Label Privacy Guarantees in ML

• Label privacy guarantees are defined as differential privacy conditions that restrict changes in a model’s output when only the private label is altered.
• Observational auditing methods leverage proxy label generators and counterfactual sampling to quantify privacy loss without costly retraining.
• Empirical evaluations on large-scale datasets show that rigorous auditing can detect privacy loss, guiding improvements for deployment-scale ML systems.

Label privacy guarantees formalize and audit the risk that a machine learning model's output or deployment procedure allows adversaries to infer the private label (or more generally, any protected attribute) of an individual in a dataset. In contrast to classical membership inference, which focuses on the presence or absence of a record, label privacy guarantees are defined with respect to changing only the private label (holding the public attributes fixed) of a record. Recent advances in observational auditing have enabled rigorous, scalable measurement of label privacy loss—quantified as a differential privacy (DP) parameter—without the engineering burden of retraining or canary injection, thus opening new directions for privacy compliance, practical algorithm design, and systems audit in production-scale ML contexts.

1. Problem Definition and Conceptual Motivation

Label privacy guarantees are designed to protect sensitive attributes in datasets, such as class labels, demographic fields, or any variable whose direct leakage could have ethical or regulatory consequences. Formally, in the simulation-based DP framework, a randomized mechanism $M$ operating on a dataset $D$ of records $(x, y)$ is $(\epsilon, \delta)$-label-DP (SIM-DP) if, for any alteration to the label $y$ of a single record (holding $x$ fixed), the output distribution of $M$ does not change much as measured by DP parameters. This prevents attackers from inferring $y$ given $x$ and the system output, up to the desired privacy level.

Traditional approaches, such as membership inference attacks or one-run DP audits, require modifying the dataset (removing/injecting canaries or re-running training). Such interventions are often prohibitively expensive or impractical on large systems. Observational auditing leverages the inherent randomness in natural data distributions to conduct audits over static, post-training models by simulating label perturbations and evaluating the resistance of $M$ to such attacks (Kalemaj et al., 18 Nov 2025).

2. Theoretical Foundations: Simulation-Based Label Differential Privacy

The defining property is based on the existence of a simulator $\mathrm{Sim}(D', x)$ that generates outputs statistically close to those of $M$—without knowing the true private label $y$ of $x$:

$$\Pr[M(D) \in E] \leq e^\epsilon \Pr[\mathrm{Sim}(D \setminus \{(x, y)\}, x) \in E] + \delta,$$

for any event $E$ (Kalemaj et al., 18 Nov 2025). For label privacy, $\mathrm{Sim}$ is typically constructed by sampling a "counterfactual" label from a conditional distribution $\mathcal{D}'(y \mid x)$, independent of the true $y$, and appending $(x, y')$ to the dataset before running $M$.

Two formal auditing theorems follow:

• Pure DP ($\delta=0$): For any adversary $A$ attempting to distinguish the true-vs-counterfactual labels in $m$ records, the correct guessing count $C$ cannot exceed a binomial tail determined by $\epsilon$, providing a sharp lower bound on the realized privacy loss.
• Approximate DP (with proxy label distribution): If $\mathcal{D}'$ is $\tau$-TV close to $\mathcal{D}$, then the audit loss is shifted accordingly in the adversary's expected success rate, which can be tightly upper-bounded (Kalemaj et al., 18 Nov 2025).

This formalism generalizes classical membership inference-based DP audits to arbitrary protected attributes and is grounded in the simulation-based DP literature.

3. Observational Auditing Protocol for Label Privacy

The methodology for observational auditing of label privacy leverages real or synthetic data, a trained model $M$, and a proxy label generator $\mathcal{D}'$. The protocol proceeds as follows (Kalemaj et al., 18 Nov 2025):

1. Sample data: Select $m$ records $(x_i, y_i^0)$ from $\mathcal{D}$.
2. Generate counterfactuals: For each $i$, sample an alternative label $y_i^1$ from $\mathcal{D}'(\cdot \mid x_i)$.
3. Mix labels: Flip unbiased coins $b_i \sim \mathrm{Bernoulli}(1/2)$ to choose, for each $i$, either the true label or a counterfactual.
4. Aggregate dataset: Build a mixed dataset $D^b = \{(x_i, y_i^{b_i})\}_{i=1}^m$.
5. Attacker's challenge: Provide the model output and $D^b$ to an adversary $A$, who attempts to guess the values $b_i$ (i.e., true-vs-counterfactual) for each $i$, producing predictions $b_i'$ (with allowed abstentions).
6. Audit: Count the number of correct guesses $C$, total guesses $C'$, and compare $C$ to the expected binomial tail under $(\epsilon, \delta)$ label-DP with TV shift $\tau$ (from any mismatch between $\mathcal{D}$ and $\mathcal{D}'$).
7. Report: Output the tightest lower bound $\hat{\epsilon}$ not falsified by the observed $(C, C')$ at the target confidence level.

This protocol supports attribute inference and membership inference as special cases by appropriate choices of $\mathcal{D}'$. Notably, all steps require only post-training access to $M$ and a proxy data generator, not retraining or dataset perturbations (Kalemaj et al., 18 Nov 2025).

4. Empirical Evaluation: Method Comparisons and Results

Experiments on benchmark datasets illustrate the framework's effectiveness and scalability:

• CIFAR-10/ALIBI, PATE-FM, LP-1ST: For strong DP mechanisms ($\epsilon \leq 1$), the audit output $\hat{\epsilon}$ drops to $0.4$–$0.9$, confirming claimed privacy. As $\epsilon$ increases (no privacy), the audit rapidly identifies high privacy loss ($\hat{\epsilon} \approx 2$) (Kalemaj et al., 18 Nov 2025).
• Criteo, large $m$: The protocol accurately recovers privacy loss over tens to hundreds of thousands of canaries, even in the presence of realistic distribution shift between proxy and true labels.
• Attack sharpness vs. proxy quality: WAN tests show that loss of proxy quality ($\tau$ increases) relaxes the lower bound, but robust results persist if the proxy is accurate (e.g., from an earlier checkpoint or independent model) (Kalemaj et al., 18 Nov 2025).

This approach works for complex, large-scale systems and matches or exceeds the sharpness of classic one-run MIA/label-DP auditing, but without the engineering and computational overhead of retraining.

5. Comparison to Other Auditing and Privacy Analysis Methods

Traditional DP audits (e.g., Meta-LabelDP, one-run MIA) require retraining with injected or removed canaries and may not scale to distributed or locked-shard production training. Observational auditing of label privacy eliminates the need for such interventions, enabling audits in realistic deployment contexts with only black-box or gray-box model access. The audit applies to any model or mechanism, scales to production-size datasets, and is resilient to the full range of label DP mechanisms (Kalemaj et al., 18 Nov 2025). Classical group/attribute inference analyses and shadow-model attacks are strictly less efficient and exhibit weaker privacy detection under the observational auditing paradigm.

6. Implementation Guidance and Limitations

Best practices for implementing observational label privacy auditing include:

• Proxy generator quality: Use a well-fitted, distribution-accurate conditional label generator (proxy model). Poor proxies (high total variation difference, $\tau$) loosen the privacy bound.
• Sample size: Employ large $m$ ($\gtrsim 10^4$) for sharp tail estimation.
• Abstention and tail-fitting: Allow the attacker to abstain and concentrate analysis on high-confidence regions to maximize distinguishing power.
• Periodicity: Rerun audits on new data distribution snapshots to monitor privacy as the population drifts.
• Parameterization: Tune the audit confidence $\gamma$ and privacy slack $\delta$ to reflect deployment policy and regulatory constraints.

Limitations are primarily affected by proxy accuracy and the statistical independence of canaries. Highly correlated canaries or misaligned proxies may reduce detection power, and extremely large $\epsilon$ (noisy mechanisms) require a correspondingly larger audit set.

7. Broader Impact and Future Directions

The observational approach to label privacy auditing marks a significant advance in practical privacy compliance for machine learning. It removes the substantial engineering barriers previously required for DP certification and supports routine, scalable audits. Beyond membership and label privacy, the methodology extends naturally to any protected attribute, supports integration with regulatory documentation, and rapidly adapts as new privacy mechanisms and attack models are developed (Kalemaj et al., 18 Nov 2025).

Ongoing research directions include further relaxing the assumptions on proxy accuracy (e.g., leveraging domain adaptation or improved synthetic label generators), extending the approach to federated and continual learning pipelines, and formalizing automated responses triggered by high observed privacy loss. The method supports robust, operational, and provable privacy guarantees in real-world ML contexts.