosure risk

  3. Motivating Example • O = original data • M1 = MicZ applied to O • Conceptually, data have shrunk • D = O – M1 • N = normally distributed noise with • Mean 0 • Cov(N) = Cov(D) • M2 = M1 + N • Works well for utility and risk • Does not preserve positivity

  4. Which Methods Preserve Positivity?

  5. The Problem with Mic*

  6. Some (1/2, ¼, 1/1048576)-Wit Ideas • Transform data to remove constraints (e.g., take logs), do SDL on transformed data, and untransform • Microaggregation becomes “weighted” • How to choose noise distribution? • Use rejection sampling for additive noise • M+N|M+N>= 0 • Does it restore full covariance?

  7. More Ideas • Microaggregation with weights: move points near edges less • May be bad for risk • No longer preserves first moments • Linear transformation, if constraint satisfied (Mi-Ja) • M = {T(x): T(x) >= 0} U {x: T(x) not >=0} • ?????

  8. Other Questions • More complex constraints • x1 <= x2 (time precedence; net income <= gross) • x1 + x2 <= x3 • Are all “convexity-like” constraints alike? • Multiple constraints • Methods need to be scalable • “Soft” constraints

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