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Achieving Group Fairness through Independence in Predictive Process Monitoring

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Adding a Wasserstein term to the training loss reduces demographic parity violations in predictive process monitoring, with a tunable fairness–accuracy trade-off along a Pareto front.

desk verdict Solid proof-of-concept applying known distributional fairness metrics and a Wasserstein IPM loss to outcome-oriented predictive process monitoring; useful for PPM practitioners, but the experiments need repeated runs and baselines before the claims are secure. read the letter →

arxiv 2412.04914 v3 pith:CNIG2OZY submitted 2024-12-06 cs.LG stat.ML

Jari Peeperkorn , Simon De Vos This is my paper · ORCID
classification cs.LGstat.ML
keywords predictiveprocessmonitoringgroupfairnessdemographicparityindependenceWassersteindistanceintegralprobabilitymetricsABPCABCC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Predictive process monitoring models trained on biased historical event logs can carry demographic bias into their predictions. This paper argues that group fairness through independence—predictions unaffected by sensitive group membership—can be both measured and optimized within this setting. It brings threshold-independent distribution metrics (area between density curves and area between cumulative curves) to process monitoring, and proposes a composite loss that mixes binary cross-entropy with a Sinkhorn-approximated Wasserstein distance, weighted by a hyperparameter lambda. In controlled experiments on three simulated event logs, increasing the fairness weight moves models along a Pareto front between AUC and demographic parity violations, demonstrating a tunable trade-off. If the claim holds, practitioners gain a model-agnostic way to audit and steer fairness without committing to a classification threshold.

What carries the argument

The load-bearing component is the composite loss $L_{\text{total}}=(1-\lambda)L_{\text{BCE}}+\lambda L_{\text{IPM}}$ with the Wasserstein distance (Earth Mover's Distance), computed via the Sinkhorn approximation on minibatches of size 512, serving as $L_{\text{IPM}}$. Because the Wasserstein distance equals the area between cumulative distribution functions, the training objective aligns directly with the ABCC fairness metric. The evaluation machinery consists of the threshold-independent metrics ABPC (estimated by kernel density estimation) and ABCC (from empirical CDFs), integrated over $[0,1]$.

What would settle it

Train the same LSTM with the composite loss on a large real-world event log while varying batch size from 64 to 2048 at a fixed $\lambda$; if the reduction in test-set ABPC/ABCC between $\lambda=0$ and $\lambda=0.5$ shrinks or vanishes at small batch sizes, the batch-statistics assumption is load-bearing and the claim does not generalize beyond the controlled setup.

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Extended reading notes

Core claim

The central discovery is that distribution-based independence can be integrated directly into the training objective of an outcome-oriented predictive process monitoring classifier. The paper trains an LSTM with the composite loss $L_{\text{total}}=(1-\lambda)L_{\text{BCE}}+\lambda L_{\text{IPM}}$, where $L_{\text{IPM}}$ is the Sinkhorn-approximated Wasserstein distance between the propensity distributions of the two protected groups. Sweeping $\lambda$ from 0 to 0.5 produces a Pareto front between AUC and the threshold-independent parity metrics ABPC and ABCC on the hiring, lending, and renting simulated logs: higher $\lambda$ lowers parity violations at the cost of some predictive performance. The paper also shows that single-threshold metrics like $\Delta\text{DP}^{0.5}_b$ can report zero bias while the propensity distributions remain highly separated, motivating the distribution-level view.

Load-bearing premise

The demonstration collapses if the Sinkhorn-approximated Wasserstein distance computed on 512-sample training minibatches is not a faithful estimate of the population-level divergence between the protected groups' prediction distributions.

Editorial extensions

If this is right

  • PPM teams can audit any propensity-outputting model for demographic parity with ABPC and ABCC without choosing a decision threshold first.
  • The $\lambda$ parameter lets stakeholders select an operating point on the fairness–accuracy frontier that matches their regulatory risk tolerance.
  • Because the loss is model-agnostic, the same composite objective can be layered onto transformer-based PPM models or other gradient-trained classifiers.
  • Distribution-level metrics expose parity violations that $\Delta\text{DP}$ at a single threshold can hide, such as identical means with opposite-shaped group densities.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's own caveat that process fairness must improve in parallel implies that deploying independence-trained models as early interventions could shift rather than remove bias; an audit of separation and sufficiency would then be necessary, an extension the authors explicitly flag.
  • The slight AUC improvements at small $\lambda$ on some logs suggest the IPM term acts as a regularizer; a direct test would compare the same Pareto-front protocol with MMD or KL as the IPM.
  • The fixed batch size of 512 is a testable lever: varying batch size while holding $\lambda$ fixed should move the Pareto front if batch-statistics fidelity is the limiting factor.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper addresses group fairness in outcome-oriented predictive process monitoring (OOPPM). It adopts independence (demographic parity) as the fairness criterion, evaluates threshold-based ΔDP metrics and distribution-based metrics ABPC and ABCC, and proposes a composite loss L_total = (1-λ)L_BCE + λL_IPM, using the Sinkhorn-approximated Wasserstein distance as the IPM. Two experiments on synthetic event logs are reported: Experiment 1 measures fairness metrics on LSTM classifiers with and without the sensitive attribute; Experiment 2 sweeps λ from 0 to 0.5 on three high-bias logs and reports Pareto fronts between AUC and ABPC/ABCC. The paper concludes that distribution-based metrics are useful threshold-independent indicators and that the composite loss enables a tunable fairness–accuracy trade-off.

Significance. The contribution is conceptually useful for the PPM community: distribution-based demographic parity metrics have not been systematically explored in OOPPM, and the proposed loss is simple, model-agnostic, and implemented in PyTorch with code and full results released on GitHub. If the empirical claims are robust, the framework gives practitioners a straightforward way to audit and steer group fairness in outcome prediction. However, the evidence as presented is preliminary: the evaluation metric ABCC is closely aligned with the training objective, the batch-size assumption is unvalidated, and the single-run results lack statistical grounding. These gaps currently limit the strength of the claims.

major comments (4)
  1. [§3.2, §5.3, Fig. 4] The ABCC metric, defined as the integrated absolute difference of the empirical CDFs, is the population counterpart of the Wasserstein-1 distance used as L_IPM in Eq. (5). The paper itself notes in §3.2 that 'using Wasserstein as IPM loss is more aligned with optimizing ABCC than with optimizing ABPC.' Therefore, the observed decrease in ABCC with increasing λ in Fig. 4 is expected by construction and should not be presented as independent evidence of fairness improvement. The ABPC results, which are not directly optimized, provide the more meaningful non-circular evidence. Please rebalance the presentation accordingly—for example, report ABPC and threshold-based ΔDP at several thresholds as the primary fairness metrics, and treat ABCC as a check of the training objective rather than as an independent evaluation.
  2. [§4.2, §6, Fig. 4] The reliability of the minibatch Sinkhorn Wasserstein estimates is load-bearing for Experiment 2 but is not validated. Section 4.2 fixes the batch size at 512 'to ensure reliable computation of batch-level statistics', and Section 6 acknowledges that these losses 'rely on batch-level statistics' and recommends sufficiently large batch sizes or full-batch training, yet no sensitivity analysis is provided. Since Table 1 indicates that only about 9–30% of cases belong to the protected group and cases contribute multiple correlated prefixes, a batch of 512 prefixes contains a very small number of effectively independent protected-group samples. The empirical Wasserstein distance and its Sinkhorn approximation are biased and high-variance in this regime. Please provide a batch-size sensitivity analysis (e.g., 256, 512, 1024, full batch) and show that the Pareto fronts in Fig. 4 are stable; otherwise the observed test-time reductions could reflect optimization of batch-level noise.
  3. [§5.3] Experiment 2 is conducted as single runs without repeated seeds, and the Pareto fronts in Fig. 4 are derived from one train/test split. Because the AUC differences across λ are small (e.g., roughly 0.05 in hiring_high), it is not clear that the apparent trade-off is not a random artifact of model initialization and data sampling. Please repeat the λ sweep with multiple random seeds and report means with standard deviations or confidence intervals for AUC, ABPC, and ABCC (and ideally ΔDP at several thresholds) so that the shape of the Pareto front can be assessed statistically.
  4. [§5.3, Related Work] The paper does not compare the proposed IPM-based composite loss with existing fairness interventions in PPM, notably the adversarial debiasing approach of [19] or a simple post-processing baseline such as per-group threshold adjustment. Since the contribution is a training-time mitigation method, at least one such baseline would help calibrate its practical value and rule out that the observed trade-off is specific to this LSTM-plus-Wasserstein configuration. Even a proof-of-concept experiment would be strengthened by including a reference method.
minor comments (6)
  1. [Abstract and §1] The phrase 'composite loss function existing of binary cross-entropy' should be 'consisting of'.
  2. [§4.1] The validation set is created by splitting 20% of the prefix-outcome pairs from the training samples rather than at the case level; because multiple prefixes come from the same case, this introduces case-level leakage between training and validation, affecting early stopping and threshold tuning. Please clarify whether a case-level split was considered or state why it is unnecessary here.
  3. [§3.1] The bandwidth selection for the KDE used to estimate ABPC is not reported; please add the bandwidth selection method or the code reference.
  4. [Eqs. (1)–(2), Table 2] Notation is inconsistent: ΔDPc, ΔDPt_b, ΔDP0.5_b, and ΔDPopt_b are all used; unify the notation and always specify the threshold value.
  5. [Throughout] There are several rendering artifacts in the text (e.g., 'F airness' in the title/header, 'T raining (& V alidation) Set' in Table 1, and 'Y ers' in the Section 6 text) that should be corrected in the final version.
  6. [Fig. 4] The legend entries appear as '=0.00', '=0.05', etc., without the λ symbol; please ensure the legend and captions are consistent so that readers can interpret the λ values.

Circularity Check

1 steps flagged · score 6.0 of 10

Partial circularity: the Wasserstein IPM loss is, by the paper's own account, essentially the ABCC objective, so the reported ABCC improvements are by construction; ABPC and AUC trade-offs remain independent.

  1. self definitional [Section 3.2 (Eq. 5 discussion) and Experiment 2, Section 5.3 / Figure 4]
    "The optimal mass transformation from one distribution to the other is determined by the area between the cumulative distribution functions. In this way, using Wasserstein as IPM loss is more aligned with optimizing ABCC than with optimizing ABPC."

    Equation (4) defines ABCC as the area between the cumulative density functions of the two protected groups. The paper states that the Wasserstein distance used as LIPM in Eq. (5) is determined by exactly that same area between CDFs. Therefore, for lambda > 0, the composite loss directly penalizes a Sinkhorn/minibatch version of ABCC. Figure 4 then presents decreasing test ABCC as evidence of reduced demographic parity violation; that part of the result is the optimized objective itself rather than an independent prediction. The ABPC panels and the AUC trade-off are not directly optimized and therefore provide independent content, making the circularity partial.

full rationale

The paper's derivation chain is mostly self-contained. It does not rely on load-bearing self-citations: the only self-reference is a passing mention in future work, while the ABPC/ABCC metrics and the Sinkhorn implementation are attributed to external sources. Experiment 1 is a metric-illustration study on simulated logs with known bias levels and is not circular. Experiment 2's Pareto fronts are genuine empirical observations that include ABPC, which is not the training objective, and AUC, which is only affected indirectly through the BCE term; these give independent support to the claimed trade-off. The identified circular component is confined to ABCC: in one dimension, the Wasserstein-1 distance equals the area between CDFs, which is exactly ABCC, and the paper explicitly acknowledges this alignment. Consequently, the reduction in ABCC with increasing lambda should be read as a sanity check that the optimizer is minimizing the quantity it was designed to minimize, not as independent validation of improved fairness. No other circular step was found; the batch-size warning in Section 6 is a robustness limitation rather than a circularity.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new theoretical entities. It imports the fairness metrics, the IPM loss, the LSTM architecture, and the simulated event logs from prior work. Its free parameters are mostly experimental choices (lambda, prefix length, bandwidth, batch size, model hyperparameters). The key unstated premises are that the simulated logs are a valid fairness testbed, that the protected attribute is a meaningful binary sensitive feature, and that batch-level Wasserstein estimates generalize to the population.

free parameters (5)
  • lambda (fairness trade-off weight) = 0 to 0.5 in steps of 0.05
    Controls the balance between BCE and the Wasserstein IPM loss in Eq. 5; chosen by the experimenter to trace the Pareto front rather than fitted, but it is the key tunable knob the method introduces.
  • KDE bandwidth for ABPC = not specified
    ABPC is estimated via kernel density estimation (Section 3.1), but the bandwidth selection rule is not given; the resulting ABPC values depend on this choice.
  • Maximum prefix length = 6
    Set to 6 for all experiments (Section 5.1); shorter prefixes are padded, longer ones truncated, and this affects the feature representation and information available.
  • Sinkhorn regularization strength = not specified
    The efficient Sinkhorn approximation used inside the training loop (Section 3.2) has a regularization parameter from [33] that is not reported; results may depend on it.
  • LSTM hyperparameters (grid-searched) = layers 1 or 2; size 16, 32, or 64; batch 128-512; lr 0.0001 or 0.001; dropout 0.2 or 0.4
    Selected by validation AUC for each event log under BCE loss (Section 4.2); these are fitted model choices that influence the reported scores.
assumptions (7)
  • domain assumption Independence (demographic parity) is the appropriate fairness criterion for the studied PPM deployments
    Section 2.2 and Section 3 commit the paper to group fairness through independence, while noting alternatives like separation and sufficiency exist; the experiments measure and optimize only independence.
  • domain assumption The protected attribute is binary and available as case:protected in the event logs
    Section 2.1 defines s_i in {0,1}; Section 5.1 uses the case:protected feature; real applications may have multiple or continuous sensitive attributes, as the conclusion acknowledges.
  • domain assumption The simulated event logs from [28] provide a valid controlled testbed with known bias levels
    Section 5.1 selects three processes from the simulated logs based on bias levels and excludes the hospital log because the outcome did not correlate with sensitive features; the validity of the conclusions depends on these logs representing the phenomenon of interest.
  • domain assumption The process outcomes used as labels are, or will become, fair; the model is not asked to replicate historically biased outcomes
    Section 6 states: 'this work assumes OOPPM models are deployed in contexts where process fairness has been, or is actively being improved. Without such improvements, deploying these models risks perpetuating existing biases rather than mitigating them.'
  • domain assumption Batch-level Sinkhorn/Wasserstein estimates are representative of the population-level propensity distributions
    Section 4.2 fixes batch size 512 for IPM experiments; Section 6 warns that distribution-based losses rely on batch-level statistics and recommends large batches. The central Experiment 2 inference depends on this proxy being adequate.
  • standard math Standard results about the Wasserstein distance and empirical CDF estimation
    Section 3.2 uses the identity that the Wasserstein distance is the area between CDFs, and Section 3.1 uses KDE and empirical CDFs with the trapezoidal rule for ABPC/ABCC estimation.
  • domain assumption LSTM propensity outputs are treated as comparable scores across groups even though they may be miscalibrated
    Section 2.1 acknowledges propensities may not be true probabilities; Section 6 further warns that composite losses may worsen calibration. The metrics operate on raw propensities, so this assumption is load-bearing for their interpretation.

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Pith. "Pith review of Achieving Group Fairness through Independence in Predictive Process Monitoring." pith.science (2026). https://pith.science/paper/CNIG2OZY

@misc{pith2026241204914,
  author       = {Pith},
  title        = {Pith review of: Achieving Group Fairness through Independence in Predictive Process Monitoring},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CNIG2OZY}},
  note         = {Machine review of arXiv:2412.04914}
}
abstract

Predictive process monitoring focuses on forecasting future states of ongoing process executions, such as predicting the outcome of a particular case. In recent years, the application of machine learning models in this domain has garnered significant scientific attention. When using historical execution data, which may contain biases or exhibit unfair behavior, these biases may be encoded into the trained models. Consequently, when such models are deployed to make decisions or guide interventions for new cases, they risk perpetuating this unwanted behavior. This work addresses group fairness in predictive process monitoring by investigating independence, i.e. ensuring predictions are unaffected by sensitive group membership. We explore independence through metrics for demographic parity such as $\Delta$DP, as well as recently introduced, threshold-independent distribution-based alternatives. Additionally, we propose a composite loss function existing of binary cross-entropy and a distribution-based loss (Wasserstein) to train models that balance predictive performance and fairness, and allow for customizable trade-offs. The effectiveness of both the fairness metrics and the composite loss functions is validated through a controlled experimental setup.

Figures

Figures reproduced from arXiv: 2412.04914 by the authors.

Figure 1
Figure 1. A toy example showing the need for threshold-free independence metrics. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. A graphical depiction of the LSTM model used. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The LSTM propensity densities for the hiring event log. violations reduce. For both the renting and lending logs these trends are a little less pronounced. The renting_medium the DP metrics indicate less bias than renting_low, but this is in line with the higher S + 1 value in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The results for including IPM loss with different values for [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: The LSTM propensity densities for the hiring_high event log. 6 Practical Considerations Our work provides a practical framework for practitioners and researchers to assess and improve group fairness in OOPPM models using independence. Simpler methods such as threshold …

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. FairLoop: Software Support for Human-Centric Fairness in Predictive Business Process Monitoring

    cs.LG 2025-08 conditional novelty 4.0 of 10

    FairLoop distills predictive neural models into editable decision trees, lets users cut out unfair rules, and fine-tunes the model on corrected labels for business process monitoring.

  2. T2I-ReasonBench: Benchmarking Reasoning-Informed Text-to-Image Generation

    cs.CV 2025-08 unverdicted novelty 4.0 of 10

    The abstract and body of this submission are mismatched: the claimed T2I reasoning benchmark never appears in the body, which is an unrelated paper on fairness in predictive process monitoring.

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.