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arxiv: 2605.03945 · v1 · submitted 2026-05-05 · 💻 cs.LG · stat.ML

Integrating Feature Correlation in Differential Privacy with Applications in DP-ERM

Tianyu Wang , Luhao Zhang , Rachel Cummings This is my paper

Pith reviewed 2026-05-07 03:32 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords differential privacyfeature correlationDP-ERMtotal variation distanceprivacy relaxationempirical risk minimizationutility guarantees
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The pith

CorrDP relaxes privacy for insensitive features by their total variation distance to sensitive ones, yielding better utility in DP-ERM.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard differential privacy imposes the same strict requirements on every feature, which wastes utility when some features carry little sensitive information. The paper introduces CorrDP, a framework that relaxes the privacy parameter for insensitive features according to the total variation distance measuring their correlation with sensitive features. This relaxation is incorporated into DP-ERM algorithms by scaling the noise added to gradients based on that distance. When the distances are unknown, they are estimated directly from the data, and the resulting algorithms retain nearly the same privacy-utility guarantees. Empirical tests on synthetic and real datasets show these algorithms produce models with higher accuracy than those trained under uniform differential privacy.

Core claim

By defining a correlation-aware differential privacy notion that relaxes protection for insensitive features in line with their total variation distance to sensitive features, the paper shows that DP-ERM can achieve strictly superior utility bounds while still satisfying the formal privacy definition, with the same holding when correlations are estimated from the dataset itself.

What carries the argument

The CorrDP framework, which quantifies correlations via total variation distance to determine the allowable privacy relaxation for each feature and applies distance-dependent noise calibration in the gradient descent process for empirical risk minimization.

If this is right

  • DP-ERM under CorrDP obtains improved theoretical utility guarantees relative to standard differential privacy.
  • Estimating correlation distances from the dataset achieves comparable privacy-utility performance.
  • The framework yields higher accuracy than standard DP-ERM on both synthetic and real-world data containing insensitive features.
  • Distance-dependent noise addition in gradients is the mechanism delivering the utility improvement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar correlation-based relaxations could be applied to other DP primitives beyond ERM, such as private stochastic gradient descent in deep learning.
  • Data pipelines might incorporate automated correlation estimation as a preprocessing step to identify opportunities for privacy relaxation.
  • Alternative distance or dependence measures could be substituted for total variation distance if they provide tighter bounds on information leakage.

Load-bearing premise

The total variation distance between the distributions of insensitive and sensitive features fully captures the risk of information leakage, such that relaxing privacy based on it does not permit any unexpected privacy breach.

What would settle it

Observing a privacy violation in a constructed dataset where an insensitive feature has low total variation distance but high predictive power for a sensitive attribute under the CorrDP noise levels.

Figures

Figures reproduced from arXiv: 2605.03945 by Luhao Zhang, Rachel Cummings, Tianyu Wang.

Figure 1
Figure 1. Figure 1: Privacy-utility trade-offs for least-square regression, logistic regression, and neural network training. The shaded area around each curve shows the standard deviation error band. We do not run the Partial algorithm on the Sepsis, Credit Card, and Medical Cost datasets since it is not comparable to use the same architecture only with partial features. include additional empirical results that vary the num… view at source ↗
Figure 2
Figure 2. Figure 2: Privacy-utility trade-offs for least-square regression under ( view at source ↗
read the original abstract

Standard differential privacy imposes uniform privacy constraints across all features, overlooking the inherent distinction between sensitive and insensitive features in practice. In this paper, we introduce a relaxed definition of differential privacy that accounts for such heterogeneity, allowing certain features to be treated as insensitive even when correlated with sensitive ones. We propose a correlation-aware framework, $\textsf{CorrDP}$, which relaxes privacy for insensitive features while accounting for their correlations with sensitive features, with the correlations quantified using total variation distance. We design algorithms for differentially private empirical risk minimization (DP-ERM) under the $\textsf{CorrDP}$ framework, incorporating distance-dependent noise into gradients for improved theoretical utility guarantees. When the correlation distance is unknown, we estimate it from the dataset and show that it achieves a comparable privacy-utility guarantee. We perform experiments on synthetic and real-world datasets and show that $\textsf{CorrDP}$-based DP-ERM algorithms consistently outperform the standard DP framework in the presence of insensitive features.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper introduces CorrDP, a relaxed differential privacy definition that accounts for heterogeneity between sensitive and insensitive features by quantifying their correlations via total variation distance. It develops DP-ERM algorithms that incorporate distance-dependent noise into gradients to obtain improved theoretical utility bounds. When the correlation distance is unknown, the paper estimates it directly from the training data and asserts that this yields comparable privacy-utility guarantees. Experiments on synthetic and real-world datasets show that CorrDP-based methods outperform standard DP-ERM when insensitive features are present.

Significance. If the privacy analysis for the data-dependent estimation step holds, the framework could meaningfully improve utility in DP-ERM settings with heterogeneous feature sensitivities, a common practical scenario. The use of total variation distance supplies a concrete, quantifiable relaxation, and the distance-dependent noise mechanism is a natural algorithmic extension. The empirical validation on real data adds practical relevance, but the overall significance hinges on whether the estimation procedure preserves the claimed (ε,δ) guarantees without additional leakage.

major comments (1)
  1. [Estimation procedure for unknown correlation distance (abstract and algorithmic section)] The claim that estimating the correlation distance d from the dataset achieves comparable privacy-utility guarantees (stated in the abstract and developed in the algorithmic section) is load-bearing for the main result when d is unknown. The estimated d directly scales the noise magnitude added to the gradients in the DP-ERM procedure. The manuscript does not appear to bound the sensitivity of the total-variation estimator or to fold its privacy cost into the overall calibration; a non-private estimator therefore risks either under-noising or allowing an adversary to infer correlations (and thereby information about sensitive features) from the observed noise level or output model. A revised version must either supply a private estimator (e.g., via the Laplace mechanism on a bounded-sensitivity statistic) or prove that the estimation error can be absorbed into the existing utility bound.
minor comments (2)
  1. [Abstract] The abstract states that the framework yields 'improved theoretical utility guarantees' but does not identify the precise baseline (standard DP-SGD, prior relaxed DP notions, etc.) or the functional improvement (e.g., better dependence on dimension, sample size, or Lipschitz constant). Adding a short comparison sentence would clarify the advance.
  2. [Preliminaries / definition of CorrDP] The definition of total variation distance and its estimation should explicitly address whether features are discrete or continuous and how the estimator behaves in moderate-to-high dimensions, where finite-sample TV estimation can be biased or high-variance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The primary concern identified is the lack of a formal privacy analysis for the data-dependent estimation of the correlation distance. We agree that this aspect requires explicit treatment to substantiate the claimed guarantees and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Estimation procedure for unknown correlation distance (abstract and algorithmic section)] The claim that estimating the correlation distance d from the dataset achieves comparable privacy-utility guarantees (stated in the abstract and developed in the algorithmic section) is load-bearing for the main result when d is unknown. The estimated d directly scales the noise magnitude added to the gradients in the DP-ERM procedure. The manuscript does not appear to bound the sensitivity of the total-variation estimator or to fold its privacy cost into the overall calibration; a non-private estimator therefore risks either under-noising or allowing an adversary to infer correlations (and thereby information about sensitive features) from the observed noise level or output model. A revised version must either supply a private estimator (e.g., via the Laplace mechanism on a bounded-sensitivity sta

    Authors: We thank the referee for identifying this important gap. The current manuscript estimates the correlation distance directly from the data and asserts comparable guarantees, but does not explicitly bound the sensitivity of the total-variation estimator or allocate privacy budget to the estimation step. In the revised version we will introduce a private estimator: we will first establish that the empirical total-variation distance statistic has bounded sensitivity (linear in the inverse sample size for discrete features), then release a noisy version via the Laplace mechanism. A fixed fraction of the overall privacy budget will be reserved for this release; the remaining budget will be used to calibrate the distance-dependent noise in the DP-ERM gradients. The resulting estimation error will be absorbed into the existing utility analysis as an additive term that vanishes with the sample size, preserving the improved privacy-utility tradeoff. The abstract, algorithmic section, and theoretical statements will be updated to reflect the revised procedure and guarantees. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines CorrDP via total variation distance to relax privacy for insensitive features, then derives DP-ERM algorithms that inject distance-dependent noise into gradients. The claim that estimating the distance from the dataset yields comparable privacy-utility guarantees is presented as a separate result rather than a tautological reduction of the core theorems to their inputs. No equation is shown to equal its own fitted parameter by construction, no self-citation chain is load-bearing for the main framework, and the derivation remains independent of the estimation step. This is the normal case of a self-contained theoretical development against standard DP-ERM baselines.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; full details of assumptions and parameters are unavailable. The main elements appear to be the use of total variation distance and data-based estimation of correlations.

free parameters (1)
  • correlation distance
    Quantified using total variation distance and estimated from the dataset when unknown.
axioms (1)
  • domain assumption Total variation distance is an appropriate measure for quantifying correlations in the context of privacy relaxation.
    Used to account for correlations with sensitive features.

pith-pipeline@v0.9.0 · 5465 in / 1389 out tokens · 88825 ms · 2026-05-07T03:32:22.587861+00:00 · methodology

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