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Portable Causal Fairness Across Synthetic Data Generator Families

Steven Golob, Sikha Pentyala, Martine De Cock

arXiv:2609.03180v1cs.LG

TL;DR

The paper asks whether DECAF’s in-generator fairness cuts extend beyond one non-private GAN, a question relevant to institutions choosing synthetic-data generators. It ports the cuts to nine generators across three families and finds that they reduce parity gaps throughout, with causal diffusion leaving the smallest average gaps.

  • Problem

    Whether DECAF’s fairness mechanism extends beyond its single non-private GAN was untested, despite publishers needing to choose generators for privacy and data quality.

    Source: §2 · p. 3

  • Method

    The authors port FTU, CF, and DemPar through a shared interface to nine generators across marginals-based, GAN, and diffusion families, framing each cut as graph separation.

    Source: §3 · p. 3, §5 · p. 7

  • Results

    Across families, datasets, and privacy levels, cuts reduce downstream parity gaps; causal diffusion leaves the smallest mean gap under CF (0.099) and DemPar (0.081).

    Source: §4.2 · p. 5, §5 · p. 7

  • Takeaways & Limitations

    Institutions can choose a synthesizer for privacy or data quality while retaining a portable causal-fairness intervention.

    Source: §5 · p. 7

    Where a private structure encodes little to sever, a downstream mitigator can reach a lower parity gap on the release, while only the in-generator cut travels with the table.

    Source: §5 · p. 7

Abstract

from arXiv · show

When a statistical agency or regulator releases synthetic data in place of sensitive records, it chooses the generator that produces the table, and can shape that generator so unfair pathways are absent. DECAF made this concrete on one non-private GAN: three fairness definitions become three sets of edge cuts on the generator's causal graph. Whether the mechanism belongs to DECAF, or to causal factorisation itself, was untested. We port all three definitions to nine generators from three unrelated families (marginals-based, GAN, and diffusion, each with differentially private variants), across three levels of formal privacy guarantee, over 2,520 matched-pair runs on Adult and COMPAS datasets. The mechanism transfers everywhere, and our new causal diffusion backbone yields the fairest release of any family we tested, at fidelity close to the marginals tier. Applying the cut barely moves fidelity, only costs a downstream classifier about $0.07$ to $0.15$ AUC on average, and adding privacy guarantees don't make the data less fair.

1 Introduction

Institutions increasingly release synthetic tables instead of sensitive records, and the choice of generator also gives them a way to shape which pathways appear in the release. The paper asks whether DECAF’s graph-cut fairness mechanism transfers beyond its original non-private GAN.

1 Introduction

  • A publisher chooses the process that generates a synthetic release and can edit it so disparities routed through protected-attribute pathways need not appear in the released table.The paper situates this lever in the growing use of synthetic substitutes for sensitive records.Source: §1 · p. 1
  • DECAF factors a generator along a causal graph so that severing an edge at sampling time makes it structurally unable to use that pathway.DECAF is a single non-private WGAN-GP whose fidelity and utility trail modern private marginals-based synthesizers and diffusion models.Source: §1 · p. 1
  • DemPar cuts every directed path from protected attribute S to outcome Y, while CF cuts only paths that avoid an admissible attribute.The route through an admissible attribute survives CF.Source: Figure 1 · p. 2
  • The central question is whether edge surgery belongs to DECAF’s architecture or to causal factorisation, including when the graph is an undirected dependency graph learned from noisy counts.The distinction matters to whether the intervention can accompany generators institutions might deploy.Source: §1 · pp. 1–2

2 Background and related work

DECAF implements fairness by factoring generation along a causal graph and severing selected edges at sampling time. This section frames the open question of whether that mechanism transfers across graph types and synthesizer families.

2 Background and related work

  • DECAF writes the joint distribution as a product of conditionals, with each column generated from its graph parents; severing a parent substitutes an independently resampled marginal value without refitting.This sampling-time intervention can be cheap but may reduce fidelity when the network encounters parent combinations absent during training.Source: §2 · p. 2
  • FTU cuts the direct S →Y edge, DemPar cuts every S-to-Y path, and CF preserves paths through a modeller-designated admissible attribute.DECAF illustrates the distinction with legitimate Education →Resume →Job influence versus redlining along Race →Postcode →Loan.Source: §2 · p. 2
  • Differential privacy limits any individual’s influence through budget ε; smaller ε means stronger privacy and noisier releases.The paper treats ε=1 as tight privacy and ε=1000 as a permissive comparison approximating no privacy.Source: §2 · p. 2
  • Prior in-generator fairness work was limited to PreFair’s CF adaptation on MST, while other approaches act outside the graph or target privacy or fidelity without an edge-level fairness cut.The paper’s scope is transfer of in-generator edge surgery across families, not a head-to-head comparison of all fair synthetic-data algorithms.Source: §2 · pp. 2–3
  • DECAF’s proposed extension beyond its own GAN had not been tested, while marginals-based synthesizers and diffusion models offer alternatives across privacy and quality needs.The paper positions transfer beyond DECAF as a practical question for publishers selecting generators.Source: §2 · p. 3

3 Porting the mechanisms

The authors implement three fairness definitions through a shared interface and adapt the graph cut to nine generators across three families. They evaluate matched runs on two datasets using downstream parity, fidelity, and utility measures.

3 Porting the mechanisms

  • The three definitions reduce to graph-separation constraints on dependency structures, implemented through directed-edge severance for DAGs or undirected-pair exclusion for marginal graphs.The authors argue that the DAG representation is a design choice rather than a requirement of the fairness constraint.Source: §3 · p. 3
  • Marginals-based models exclude candidate column pairs that would create a forbidden protected-attribute-to-outcome path, before measuring those pairs and without additional privacy-accounting cost.This extends the CF-on-MST approach to PrivBayes, PrivSyn, and to DemPar and FTU.Source: §3 · p. 3
  • Causal GANs use DECAF’s surrogate substitution, while causal diffusion keeps the factorisation and replaces each sub-network with a denoiser trained by supervised noise prediction.Both expose edges through per-column networks that read only their graph parents.Source: §3 · p. 3
  • The evaluation covers Adult and COMPAS, nine generators, four mechanism settings, three role splits per dataset, five seeds, and 2,520 completed runs.Six generators carry DP guarantees and run at ε ∈ {1, 10, 1000}; causal-family DAGs are specified by hand and held fixed across generators.Source: §3 · p. 3
  • Fairness is measured as the worst-case demographic-parity gap across protected attributes, comparing positive predictions by a synthetic-trained classifier on held-out real people.The authors also record conditional parity and positive- and negative-rate balance; claims reported for parity gap hold on all four measures.Source: §3 · p. 4
  • Fairness effects are reported as matched-pair differences against runs identical in dataset, generator, ε, role split, and seed but without a mechanism.Fidelity uses marginal TVD and Cramér’s V differences; utility uses AUC and macro-F1 on held-out real data against a train-on-real reference.Source: §3 · p. 4

4 Results

Edge cuts reduce downstream parity gaps across generator families, datasets, and privacy levels; causal diffusion leaves the smallest gaps under CF and DemPar. Fairness cuts barely shift fidelity, with modest average AUC costs, while the tested privacy budgets do not blunt the cuts.

4.1 Fidelity and utility

  • On Adult, causal diffusion reaches 2-way TVD 0.103 versus DECAF’s 0.597; DP-diffusion reaches 0.218, ahead of DP-CTGAN at 0.313 and DP-GAN at 0.895.MST, a marginals-based synthesizer, reaches 2-way TVD 0.047 on Adult and 0.028 on COMPAS.Source: §4.1 · pp. 4–5

4.2 Fairness findings

  • Cuts reduce downstream parity gaps in every family, on both datasets, and at every tested privacy level; the predicted DemPar > CF > FTU ordering holds in five of six family–dataset cells.The ordering is by amount of disparity removed.Source: §4.2 · p. 5
  • CF leaves mean parity gaps of 0.099 for diffusion, 0.128 for causal GAN, and 0.152 for marginals; under DemPar, the respective gaps are 0.081, 0.089, and 0.136.These means are averaged across datasets.Source: §4.2 · p. 5, Table 1 · p. 5
  • Per severed edge, a DAG cut costs about 2.5× as much downstream utility as a marginals cut, although both graph types deliver essentially the same fairness gain per edge.Marginals cuts exclude a pair before training; DAG cuts ask a trained sub-network to extrapolate.Source: §4.2 · p. 5, Table 2 · p. 6
  • CF shifts pooled 2-way TVD by 0.001 and DemPar by 0.004; average downstream AUC costs are about 0.07 for CF and 0.15 for DemPar.The no-mechanism TVD ranges from 0.03 to 0.32 across generators.Source: §4.2 · p. 5

4.3 How this compares to intervening downstream

  • On Adult, in-generator DemPar reaches a parity gap of 0.006 at ε=10, while on COMPAS equalised-odds post-processing wins, with 0.023 versus 0.148.The in-generator cut still improves fairness over no mitigation on COMPAS.Source: §4.3 · p. 6

4.4 Privacy and fairness are nearly independent

  • Across six DP generators, parity gaps after CF remain 0.09–0.13 and after DemPar 0.08–0.12 at ε=1, 10, and 1000.DP-SGD on a weight-clipped discriminator collapses DP-GAN’s outcome to one class in 168/360 runs; CTGAN and diffusion substitutions reduce this to 1/360 and 0/360.Source: §4.4 · pp. 6–7

5 Discussion

Edge surgery transfers across causal-factorized generators, and causal diffusion produces the fairest releases tested. The discussion weighs fairness against fidelity and privacy, and notes that only an in-generator cut travels with the released table.

  • The fairness definitions compile across nine generators, both datasets, and every privacy budget, letting institutions choose synthesizers for privacy, fidelity, or maturity while retaining the fairness lever.Source: §5 · p. 7
  • Under CF and DemPar, causal diffusion leaves the smallest downstream parity gaps (0.099 and 0.081), ahead of causal GAN (0.128, 0.089) and marginals (0.152, 0.136).Source: §5 · p. 7
  • At ε=10, marginals show lower CF gain because their graph has fewer S ⇝Y edges to sever, yet finish within a few points of other families on fairness after.Source: Figure 3 · p. 7
  • Marginals remain the fidelity-and-privacy default, while causal diffusion suits fairness-focused releases; causal GAN trails on fidelity and utility, and DP-GAN fails outright.Source: §5 · p. 7
  • On Adult, CF costs 6 AUC points for 41% gap removal on marginals, 16 (78%) on causal GAN, and 18 (76%) on causal diffusion; COMPAS costs less.Source: §5 · p. 7
  • Where private structure has little to sever, downstream mitigation can achieve a lower parity gap, but the in-generator cut is the only intervention that travels with the public table.Source: §5 · p. 7

A Role splits

Table 4 specifies three protected, admissible, and outcome role splits for each dataset; the splits vary the admissible set used by CF.

  • Each dataset has three role splits defining protected S, admissible A, and outcome Y; the narrower admissible set is intended to make CF behave more like DemPar.Source: Table 4 · p. 9

B Per-edge cost of the cut

Normalizing by severed edges shows similar CF fairness gains across graph types but higher utility cost for DAG cuts. On Adult, private marginals graphs also omitted the direct protected-to-outcome edge in all 15 matched pairs, making FTU a no-op.

B Per-edge cost of the cut

  • ≈0.03 gap-per-edge under CF contrasts with utility costs of 0.033 AUC per edge for DAGs and 0.014 for marginals graphs.The reported utility costs are means across datasets; the table reports matched-pair means and restricts trials to baseline AUC > 0.6.Source: Table 5 · p. 10, B Per-edge cost of the cut · p. 10
  • DAG cuts cost more utility per edge because they make trained subnetworks extrapolate to unseen parent combinations, while marginals cuts exclude pairs before training.The resulting DAG fidelity hit can propagate to every downstream column.Source: B Per-edge cost of the cut · p. 10
  • On Adult, private marginals graphs lacked the direct protected-to-outcome edge in all 15 matched pairs, so FTU was a no-op.The structure selected under the privacy budget already satisfied this fairness definition before a fairness constraint was imposed.Source: B Per-edge cost of the cut · p. 10

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