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Statistical Methodology for the Automatic Confidentialisation of Remote Servers at the ABS

Statistical Methodology for the Automatic Confidentialisation of Remote Servers at the ABS. Session 1 UNECE Work Session on Statistical Data Confidentiality 28-30 October 2013 Daniel Elazar daniel.elazar@abs.gov.au. Confidentiality Risks for Remote Server Outputs.

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Statistical Methodology for the Automatic Confidentialisation of Remote Servers at the ABS

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  1. Statistical Methodology for the Automatic Confidentialisation of Remote Servers at the ABS Session 1UNECE Work Session on Statistical Data Confidentiality28-30 October 2013 Daniel Elazar daniel.elazar@abs.gov.au

  2. Confidentiality Risks for Remote Server Outputs Known Types of Attack from the literature • Tabular attacks • Averaging • Differencing • Scope coverage • Sparsity • Regression attacks • Tabular attacks as above, plus • Leverage • High R2 – saturated or ideal model fit • Influence • Solving model equations

  3. TableBuilder Functionality

  4. TableBuilder Protections

  5. DataAnalyser Functionality Analysis Procedures /Specifications Exploratory Data Analysis Transformations / Derivations Output Formats Outputs Robust Linear Regression Binomial logistic Probit Multinomial Poisson Diagnostics Weighted Analysis • Logical derivations • Categorical/ Dummy variables • Category collapsing Expression Editor for categ. vars Drop variables / records Action List CSV Storage of intermediate datasets • R-squared • Pseudo R-squared • Coefficients • Standard errors Other Diagnostics • Summary statistics • (sums, counts) • Summary Tables • Graphics • (side-by-side box plots) Summary statistics (count) Graphics • Written in R • Full User Authentication • Audit System • Workflow Control • Data Repository Interface • Metadata Handler

  6. DataAnalyser Protections (additional to TB)

  7. So where’s the Risk in Regressions? x1,x2,…,xn x1 x1,x2,…,xk Saturated Model Sparse Model The Perfect Model y x c Leverage Attack

  8. Scope-Coverage (Differencing) Attack Case 1 Case 2 Age Age 95 96 95 96 15 15 A B A B Other Characteristics Other Characteristics Confidentialised outputs from requests A and B differ slightly  unit(s) (in red) exists in set B excluding A and are likely to be rare/unique Confidentialised outputs from requests A and B are exactly the same  There are no units in set B excluding A

  9. Perturbation of Unweighted Counts Unweighted Count (UWC) pcol_index prow_index pUWC = UWC + p p = pTable[ prow_index,pcol_index ] Perturbation Table

  10. Perturbation of Unweighted Counts p = pTable[ prow_index,pcol_index ] 32 bits 8 bits 8 bits 8 bits 8 bits C D is the bitwise XOR operator. + (mod 2), for ’th bit

  11. The Perturbation Algorithm:

  12. Perturbation of Weighted Continuous Values where direction mTable[i] magnitude noise

  13. Perturbation of Regression Estimates For generalised linear models, perturbation is applied to the score function using the following algorithm: Begin with an initial value Solve to obtain an unperturbed MLE Calculate the perturbed score function evaluated at applying the continuous perturbation to each summand in . This results in a vector of perturbation values, Solve using IRLS with initial value to obtain the perturbed estimate .

  14. Future Directions

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