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Preserving Positivity in Microdata Release: Challenges and Methods

This document addresses the issue of releasing masked microdata while preserving positivity constraints across all data records and attributes. Original data is analyzed and transformed using methods such as microaggregation and noise addition, but traditional techniques often fail to maintain positivity, leading to potential disclosure risks. The text explores various methods to preserve positivity, including weighted microaggregation, transformations with linear constraints, and rejection sampling for noise distribution. Additionally, it discusses the implications of more complex constraints and the scalability of these methods.

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Preserving Positivity in Microdata Release: Challenges and Methods

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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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