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arxiv: 2606.08259 · v1 · pith:P5T5EVNRnew · submitted 2026-06-06 · 💻 cs.LG

Differentially Private Synthetic Data via APIs 4: Tabular Data

Toan Tran , Arturs Backurs , Zinan Lin , Victor Reis , Li Xiong , Sergey Yekhanin This is my paper

Pith reviewed 2026-06-27 19:57 UTC · model grok-4.3

classification 💻 cs.LG
keywords differential privacysynthetic tabular dataprivate evolutionhigh-order correlationsdata synthesisevolutionary algorithms
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The pith

Tab-PE evolves synthetic tabular data under differential privacy to better preserve high-order correlations than marginal-based methods.

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

The paper extends the Private Evolution framework to tabular data by introducing Tab-PE, an algorithm that iteratively refines candidate synthetic datasets. It applies low-cost heuristic operators specialized for tables to create variations, privately scores the results, and keeps the highest-quality samples for the next round. This targets the gap where prior differential privacy methods minimize errors on low-order marginals but lose utility on datasets with complex feature interactions. Experiments on real and simulated data show Tab-PE raises downstream classification accuracy by as much as 10 percent and runs 28 times faster than the leading baseline AIM.

Core claim

Tab-PE iteratively improves a candidate dataset via an evolutionary process that leverages tabular-specialized operators to produce variations, privately scores them, and selects the highest-quality samples to retain and propagate. In contrast to the original PE, which relies on large foundation models, Tab-PE employs heuristic operators with significantly lower computational costs. Through extensive experiments on real-world and simulation datasets, Tab-PE substantially outperforms prior baselines on datasets exhibiting high-order correlations, improving classification accuracy by up to 10 percent while running 28 times faster than AIM.

What carries the argument

Tab-PE evolutionary loop, which applies tabular heuristic operators to generate variations, privately evaluates quality, and propagates top samples under differential privacy.

If this is right

  • Synthetic tabular data produced by Tab-PE supports higher-accuracy machine learning models on tasks involving feature interactions.
  • The approach scales to larger tabular datasets because the operators avoid the cost of foundation models.
  • Differential privacy can be enforced on tabular synthesis while retaining more utility on correlated features than low-order marginal methods allow.

Where Pith is reading between the lines

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

  • The same evolutionary pattern with domain-specific cheap operators may apply to other structured data formats beyond tables.
  • Lowering dependence on large models could make differentially private synthesis practical in resource-limited settings.
  • Designing additional operators tuned to specific correlation patterns might further close the utility gap on particular datasets.

Load-bearing premise

Heuristic operators with low computational cost are sufficient to generate useful variations that capture high-order correlations under differential privacy constraints.

What would settle it

A controlled test on a dataset with documented high-order correlations in which Tab-PE fails to exceed AIM in classification accuracy or runtime after multiple evolution iterations.

Figures

Figures reproduced from arXiv: 2606.08259 by Arturs Backurs, Li Xiong, Sergey Yekhanin, Toan Tran, Victor Reis, Zinan Lin.

Figure 1
Figure 1. Figure 1: Stress test for high-order correlation modeling with XOR simulation datasets at ϵ = 1.0. The binary label is assigned based on the parity of the number of positive features among all features, which requires capturing full-order correlations. UB stands for Upper Bound using private data. LB represents random guess. In this work, we focus on investigating this gap. We con￾struct a stress test with XOR corre… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of Tab-PE’s workflow. The process starts with an initial set of synthetic samples and iteratively refines them through variations and private scoring. Overview. Sample s = {xcat(1) , . . . , xnum(1) , ..., c} includes categorical attributes xcat and numerical attributes xnum, and class label c. Xcat(i) and Xnum(j) denote the domains of cat￾egorical attribute i and numerical attribute j, respec… view at source ↗
Figure 3
Figure 3. Figure 3: The test accuracy on SCM simulated datasets under various privacy budgets. bility of the baselines and Tab-PE using an extreme case of XOR simulation datasets. We then conduct extensive experiments on realistic simulated datasets with multiple non-linear underlying functions and real-world datasets with high-order correlations, under various privacy constraint settings. We also evaluate the methods on wide… view at source ↗
Figure 4
Figure 4. Figure 4: The runtime of the methods under different privacy budgets and dataset sizes. In the left figure, each method is shown with multiple markers, corresponding to various query degree settings. PrivSyn has only one marker as it does not have this hyperparameter. not necessarily translate to high-order and downstream utili￾ties. Conversely, better matching high-order patterns can be slightly inferior at low-ord… view at source ↗
Figure 6
Figure 6. Figure 6: Comparing the proposed random-walk for variation generation with genetic algorithm operators. Simple variation operator can be effective. We adapt the genetic algorithm design (crossover and mutation) from PrivGSD (Liu et al., 2023) to VARIATION API in Tab-PE. The detailed implementations are provided in App. D.6.2 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The performance of different selection strategies. Tab-PE implements a two-stage strategy: 5 iterations for sampling and 10 iterations for ranking (Artificial Characters; ϵ = 1.0). Extremely High-Dimensional Dataset. We experiment on flattened MNIST dataset with 196 attributes (rescaled to 14×14 pixels) and 10 classes. This dataset is not only high-dimensional but also expresses complex high-order correlat… view at source ↗
Figure 9
Figure 9. Figure 9: Datasets with low-order correlations. These are widely used in prior evaluations. 2 4 6 Max depth 0.2 0.4 0.6 0.8 1.0 Accuracy Artificial-Characters 2 4 6 Max depth 0.2 0.4 0.6 0.8 1.0 Accuracy Person-Activity [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Datasets with high-order correlations – our focus. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: XOR dataset with 2 features. The colors represent classes. 2 4 6 Xgboost Max depth 0.4 0.6 0.8 1.0 Accuracy XOR-1-features 2 4 6 Xgboost Max depth 0.4 0.6 0.8 1.0 Accuracy XOR-2-features 2 4 6 Xgboost Max depth 0.4 0.6 0.8 1.0 Accuracy XOR-3-features 2 4 6 Xgboost Max depth 0.4 0.6 0.8 1.0 Accuracy XOR-4-features [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: XOR Simulation Datasets. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: SCM Simulation Datasets. C.2. Evaluation Metrics We consider the following metrics to evaluate the quality of synthetic data. Downstream utility The downstream utility reflects how well the synthetic data capture the correlation between features and labels. These metrics are the most important ones for studying high-order correlations. For consistency, we use the same SOTA classifier TabICL (Qu et al., 20… view at source ↗
Figure 14
Figure 14. Figure 14: Synthetic Datasets generated by Tab-PE over iterations for the XOR dataset with 2 features. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Running Time and Test Accuracy of the baselines while varying the degree of marginal queries. The trivial accuracy (random guessing) is 50%. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: illustrates the linear and polynomial decay schedules for the mutation rate. Generally, the polynomial decay provides a higher mutation rate at the early stage for exploration while maintaining a smaller mutation rate at the later iterations for better refinement. This leads to better performance of the polynomial schedule over the linear decay, as shown in [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: The performance of Tab-PE with different mutation rate decay schedules. D.6.2. VARIATION OPERATORS We compare the proposed random walk strategy and a genetic algorithm-based design from an existing work – PrivGSD (Liu et al., 2023). It is worth noting there are significant differences between Private Evolution and PrivGSD. PrivGSD is a method that heavily relies on marginal queries. PrivGSD first defines … view at source ↗
Figure 18
Figure 18. Figure 18: Samples generated by the methods for the flattened MNIST dataset with ϵ = 1.0 . The first row corresponds to the real data. The remaining rows correspond to the synthetic data generated by the baselines and Tab-PE. D.8. Additional High-Order Real-World Datasets We compare Tab-PE with AIM on several high-order real-world datasets, including Insurance4 , Monk5 , and Walking Activity6 . Tab. 9 provides the r… view at source ↗
Figure 19
Figure 19. Figure 19: Tab-PE performance while varying the number of synthetic samples Dsyn. Number of iterations A larger number of iterations T allows more refinement of the synthetic data, but also leads to a larger noise scale σ [PITH_FULL_IMAGE:figures/full_fig_p030_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Tab-PE performance while varying the number of iterations T. Number of sampling iterations The number of sampling iterations Tsampling controls how many times we employ the sampling-with-replacement strategy [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Tab-PE performance while varying the number of sampling iterations Tsampling. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Tab-PE performance while varying the mutation initial rate µinit in VARIATION API. Decay factor γ This parameter controls how fast the mutation rate decays. A smaller γ leads to a faster decay. A value at 1.0 is equal to a linear decay [PITH_FULL_IMAGE:figures/full_fig_p031_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Tab-PE performance while varying γ in the mutation rate schedule decay. Categorical-numerical weight λ This parameter controls the relative importance of categorical features and numerical features in the variation generation. A larger λ means more focus on categorical features. A value of 0 means only numerical features are considered. Tab. 10 presents the performance of Tab-PE with different settings of… view at source ↗
Figure 24
Figure 24. Figure 24: Hyperparameter search for Tab-PE on the Artificial Characters dataset for ϵ = 1.0. Hyperparameter configuration across privacy settings In [PITH_FULL_IMAGE:figures/full_fig_p032_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Ordering of the best hyperparameters for ϵ = 1.0, ϵ = 3.0 and ϵ = 10.0. D.10. Oversampling Study Following the simple recipe from PrivGSD (Liu et al., 2023), we conduct oversampling by randomly duplicating the samples [PITH_FULL_IMAGE:figures/full_fig_p032_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Tab-PE performance while enhancing by oversampling. the analytic Gaussian Mechanism (Balle & Wang, 2018). In practice, our implementation uses the diffprivlib library to calculate this noise scale. We conduct an experiment spending 0.02 of the total privacy budget (ϵ = 1.0) to privately estimate the class counts [PITH_FULL_IMAGE:figures/full_fig_p033_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Tab-PE performance with noisy and clean class counts. E. Limitations & Future Work Although the results are promising, there are still limitations. First, while Tab-PE consistently outperforms the baselines in capturing high-order correlations with better ML utilities, it underperforms on low-order fidelity, which primarily reflects low-order statistics. Second, the gap between Tab-PE and the upper bound … view at source ↗
read the original abstract

This paper investigates the problem of generating synthetic tabular data with differential privacy (DP) guarantees, enabling data sharing in sensitive domains. Despite extensive study, state-of-the-art methods often focus on minimizing low-order marginal query errors and overlook the challenges posed by high-order correlations. To address this gap, we extend the Private Evolution (PE) framework, originally developed for DP-compliant image and text synthesis, to tabular data. We introduce Tab-PE -- an algorithm for synthetic tabular data generation under DP constraints. Tab-PE iteratively improves a candidate dataset via an evolutionary process that leverages tabular-specialized operators to produce variations, privately scores them, and selects the highest-quality samples to retain and propagate. In contrast to the original PE, which relies on large foundation models, Tab-PE employs heuristic operators with significantly lower computational costs, making PE more practical and scalable for tabular data. Through extensive experiments on real-world and simulation datasets, we demonstrate that Tab-PE substantially outperforms prior baselines on datasets exhibiting high-order correlations. Compared to the best baseline -- AIM, Tab-PE improves classification accuracy by up to 10% while running 28 times faster.

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

3 major / 2 minor

Summary. The paper extends the Private Evolution (PE) framework to tabular data via Tab-PE, which uses heuristic operators (instead of foundation models) in an evolutionary loop of variation generation, private scoring, and selection to produce DP synthetic tabular data. It claims that on datasets with high-order correlations, Tab-PE outperforms the best baseline (AIM) by up to 10% classification accuracy while running 28x faster, addressing limitations of prior methods focused on low-order marginals.

Significance. If the empirical claims hold and the heuristic operators demonstrably recover high-order interactions under DP, the work would provide a practical, scalable alternative to both marginal-based DP synthesizers and expensive foundation-model PE methods for tabular data, with direct utility for downstream ML tasks in sensitive domains.

major comments (3)
  1. [Abstract and §3 (algorithm description)] The central claim that Tab-PE captures high-order correlations (Abstract) rests on the heuristic operators generating variations that allow private selection to recover k-way interactions for k>2. No explicit construction, proof sketch, or targeted ablation is provided showing that low-cost local edits (row/column swaps, single-feature perturbations) propagate higher-order signals rather than merely refining low-order marginals under the added DP noise.
  2. [§4] §4 (experiments): the reported gains (up to 10% accuracy, 28x speed vs. AIM) are presented without error bars, statistical significance tests, or dataset characterizations that quantify the degree of high-order correlation present; this makes it impossible to attribute improvements specifically to high-order recovery versus better low-order fidelity.
  3. [§4.3] No ablation isolating the contribution of the evolutionary loop versus the private scoring/selection step is reported, leaving open whether the advertised high-order advantage is load-bearing or could be achieved by simpler marginal methods with the same operators.
minor comments (2)
  1. [§3] Notation for privacy parameters (ε, δ) and the exact form of the private scoring function should be stated explicitly in §3 rather than left implicit from the original PE papers.
  2. The title references 'via APIs 4'; a brief sentence situating Tab-PE relative to the prior papers in the series would improve context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major comment point-by-point below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract and §3 (algorithm description)] The central claim that Tab-PE captures high-order correlations (Abstract) rests on the heuristic operators generating variations that allow private selection to recover k-way interactions for k>2. No explicit construction, proof sketch, or targeted ablation is provided showing that low-cost local edits (row/column swaps, single-feature perturbations) propagate higher-order signals rather than merely refining low-order marginals under the added DP noise.

    Authors: We agree that the current manuscript lacks an explicit discussion or targeted ablation clarifying how the heuristic operators enable recovery of k>2 interactions. The operators are intended to allow iterative mixing that propagates higher-order signals through selection, but this rationale is only implicit. In the revised version we will add a short explanatory paragraph in §3 describing the mechanism by which local edits can surface higher-order dependencies under the evolutionary loop, together with a focused ablation measuring higher-order marginal fidelity. revision: yes

  2. Referee: [§4] §4 (experiments): the reported gains (up to 10% accuracy, 28x speed vs. AIM) are presented without error bars, statistical significance tests, or dataset characterizations that quantify the degree of high-order correlation present; this makes it impossible to attribute improvements specifically to high-order recovery versus better low-order fidelity.

    Authors: The referee correctly notes the absence of error bars, significance testing, and quantitative high-order correlation metrics. These omissions weaken attribution of gains. We will revise §4 to report means and standard deviations over multiple independent runs, include paired statistical tests for accuracy differences, and add dataset characterizations (e.g., average k-way mutual information for k=3,4) that quantify the presence of higher-order structure. revision: yes

  3. Referee: [§4.3] No ablation isolating the contribution of the evolutionary loop versus the private scoring/selection step is reported, leaving open whether the advertised high-order advantage is load-bearing or could be achieved by simpler marginal methods with the same operators.

    Authors: We acknowledge that an ablation separating the iterative evolutionary loop from a single application of the operators plus private scoring is missing. Such an experiment would clarify whether iteration is essential. In the revised manuscript we will add this ablation in §4.3, comparing full Tab-PE against a non-iterative baseline that applies the same operators and scoring once, to demonstrate the contribution of the evolutionary process to high-order fidelity. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical claims

full rationale

The paper describes an algorithmic extension (Tab-PE) of the Private Evolution framework using heuristic operators for DP synthetic tabular data and supports its claims solely through empirical experiments comparing classification accuracy and runtime against baselines like AIM. No mathematical derivations, equations, fitted parameters, or uniqueness theorems are present that could reduce any prediction or result to inputs by construction. Any reference to the original PE framework functions as background rather than a load-bearing self-citation chain for the new empirical results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The approach relies on standard differential privacy definitions and evolutionary search concepts from prior work; no new free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.1-grok · 5738 in / 1023 out tokens · 17681 ms · 2026-06-27T19:57:06.538816+00:00 · methodology

discussion (0)

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