Estimating Identification Disclosure Risk Using Mixed Membership Models.

Area of Science:

• Statistics
• Data Privacy
• Computational Statistics

Background:

• Statistical agencies must protect data confidentiality to prevent re-identification.
• Disclosure risk assessments often involve estimating the probability of unique records based on key variables.
• Log-linear models are commonly used but can be biased with sparse data.

Purpose of the Study:

• To propose an alternative to log-linear models for disclosure risk assessment in sparse datasets.
• To introduce a Bayesian Grade of Membership (GoM) model for multinomial variables.
• To evaluate the accuracy of Bayesian GoM models compared to log-linear models.

Main Methods:

• Developed a Bayesian Grade of Membership (GoM) model for multinomial variables.
• Implemented an MCMC algorithm for model fitting.
• Evaluated model performance using US Census Bureau microdata samples.

Main Results:

• Bayesian GoM models provide more accurate estimates of the total number of unique records in samples compared to log-linear models.
• GoM models yield superior record-level predictions of uniqueness.
• The proposed method mitigates bias issues inherent in log-linear models with sparse contingency tables.

Conclusions:

• Bayesian GoM models are a more reliable alternative for disclosure risk assessment with sparse data.
• This approach enhances the accuracy of confidentiality protection for statistical agencies.
• The study demonstrates the practical utility of Bayesian GoM models in real-world data privacy scenarios.