Statice Privacy Assessment

• Statice Privacy Assessment is an attack-based framework that quantifies post-hoc privacy risks—singling-out, linkability, and inference—in synthetic datasets.
• It applies formal information-theoretic principles and simulated adversarial attacks to deliver legally relevant risk metrics aligned with GDPR.
• The modular, scalable tool Anonymeter enables actionable remediation steps by setting quantitative thresholds for privacy risk in complex data environments.

Statice Privacy Assessment refers to a principled, attack-based evaluation framework for quantifying ex-post privacy risk in synthetic datasets, especially in the context of regulatory requirements such as the European General Data Protection Regulation (GDPR). Developed as an open-source tool—Anonymeter—by the Statice research group, this framework delivers rigorous, reproducible estimates of the key privacy risks mandated under GDPR: singling-out, linkability, and attribute inference. The Statice approach is grounded in formal information-theoretic principles, employs risk quantification rooted in simulated adversarial attacks, and is modular and scalable to very large and complex datasets. It serves as a privacy-assessment gold standard for synthetic data release workflows and drives actionable remediation based on quantitative thresholds (Giomi et al., 2022, Alvim et al., 2022).

1. Foundational Privacy Risk Metrics

The Statice privacy assessment formalizes three principal privacy risks aligning with factual anonymization criteria under GDPR:

1. Singling-out risk ($R_{SO}$): The probability that an adversary can isolate an individual in the original data based on a predicate formulated using the synthetic release.
2. Linkability risk ($R_{L}$): The likelihood that two external fragments of information can be linked to the same individual in the original data via the synthetic dataset.
3. Inference risk ($R_{I}$): The probability that an adversary can infer a secret attribute of a target given auxiliary (known) information.

Each risk is computed by comparing adversarial success rates on (i) training data (used to generate the synthetic release), (ii) held-out “control” data (not seen by the generator), and (iii) a naive baseline (random guess). The normalized risk metric is:

$$R = \frac{r_{\text{train}} - r_{\text{control}}}{1 - r_{\text{control}}}$$

where $r_{\text{train}}$ and $r_{\text{control}}$ are attack success rates on the respective datasets. This normalization accounts for population-wide inference and avoids overestimating risk in high-utility scenarios (Giomi et al., 2022).

2. Attack-Based Assessment Methodology

The framework treats the data generation process as a black box and relies on explicit adversarial attack simulations to evaluate risk rather than solely on syntactic privacy guarantees or match-count statistics. For robust evaluation:

• Singling-out attacks sample synthetic records, derive univariate/multivariate predicates that uniquely identify targets, and then check their selectivity against the original and control datasets.
• Linkability attacks split attribute sets $(A, B)$, simulate external knowledge of $A$ and $B$ for targets, and measure if nearest neighbors under $A$ and $B$ in the synthetic release overlap.
• Inference attacks select auxiliary–secret attribute pairs, let the adversary estimate the secret attribute from the synthetic nearest neighbor (tolerance specified for continuous attributes).

Naive attacks (uninformed random guesses) and control attacks (on held-out real data) establish baselines. For each attack, the framework reports raw success rates, attack strengths ($s = r_{\text{train}} - r_{\text{naive}}$), and confidence intervals (Wilson) (Giomi et al., 2022).

3. Legal Alignment and Regulatory Relevance

Statice follows the GDPR's risk-based paradigm: it quantifies, rather than eliminates, post-hoc re-identification and attribute inference risks. The methodology directly operationalizes Recital 26 and Article 4(5) (pseudonymization/anonymization) through explicit quantification of the factual risks recognized by WP29 and the EDPB. Rather than relying on conventional k-anonymity or match-counts, which can understate subtle privacy leakages, it directly simulates plausible attacks under legal adversary models and benchmarks results with naive and control baselines to yield legally relevant, interpretable outputs suitable for Data Protection Impact Assessments (DPIA) (Giomi et al., 2022, Alvim et al., 2022).

4. Scalable Computational Workflow and Implementation

The assessment algorithm is optimized for very large microdata, including (but not limited to) high-cardinality and longitudinal datasets:

1. Input partitioning: The original data is split into training (for generative modeling) and control (for baseline calculation).
2. Risk computation: For each risk:
   • Extract and enumerate candidate predicates, attribute sets, or auxiliary–secret pairs.
   • For each synthetic record, simulate the relevant adversarial attack.
   • Aggregate observed attack outcomes on training, control, and synthetic data.
   • Calculate normalized risk metrics and output confidence intervals.

The implementation handles single- and multi-table joins, streaming for memory efficiency, hash-based group-and-count operations for QID combinations, and multiprocessing for high-throughput environments. Empirical evaluations demonstrate $10\times$ speedup over previous leading tools (e.g., Groundhog) on $|N| \sim 10^5$–$10^7$ (Alvim et al., 2022, Giomi et al., 2022).

Algorithmic Sketch (Bayes vulnerability, min-entropy leakage, and mutual-information leakage):

V_prior = max_x prior[x] V_post = sum_y p_y[y] * max_x C[y][x] min_leak_mult = log2(V_post / V_prior) H_prior = -sum_x prior[x] * log2(prior[x]) H_post = sum_y p_y[y] * (-sum_x C[y][x] * log2(C[y][x])) I_leak = H_prior - H_post

5. Empirical Validation and Quantitative Results

Experiments span public tabular datasets (UCI Adult, Texas Hospital Discharge, US Census) and artificial privacy-leak scenarios (leaky synthesizer replacing synthetic with real training records at variable rates):

• All three risk metrics ($R_{SO}$, $R_L$, $R_I$) exhibit strict linearity with the fraction of leaks inserted.
• Differentially private synthesizers (DP-CTGAN) reduce risks across all metrics—by 2–4x for linkability/inference, and ≈25% for singling out—relative to non-private baselines.
• Linkability risk is consistently the lowest, reflecting that synthetic data, when properly generated, breaks direct mapping between real and synthetic records.
• Empirical risk scores allow setting actionable thresholds (e.g., $R < 0.05$ as “low risk”) (Giomi et al., 2022, Alvim et al., 2022).

Representative Results Table:

Dataset	Method	$R_{SO}$	$R_L$	$R_I$	Utility
Adults	CTGAN	0.055	0.0012	0.0161	88
Adults	DP-CTGAN	0.044	0.0007	0.0106	79
Texas	CTGAN	0.003	0.0009	0.0098	88
Texas	DP-CTGAN	0.005	0.0007	0.0095	71
US Census	CTGAN	0.004	0.0029	0.0286	74
US Census	DP-CTGAN	0.003	0.0006	0.0131	63

“Utility” reflects average marginal and dependency statistics, not privacy risk (Giomi et al., 2022).

6. Practical Guidance and Actionable Recommendations

Statice's privacy assessment framework prescribes integrating ex-post privacy testing as a mandatory release step for any synthetic data. Recommended workflow:

1. Partition real data into training and control sets.
2. Fit the generator on the training set, generate synthetic data.
3. Run the Anonymeter pipeline (risk computation on all three risk types).
4. Review all output risk metrics with confidence intervals.
5. Apply mitigation (e.g., increase privacy parameters in DP, coarsen attributes, enforce k-anonymity) for any risk with $R$ above the pre-set release threshold.
6. Document privacy-assessment results and mitigation steps in DPIA or similar regulatory filings.

Recommended risk threshold for public release is $R \leq 0.05$ for all three risks. Output reports are designed for both technical and policy stakeholders, supporting transparency and auditability (Giomi et al., 2022).

Remediation strategies:

• Increase the strength of privacy noise (lower $\epsilon$ for DP).
• Remove/coarsen quasi-identifiers with high cardinality.
• Reduce generative model capacity to avoid overfitting.
• Post-process synthetic data with additional privacy-preserving transformations.

7. Extensions and Scientific Context

The Statice framework is extensible: modularity in attack definitions allows additional or custom risk metrics (e.g., membership inference, subpopulation re-identification). It can handle formally specified or empirical adversary models and is compatible with formal quantitative information flow (QIF) theory, facilitating precise, scalable risk estimates even for very large and complex datasets (e.g., national educational censuses of >50M rows and 90 attributes) (Alvim et al., 2022). The separation of prior, channel, and gain lets risk analyses adapt to evolving threat landscapes with no core algorithm changes, supporting scenario-based exploration critical for privacy and policy decision-making. The framework’s open-source codebase and transparent, report-driven outputs are intentionally designed for explainability to both technical and policy audiences, reinforcing scientific and regulatory rigor.

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References:

• "A Unified Framework for Quantifying Privacy Risk in Synthetic Data" (Giomi et al., 2022)
• "Flexible and scalable privacy assessment for very large datasets, with an application to official governmental microdata" (Alvim et al., 2022)