Controlled Model Debiasing through Minimal and Interpretable Updates
Authors: Federico Di Gennaro
Thibault Laugel
Vincent Grari
Marcin Detyniecki
Venue: Accepted by TMLR ()

Abstract: Traditional approaches to learning fair machine learning models often require rebuilding models from scratch, typically without considering potentially existing models. In a context where models need to be retrained frequently, this can lead to inconsistent model updates, as well as redundant and costly validation testing. To address this limitation, we introduce the notion of controlled model debiasing, a novel supervised learning task relying on two desiderata: that the differences between the new fair model and the existing one should be (i) minimal and (ii) interpretable. After providing theoretical guarantees to this new problem, we introduce a novel algorithm for algorithmic fairness, COMMOD, that is both model-agnostic and does not require the sensitive attribute at test time. In addition, our algorithm is explicitly designed to enforce minimal and interpretable changes between biased and debiased predictions in a binary classification task—a property that, while highly desirable in high-stakes applications, is rarely prioritized as an explicit objective in fairness literature. Our approach combines a concept-based architecture and adversarial learning and we demonstrate through empirical results that it achieves comparable performance to state-of-the-art debiasing methods while performing minimal and interpretable prediction changes.

Published in Transactions on Machine Learning Research (06/2025)
Controlled Model Debiasing through Minimal and Inter- pretable Updates
Federico Di Gennaro 1.2 EPFL, Lausanne, Switzerland
federico. dippeer
Thibault Laugel
thibault. laugel Gara. com
AXA, Paris, France
TRAIL, LIP6, Sorbonne Universilé, Paris, France
Vincent Grari
AXA, Paris, Fronce
TRAIL, LIP6, Sorbonne Université, Paris, France
Marcin Detyniecki
AXA, Paris, Fronce
TRAIL, LIP6, Sorbonne Université, Paris, France
Polish Academy of Science, IBS PAN, Warsow, Polond
Reviewed on OpenReview: https:
// // optnr/viewwwwww..o net/ forum? id= 89-8944449jp0
Abstract
Traditional approaches to learning fair machine learning models often require rebuilding models from scratch, typically without considering potentially existing models. In a context where models neod be retrained frequently, this can lead inconsistent model updates, well as redundant and costly validation testing. To address this limitation, introduce the notion of controlled model debiasing, novel supervised learning task relying two desiderata: that the differences between the new fair model and the existing one should be (i) minimal and (ii) interpretable. After providing theoretical guarantees to this new problem, we introduce a novel algorithm for algorithmic fairness, COMMOD, that is both model-agnostic and does not require the sensitive attribute at test time. In addition, our algorithm explicitly designed
enforce minimal and interpretable changes between bi- ased and debiased predictions in a binary classification lask property that, while highly desirable in high-stakes applications, is rarely prioritized literature. Our approach combines concept-based architecture and adversarial learning and we demonstrate through empirical results that it achieves comparable performance to state-of-the-art debiasing methods while performing minimal and interpretable predic- tion changes. Code to reproduce the experiments available on the following repository: http:///oooooooeerreeeeroooooooo mod.-leedddddddd--diiiiiinn
explicit objective in fairness
1 Introduction
The increasing adoption of machine learning models high-stakes domains such as criminal justice (Klein- berg et al. 2016) and credit lending (Bruckner) 2018) has raised significant. concerns about the potential biases that these models may reproduce and amplify, particularly against historically marginalized groups. Recent public discourse, along with regulatory developments such the European AI Act (2024/1689), has further underscored the need for adapting AI systems to ensure fairness and trustworthiness (Bringas Col- menarejo et al. 2022). Consequently, many of the machine learning models deployed by organizations are,
Equal contribution.
Work carried out during an internship AXA.

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may soon be, subject to these emerging regulatory requirements. Yet, such organizations frequently in- vest significant resources (e.g. time and money) in validat their models with the assistance of domain experts before deploying them at scale (e.g. Mata et al. (2021) for dam safety monitoring and [Topra et al. (2021) for precision medicine), to ensure their performance and trustworthiness. Hence, as new regulatory constraints emerge, the ability lo make these models comply with new constraints while minimizing the need for revalidation has thus become critically important.
The field of algorithmic fairness in classification framework has experienced rapid growth in recent years, with numerous bias mitigation strategies proposed (Romei & Ruggieri 2014 Mehrabi et al. 2021). These ap- proaches can be broadly categorized into three types: pre- pre-processing (o.g. Belrose et al. (2024)), in-processing (e.g. ---anann et al. (2018)), and post-processing learning pipeline at which fairness enforced. While the two former categories do not account at all for any pre-existing biased model being available for the task, post-processing approaches aim to impose fairness by directly modifying the predictions of a biased classifier: this naturally imposes some kind of consistency between the new, fair model and the old, biased one. However, these methods are generally deemed to achieve lower performance, and the changes performed are generally not traceable.
Karmiran et al. 2010 based on the stage of the machine
Motivated by these considerations, in this paper we consider a new paradigm, proposing to frame algorithmic fairness as a model update task. The goal is thus to enforce fairness through small and understandable updates to a pretrained model, presumably biased, in order to facilitate model monitoring. For this purpose, we introduce the notion of Controlled Model Debiasing, based on two intuitive desiderata: (i) changes wet the new model and the existing one should be minimal, and (ii) these changes should be understandable. We stress the fact that requiring minimal updates ensures that change as few existing decisions as possible, which preserves model stability, reduces the operational burden of re-validation, and maintains user trust in settings where consistency is critical. At the same time, enforcing interpretable updates means each model change can be clearly explained to domain experts and stakeholders inteeoooderssfcciiiattinn faster audit cycles, clearer accountability, and casier troublcshooting when fairness constraints interact with real-world business rules.
Our formulation combines assumptions from both post-processing and in-processing approaches, proposing to learn new fair model by leveraging a previously trained biased one. After providing theoretical guaran- tees on the solution and fcasibility of this new proposed problem, introduce COMMOD (COncept-basce Minimal MOdel Debiasing), our method to address it. Leveraging the fields of concept-based interpretabil ity (Alvarez Melis & Jaakkola, 2018 Koh et al. (020b) and fair adversarial learning (Zhang et al. 2018 Grari et al., 2021), COMMOD is model-agnostic, interpretable debiasing method that aims to improve fairness in an interpretable way, while minimizing prediction changes relative to the original model. Through experiments, we demonstrate that our method achieves comparable fairness and accuracy performance to existing algorithmic fairness approaches, while requiring fewer prediction changes. Additionally, we show that COMMOD enables more meaningful and casier-to-undersaale prediction changes, enhancing its utility in practice. To summarize, our contributions are as follows:
We introduce a new notion of Controlled Model Debiasing, which aims to account for a previously trained model by performing minimal and interpretable updates to mitigate bias (Section 3 To the best of our knowledge, we are the first to address interprelability directly in the updating process.
We provide two thcoretical guarantees for the proposed problem: the formulation of the Bayes- Optimal Classifier in a fairness-awen aware setting and the feasibility of the problem in the general setting (Section
We introduce a new method, COMMOD, to address the new optimization problem in a model- agnostic, fairnes--unwwree setting (Section 5 We validate its performance through experiments on classical fairness datasets, showcasing its debiasing efficacy and ability to perform fewer and more interpretable changes (Section 0
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2 Background and notation
Let X' S Rd be an input space consisting of features and y an output space. In a traditional algorithmic fairness framework in supervised learning, we want an algorithm that outputs Y E y such that Y is unbiased from sensitive variable S, only available at training time. For the sake of simplicity, we focus in this paper a binary classification problem where y = {0, 1) and for which also the sensitive attribute S takes values on a binary sensitive space S = (0,1).
2.1 Group fairness
Over the years, several notions of fairness have been proposed in the literature to define whether not variable Y is unbiased from sensitive variable S (work et al., 2012 Hardt et al. 20166; Jiang et al. 2020). In this paper, we focus on two of the most used ones: Demographic Parity (Calders et al. 2009) and Equalizing Odds (Hardt et al. 2016).
2.1.1 Demographic Parity
A classifier satisfies Demographic Parily (DP) if the prediction y is independent from sensitive attribute S. In the case of binary classification, this is equivalent to IP 1 s 0) P(Y = S = =1). Hence, Demographic Parity can be measured using the P-rule:
(P( - P =
P( = 1
P-Rule min
P(Ý 1 P(Ý 1|S=1)
2.1.2 Equalizing Odds
A classifier satisfies Equalizing Odds (EO) if the prediction Ý is conditionally independent of the sensitive attribute given the actual outcome Y. In the case of a binary classification problem, this is equivalent to PPC = Y y. S 0) = PP 1 measured using the Disparate Mistreatment (DM) (Zaaar al. 2017
y, = 1), for all y E (0. Hence, Equalizing Odds can be
ATPR TPRs=1 -PRssol AFPR FPRs-1 FPRs=ol
where TPRs_a- p(ś 1, S 5= FPRs=. = p( 1|Y 0, =)s), and E {0, 1). In the rest of the paper, we use DM = ATPR + AFPR.
2.2 Mitigation strategies
Bias mitigation algorithms are generally grouped into three different categories, based on when the debiasing process is carried on in the machine learning pipeline (Romei & Ruggieri 2014). In particular, pre-processing methods (e.g. Zemel et al. (2013) modify the training data such that they are unbiased with respect to S. In-processing methods (e.g. Zhang et al. (2018)) aim to train a new, fair, classifier by integrating some fairness constraints in the optimization objective. Finally, post-procee pes-pprcessing methods aim to achieve fairness by adjusting the predictions f/ (or the predicted probabilities) of an already existing model f: X' + y. As such, a notion of predictive similarity between these two sets of predictions often being optimized, either directly (Jiang et al. 2020 Nguyen et al. 2021 Alghamdi et al. 2022 indirectly through heuristics (Kami- ran et al. 2018). However, rather than assumedd end-goal, this objective generally remains proxy for the true goal of optimizing accuracy, as the true labels Y are generally assumed to be unavailable at inference time in the post-processing setting. Furthermore, these approaches generally suffer from several limitations, such as not being model-agnostic (Calders & Verwer 2010 Kamiran et al. 2010 Du et al. 2021), or re- quiring access to the sensitive attribute test time (Hard et al. [0066] Pleiss et al.) (017), which greatly hurt their practical use. On this topic, we provide a review of existing post-processing approaches and their limitations in Table 2 in Appendix.
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3 Controlled model debiasing
Let us now consider context where a model X - [0, 1] that outputs cach input 2 E X' to a predicted probability PP(Y = 1|x x). Suppose now this model needs to be updated into fairer model g (with respect to specific fairness definition discussed in Section 2.1 while trying to maintain the accuracy of f. As discussed in Section ! blindly training can be harmful for several reasons. First, Krco et al. (2023) have shown that some bias mitigation approaches performed needlessly large numbers of prediction changes for similar levels of accuracy and fairness. Yet, a large number of inconsistent decisions may negatively impact users' trust, as shown by Burgeno & Joslyn| (2020) in the context of weather forecast. On top of this, beyond statistical testing, models in production may undergo extensive lesting by domain experts (Tsopra et al, 2021). In this context, being able to understand the changes from one model to the other would be crucial to not being forced to undergo all the testing again, in addition to incrcasing expert trust. Driven by the above-mentioned considerations, we introduce the notion of Controlled Model Update, which is based on the following notions of Interpretable and Minimal updates.
3.1 Interpretable updates
To facilitate the adoption of a new model 9, we propose generate explanations that describe how the debiasing process modified the old model f. Contrary to traditional XAI methods (see Guidolti al. (2018) for survey), rather than explaining the decisions of the model g, our aim here is to generate insights about the differences between f and g. An intuitive solution to this problem would be to first train fair model and then generating explanations for these differences in a post-hoc manner, akin to Renard et al. (2024). However, post hoc interpretability methods, in general, are often criticized for their lack of connection with ground-truth data (Rudin 2019: Laugel et al. 2019 Therefore, in order to ensure better trust in the new model, we pursue the direction of sclf-explainable models (Alvarez Melis & Jaakkola 2018), generating global explanations for the differences between y and f while learning the predictive task.
3.2 Minimal updates
The constraint of ensuring that the new model remains as similar possible to the initial one can be directly added to the training objective. In particular, to the usual optimization problem of fairness, we added a constraints that control the probability for a prediction / to change label after the debiasing process. We emphasize once again that making minimal changes to a biased model is beneficial in cases where the model has already been validatod basod on user nceds. Significant updates to make the model fairer might risk no longer satisfying those needs, requiring once again a costly validation. We then frame our problem in traditional algorithmie-fainnes way, in which the selfexxplanaable model g is required to be accurate and fair. On top of these constraints, is required to be similar to according to distance function distø: [0, 1] x [0, + Rz0, where dist Ex=pl (xxx(e(((X) g(X)]. The combination of these desiderata allows us to understand what changes are required from a biased model to become fairer focusing on minimal adjustments.
Let fair(-) be the fairness criteria (e.g. Demographic Parity or Equalizing Odds). Further, let us define the predictions (after threshold) of the biased model f and edited model g as ÿ- [(x))00.5 and V == 1gx))>0 respectively. We can then formalize our optimization problem through the following Controlled Model Update objective:
min Acc(Y, Y) S.l. lair(P) 7
(1)
(ist Sp
where 7 E R4 and p E R. One could also notice that, by fixing ((f,g) = (//00005) (g>0.b)l, the distance becomes dist& g) = P(L' # Y). Through the paper, this the distance we will refers to in our exper- iments, but a bricf discussion on other possible distances (i.c. different Φ) is reported in Scction 5.1 and Appendix D.4 Observe that setting p = 0, i.. forbidding any prediction change happen, imposes g = f. On the contrary, the more p increases and the more g is free to differ from f and, ideally, to reach higher
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fairness scores. When p 1, Eq. becomes classical algorithmic fairness learning problem. Notice also that the interpretability is all carried by the self-explainable model itself, and hence it will be not explicitly appear in the optimization problem of Equation ! We will discuss our self-explainable model g in Section 2
4 Theoretical guarantees on the minimal update problem
In this section, we present two theoretical contributions to the problem formalized in Eq. 1 where we used as distance (f)) TP'' # V). First. (Section 4.1). we show that is possible to define the Bayes Optimal Classifier of the problem in the fairness-aware setting. Then, in Section 1.2 we assess the feasibility of the problem in general, giving guarantees on the trade-off between fairness and number of prediction
changes. All proofs can be found in Appendix B
4.1 Result 1: Bayes-optimal classifier in fhimess-award setting
Let (X, Dint be a joint distribution on X' x {0.1} x {0,1} {0,1), where X is the instance, Y the target feature, S the sensitive variable, and y the output of the black-box classifier. Let 'D be the distribution over (X, Y): D suitable distribution (DP or EO) over (X,S) and DD* a distribution over (X, V.). We want to show that despite the new constraint on the number of changes, our optimization problem in Eq. 1 still has analytical solution (i.e. the Bayes-optimal classifier (BOC)) in fairness aware setting knowing the true distributions above mentioned. To do so, we leverage the work of (Menon & Williamson| 2018). who defined the BOC in the traditional fairness setting, relying on a reformulation of the optimization problem using the notion of cost-sensitive risk!" For what concerns the fairness constraint, they show (Lemma 3) that P- R-Rule(g) 2 r is equivalent to C.Sbl (g. D,6) 2 k, where CSSaaty D,0) = (1 (1-6)- -N D) - F.RgP D) is the balanced cost-sensitive risk and 1/(1 +T). Following the same idea, we first establish the equivalence between the constraint the number of changes and a cost-sensitive risk:
Lemma 4.1. Pick any random classifier g. Then, for any E [0,
P(P' # #8) S ppp + CSbal ,D',c))) S p.
with CS (g: -1 FNR(:: D*) c FPR(g: D Pand c- PP( 1).
Finally, in similar fashion of the main result in Menon & Williamson, 2018 about the Optimal Classifier, can define for any cost e, 2, e* E [0,1, Afair, Aratio E IR the Lagrangian Ros(g; D, D, D*) of the optimization problem in Eq. [ as:
Asoir CSeal D,C) CS(g; Ros(g:D,D,DD) -0l::
(2)
AratioCStaa (g; D* c²*).
Proposition 4.2 (Fairness-awaal aware Bayes-optimal classifier). The Bayes optimal classifier of Res in fairness aware setting and knowing the distributions D, D.D,D D is given by
Jopt (x) arg min D,
(1l o os (x) [xE [0.
gE(0.1j
where
((x) P(Y 1 | X x), ()x) P(S 1 x), =
P(P) X x),
(x) = n)(z)) c- Aratio (π(z) - 2) - Afair(1 (x) (x) - -())
and Hz)=)= = 1 + a: a1 (2=0) is the modified Heaviside (or step) function for a parameler 1) E [0,1].
1 From Menon & Williamson (2018): The risk of randomized classifier g: X + (0, 1) computed on Y is called cost sensitive
risk for a cost parameter e E (0. 1) and न P(Y = 1) if it can written as CS(g. c) = n (1 c) - PN D) + (1 m) :
FPR(g D), where FN R2VR(g:2) D)= = Exyv=1 9(X) and F PPR D) = [x])=]
"Notice that we changed the distribution w.r.t. FPR and FNR computed. Hence, FN P( = o 8 1) and
F D*) = P(Ý 11p 0).
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Despite its theoretical importance, the BOC presented in Proposition 3.2 remains impractical for computa- tion, as the joint and marginal distributions of the random variables S, Y, P. are typically inaccessible in real-world applications. Furthermore, the above result only holds within a fairness-aware setting, a context that is uncommon in practical scenarios. For this reason, we introduce in Sec. 5 a novel algorithm that opti- mizes a relaxed form of the optimization problem Eq. | which does not require knowledge of the sensitive attribute at test time. Finally, note that this result can be directly adapted to EO, since the additional constraint we bring does not depend on the fairness criteria, and Menon & Williamson (2018) also applies to EO.
4.2 Result 2: fairness level under a maximum change constraint
We now aim to theoretically understand what happens experimentally to the trade-off between fairness score and the similarity between f and g defined in Eq. [ For this purpose, study the impact that K changes to the predictions of can have on P-Rule and on Disparate Mistreatment (DM).
Let us consider a set Set[(X; Y,, S,) with S, E {0, }} and Y; E 10, Then, we can define the following quantitics
7e1 (J) { S. =s, f(X.) = 13}, (00 = |{ S, = =, f(X)) 03| where [set]| stays for the size of such set. Then, with C = So/S1, the empirical P-Ruk of f is
P-Rule(f)- min(c C. milf) 'o(f) è 2
Definition 4.3. (Switching point) The switching point K2 is the minimum number of changes required to get a P-Rule(g) & 1 starting from P-Rule(f).
Informally, the switching point refers to the phenomenon in which, starting from one of the two functions forms in the minimum definition of the P-Rule, we switch to the reciprocal form definition. With this in mind, we can prove the following proposition:
Proposition 4.4 (Extreme-ftip optimality for Demographic Parity). Given K changes with K < Kg, the macimum P-Rule can get by editing with K flips the predictions of a model I is achieved by either dedicating all the flips to one side of the division (f( us no(S).
Note that, in minimal changes regimes of these paper, the it is reasonable to assume that K < K,, We believe this result represents a significant milestone in the theoretical characterization of the effects of debiasing a model using DP as a fairness measure. Although this result provides valuable insights into the dynamics of the debiasing process, Proposition 4.4 does not account. for the potential impact of these optimal changes on model accuracy. This highlights the possibility that, in the context of algorithmic fairness where the goal is to balance fairness and accuracy deeiissig algorithms may prioritize alternative changes that minimize adverse effects on accuracy. On top of this, this theoretical result would be algorithmically applicable only in fairness aware setting due to the fact that the knowledge of proportion Tij, i,j E (0, 1} is required.
Extension of the result to Equalized Odds Further, this result could be also presented for F.O and a proof follows more or less the same argument. In fact, we can define
No. = [[i S. s. Y, wAt.
8, e (0.
i.. the number of instances in group with label y. The core insight is that, when you split K flips between TPR-adjusting and FPR-adjusting actions, the resulting DM is piecewise-linear function of the allocation. A convex (affine) function a compact interval always achieves its minimum at one of the endpoints and hence the best you can do is to devote all K flips to whichever single action gives the larger per-flip reduction in disparity. In particular, we can prove the following:
Proposition 4.5 (Optimal allocation for minimizing Disparate Mistreatment). Let f be a fixed base classifier and define
=
max sE(0,) N.,1
5 = mAX
sE
} N
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For any integer K 2 1, consider all post-processed classifiers obtoined by flipping eractly K labels of f. If x E [) denotes the number of flips devoled to reducing the TPR-gap (and K - those for the FPR-gap), the minimum Disparate Mistreatment over 2 E {I...., K} is attained at an endpoint:
0,
8 > 7, any x E [0, K].
Topt
5 = 7,
8 < 7-
This means that the best strategy is to devote all K flips to whichever type of flip gives the larger per-flip reduction.
5 COMMOD: an algorithm for controlled model debiasing
As previously mentioned, while the BOC of Proposition 4.2 is theoretically relevant in the Fairness- Shirness-waare
setting, it lacks practical utility. In order to solve Problem ! we thus propose a new algorithm, called COM- MOD, circumventing these limitations and integrating the interpretability objective described in Section 3
COMMOD aims to edit the probabilities scores f(X) of the biased model into scores g(X), whose associated predictions y 1(())>0.5 are more fair and whose predictive quality is measured through a loss function
Ly (r()(X),)) Y) (e.g. the binary cross-entropy loss). The update is done through multiplicative factor r(X) as follows:
g xX) = o(((()(nnngg
(3)
where (-) is the sigmoid function to ensure g(X) [0, and fiogit is the logit value of the biased model f. Besides being intuitive, this formulation enables a more direct modelling of the differences between f and g, Y + / if and only if rX)) < O. We then propose to model the ralio Tw, as Neural Network with parameters Wy and taking as input X. In the subsections below, we describe how both desiderata of similarity and interpretability are integrated in COMMOD.
5.1 Penalization term for minimal updates
We propose to minimize model changes by adding penalization term Cratio- Numerous similarity measures between / and can be considered, depending on the considered scenario: for instance, existing works in post- processing fairness generally focus on distances between distributions such as the Wasserstein distance (Jiang ct al. 2020) or the KI-divergence (Tifrca et al. 2023). Here, we propose to use cither a mcan squared norm function Eratio (X)) = [|re, (X) 1 defined by a positive-defiite inner product M. This term ensure that the score f(X) is not modified unnecessarily, and thus that the calibration of g remains consisteent (cf. Figure 9 in App. D.4 for related discussion). For the sake of simplicity, in the experiments of our paper we set M- = I, recovering the classical Euclidean distance. More generally, by choosing M diag(w), wa) > 0, one recovers weighted Euclidean norm ||Mw, (X) 11 Σ wy (X); 1) Similarly, setting M = E-1, with the (positive-definite) feature covariance matrix, yields the Mahalanobis distance (rw, (X) - 1 (rw,, (X) 1). In likelihood- based settings one can even take M to be the Fisher-infommatonn matrix, providing local quadratic approximation to the KL divergence.
5.2 Concept-based Architecture for Interpretable Changes
In our approach, we prioritize interpretability by utilizing self-explainable model. Sparse Linear Regression are generally considered to be interpretable. On top of that, inspired by the growing body of works
concepts [Koh et al. 2020a Yuksekgonul et al. 2023 Fel et al. 2023 Zarlenga et al. 2023) propose to learn & concepts C:A. - IR in an unsupervised manner where every concept is a sparse lincar combination of the input features. Consistently with previous works, we also posit that these concepts should be both diverse (Alvarez Melis & Jaakkola, 2018 Fel et al. 2023 Zarlenga et al. 2023) to be meaningful and the least rodundant possible. Hence, the model g is interpretable due to the structure of Tw, that a neural network without activation functions. The final architecture Tw, consists of an initial (lincar) bottleneck that maps the input features X into k concepts, followed by an output layer that linearly combines these concepts to produce
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the multiplicative ratio needed for the update. By using linear combinations for both the features-to- conceets mapping and the pnncepts-to-output mapping, we can directly examine the learned weights to understand the direction (positive or negative) in which each concept and, by extension, each feature contributes to the value of the ratio. This level of interprotability was not achievable in previous models like TabCBM (Zarlenga) et al. 2023 To ensure that the learned concepts are meaningful, we introduce penalization terms for diversity and sparsity, similar to those considered in the existing interpretability literature (Zarlenga ett al.) 2023; Yuksekgonul et al.) 2023] Khurana & Galhotra 2021). Given our linear architecture, these terms defined follows: for sparsity, we
Lasso penalization term, and for diversity, define the penalization as diiversity = Eissk p(Wi, W where denotes the cosine distance and W W are the network's weights from input features to concepts i and j respectively. The combined penalization term is then given by Leoncepts = Ldiversity Leparsity.
Beyond ensuring interpretability, using a linear transformation rather than a more complex architecture stems from our observations that it often lead to comparable results along our metries of interest (see D.3 in the Appendix) an observation also made by (Tifrea al., 2023
5.3 Final model
To enforce fairness, we propose to leverage the technique proposed by Zhang et al. (2018), which relies on dynamic reconstruction of the sensitive attribute from the predictions using an adversarial model Awn y - 8 to estimate and mitigate bias. The higher the loss Ls (hwr, (X), (ogtt ()) of this adversary is, the more fair the predictions Iw, (X) are. Furthermore, this allows us to mitigate bias in fairness bline setting (i.e. without access to the sensitive attribute at test time), thus overcoming the limitation of most post-processing fairness methods (ef Table 2h
We then use our rescaling network Twy: implemented as a purely linear mapping without activation functions (cf. Section 5.2) on the other hand, both the adversary hws, and the predicting network Iwr are standard fully connected networks with non-linear activations. Thus, the relaxed version of Equation for DP can be written as:
min E[CY(gw, (X),
[1]
We
s.t ElSs (Fw, (X) (oggt (X), 2 é'
[2]
(4)
and C[ (Tas (X)) S n/
[3]
with e', 7/> 0. In practice, we relax Problem integrating the interpretability constraints on the concepts:
arg min max Wy
Ly (Sw, (2:)) y1)
Wh
N
Aeair Ls (twn (Fws (2oi (x,)), 8;)
(5)
+ Aratio (ratso (I:))
+ Sconcepss (Fer, (x:)),
with Atairy Aratio and Aconcepts three hyperparameters and with Cy and Ls binary cross-entropy losses. Similarly to 4Zhang et al.) 2018)) this loss function can easily be adapted to address EO by modifying the adversary hww, to take as both the true labels Y and the predictions Iw, (X).
6 Experiments
After describing our experimental sotting, we propose this scction empirically evaluate the two dimen- sions of the controlled model update: the ability achieve accuracy and fairness with minimal (Section 6.2 and interpretable (Section 6.3) prediction changes.
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Method
Q1 Fairness
Q2 Fairness
Q3 Fairness
Q4 Fairness
Q3 Acc
Q4 Acc
Q2 Acc
Q3 Acc
Q2 Acc
Q1 Acc
Q2 Acc
Oracle (ROC)
0.18
0.08
0.26
0.33
Law School
Oracle (LPP)
0.08
0.12
LPP
0.11
0.07
0.15
0.19
0.23
0.21
Zhang
0.17
0.12
0.23
0.18
0.28
0.34
0.28
FRAPPE
0.03
0.16
0.18
0.24
0.21
COMMOD
0.07
0.01
0.10
0.08
0.13
0.24
0.18
Oracle (ROC)
0.02
0.03
0.05
0.06
0.09
Compas
Oracle (LPP)
0.02
0.01
0.03
0.03
0.06
LPP
0.08
0.04
0.14
0.12
Zhang
0.09
0.07
0.16
0.12
0.14
0.20
0.16
FRAPPE
0.18
0.24
0.21
0.28
COMMOD
0.05
0.01
0.09
0.09
0.05
0.20
0.06
Table 1: Avg. percentage of prediction class changes for various quartiles of accuracy and fairness the Law School and Compas dataset (DP). The missing values indicate that no model trained with the corresponding method ended up in this quartile definition.
6.1
Experimental protocol
6.1.1 Datasets
We experimentally validate two binary classification datasets, commonly used in the fairness literature (Hort et al. 2024): Law School (Wighlman 1998) and Compas (Angwin et al. 2016). The sensitive attribute for both datasets is race.
6.1.2 Competitors and baselines
To assess the efficacy of COMMOD, we first use an in-processing debiasing method, AdyDebias (Zhang et al.
2018). described in Section 2.1 We use the implementation provided in the ATF360 library (Bellamy itt al. 2018). Additionally, as discussed Section 6.2 post-processing debiasing methods also use pretrained classifier input. Yet, most methods are not directly comparable as they are not model- agnostic require the sensitive attribute test time. Two exceptions LPP (Xian & Zhao 2024| and FRAPPE (Tifrca et al. 2023). which
competitors. Furthermore, although not directly comparable, algorithms proposed by Xian & Zhao (2024) (thal we name Oracle (LPP)) and ROC (Kamiran et al. 2012) (Oracle (ROC)) as baselines. As they directly use the sensitive attribute to make predictions, these two algorithms are expected to outporform all the others.
we include the lairness-
6.1.3 Set-up
A After splitting each dataset in Derain (70%) and Dusst (30%), train pretrained classifier f to optimize solely accuracy, In these experiments, use Logistic Regression classifier from the scikit-learn library, but any other classifier could be used since COMMOD and the proposed competitors are model-agnostic. We then train COMMOD, the competitors and the baselines on Drrain, varying hyperparameter values for each method to achieve a range of fairness and accuracy scores over Dreat- For COMMOD, we set a fixed value for the number concepts A: for Law School and for Compas. Further details on implementation are available in Section of the Appendix.
6.2 Experiment 1: achieving fairness through minimal changes
this first experiment, we aim to assess the ability of COMMOD to achieve competitive results terms of fairness and accuracy while performing a lower number of changes. For this purpose, we measure the proportion P of prediction changes between the black-box model and the fairer model on the test set Drest- Although COMMOD optimizes continuous similarity metric over probabilities, for comparability with the

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Published in Transactions on Machine Learning Research (06/2025)
LAW SCHOOL
COMPAS
Q1 Faimesss
Q2 Fairness
Q1 Fairness
Q2 Faimess
COMMOD
0.30
UPP Gracie (ROC)
Changes
Changer
Dracle (LPD)
0.20
COMMOD LPP
0.20
FRAPPE
Oracle (LPP)
0.10
Zhang
0.00
Q3 Faimess
Q4 Fairness
Q3 Fairness
Q4 Faimess
0.40
0.30
0.30
Changes
0.20
0.20
0.10
0.10
0.00
0.00
0.60
0.65
0.80 0.60
0.70 Accuracy
0.75
0.80
0.60
0.62 Accuracy
0.64
0.66
0.62 Accuracy
0.64
Accuracy
LAW SCHOOL
COMPAS
Q1 Fairness
Q2 Fairness
Q1 Fairness
Q2 Faimess
0.25
% Changes
0.20
Changes
0.20
0.15
COMMOD
0.15
0.10
(RDC)
0.05
Zhang
[LPP]
%
0.05
FRAPPE
0.00
0.00
Q3 Fairness
Q4 Fairness
Q3 Fairness
Q4 Faimess
0.25
0.25
% Changes
0.20
Changes
0.20
0.15
DOKIMOD
LPP
0.10
0.10
Dracie (ROC)
Dracle (LPP)
0.05
Zhang
0.00
0.00
FRAPPE
0.65
0,70
0.75
0.80
0.65
0.70
0.75
0.60
0.62
0:64
0.66 0.60
0.62 Accuracy
0.64
0.66
Accuracy
Accuracy
Accuracy
Figure 1: Number of prediction class changes (y-axis) for comparable levels of fairness (P-Rule or DM quartiles Q1-Q4) and accuracy (x-axis) for DP (top) and EO (bottom) on Law School and Compas.
baselines in this section, we report performance using accuracy, that a discrede metric. Indeed, several competing methods intervene by directly flipping labels, so continuous measures (e.g., calibration error) would not place all approaches scores remain well-behaved, we also analyze their calibration (cf. Figure in the Appendix). As P is directly linked to the fairness and accuracy levels of the models, we intend to evaluate P for models with comparable levels of fairness and accuracy. To do so, we discretize the fairness scores into four segments, defined as quartiles the scores of Debiaas Q1 corresponds to the most biased models, and Q4 to the most fair ones. The full details of these segments are available in Appendix C.3 along with a robustness analysis (cf. Appendix D.1p in which, to ensure that our results do not depend on the specific segment definition chosen, we reproduce the same experiment with other segment definitions. For each segment, we then display the Pareto graph between P (y-axis, lower is better) and Accuracy (x-axis, higher is better) in Figure I in this reprosentation, the most efficient method will be the closest one to the bottom left corner. An aggregated view of these results can be found in Table II
the same footing. Nevertheless, to verify that COMMOD's probability D
We observe that for similar levels of accuracy and fairness, COMMOD consistently achieves lower values of number of changes than its competitors. For less fair models (segment Q1), the difference more subtle: as models put less emphasis on fairness than on accuracy, they tend to adopt a similar behavior, i.c. the one of the biased model f. In other segments however, the value of COMMOD more notable.
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6.3
Experiment 2: interpretability of the model updates
In this second experiment, we aim to evaluate the quality of the explanations generated with COMMOD.
6.3.1
Illustrative results
Concept
Concept
0.0005
P( + 8))
0.04
-0,0005
Xco
1.0
0.02
0.0010
Xco
0.0
0.00
Xa
0.0
-000015
Xc.
0.08
cat, Gr eater 45
c_charge_ esc Poss
c_charge _ esc Poss yrralidino valerophen
__chage_dd d esc Delive Of Drug Paraphern
yrrolidina valerophen
Figure 2: Example of explanation for Compas, Left: feature contributions to the concepts. Right: P(Ý * 81) for the segments described by these features.
Starting with example of explanation concepts, obtain final test P-Rule score of 0.78 (up from 0.60 with f' and accuracy of 0.62 (down from 0.66) with p = 0.08. The first two plots of Figure highlight the diversity between these concepts, as they target different features. For instance, the concept Co, contributing positively (w = 0.41) to class changes, is primarily activated by older individuals; on the other hand, C1, contributing negatively (w' -0.23), targets specific crime category. In the third graph, we calculate the probability values PPY * PT) in the corresponding the instances activated by the corresponding features. Although preliminary, these observations show the potential of COMMOD to explain the debiasing process.
the Compas Datasct. After training COMMOD with k: 2
6.3.2 Quantitative results
Sparsity and diversity. We now aim to generalize the previous observation by verifying that the concepts Iearned are diverse and sparse over the features of X. To assess sparsity, we evaluate the total concept sparsity computed by summing across concepts the sparsity of each matrix after applying a threshold of 6 = 0.01: Eisk ||* ello- For diversity, we measure the Jaccard Index between the signed non-null coefficients: diverse concepts may still use the same feature of X if said feature contribution is in the opposite direction. As baseline, compare COMMOD (with k = 2) with FRAPPE (Tifrea et al. 2023). when the latter is trained using a linear network with the same architecture the one used for our ratio Tw, for their additive term. Figure 3 highlights that for all levels of number of changes, the concepts learned using COMMOD are indeed more sparse and diverse as expected.
Locality. Finally, we aim to show that the instances targeted by COMMOD are generally located in regions that are easier to interpret. Concretely, the objective of this evaluation is to assess whether COMMOD enforces fairness by targetting bigger regions of the feature space rather than performing scattered individual changes, which would be more challenging understand for user. In classification, there exists theoretical understanding how class of models is interpretable based on how it can be translated into decision tree (Bressan et al. 2024). Driven by this work, we propose new evaluation protocol relying measuring the accuracy of a decision tree of constrained depth trained to predict whether an instance has its prediction changed or not (i.e. on labels l The idea behind this evaluation protocol is that a decision (ree with a constrained depth will more accurately model prediction changes if these changes can be described with a lower number of features, and if these instances are more concentrated in the feature space. We report Figure the F1 scores of the decision trees trained predict the class changes of COMMOD, FRAPPE and AduDebias. We observe that for all values of maximum tree depth considered, thanks to the regularization
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LAW SCHOOL
LAW SCHOOL
Concept Redundancy
Total Concept Sparsity
0.5
FRAPPE (Tifrea et al. 2023)
FRAPPE (Tifrea et al. 2023)
COMMOD (Ours)
COMMOD (Ours)
0.4
0.3
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
% changes
%
changes
Figure 3: Comparison of concept redundancy (left, lower is better) and sparsity (right, higher is better) for the Law School datasct between FRAPPE and COMMOD.
LAW SCHOOL
COMPAS
0.8
0.9
0.7
0.8
0.6
Score
Score
0.7
0.4
0.6
0.3
0.2
AdvDeblas (Zhang et al., 2016)
AdvDeblas (Zhang et al., 2018)
(Tifrea 2023)
0.1
(Tifrea al., 2023)
COMMOD (Ours)
COMMOD (Ours)
10
Max Depth
Max Depth
Figure 4: Avg. Score with standard deviations computed over runs for each model (with similar levels of both fairness and accuracy) of a decision tree trained on labels 1 y depending on the tree depth.
with Leoncept, the predictions changed by COMMOD indeed much easier to interpret with decision tree.
6.4 Sensitivity analysis
Most of the results presented earlier were conducted using one random seed, as concurrently observing the three metrics of interest (accuracy, p-rule and number of changes) across different seeds is difficult to visualize. Indeed, changing the seed of the experiments results in different train-test data splits, and in a different biased model f the end. Ultimately, this impacts the results of COMMOD, as the accuracy reached by the biased model defines an upper bound for all the other models (disregarding the models complexity). We therefore aim to confirm that the performance of COMMOD are majoritarely driven by the performance of the biased model and the values chosen for COMMOD's hyperparameters.
To do so, we replicate with 20 different seeds the experimental protocol described in the paper: splitting the data, training a biased model, and training COMMOD with various parameters (we set Afasr to values varying between 0.5 and 1.5, and Ayatio values varying between 0.01 and 0.1). We then model the rela- tionship between the performance of COMMOD and the performance of the biased model and COMMOD's hyperparameters using three linear regression models:
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dist(f.g) ~ Bu + fifairy + Szacey + AsAratio + 312 Accg ~ Bu + 31 f + $zace, + AaAratio + 34 fair, ~ Bo + f + $zace, + ArArio + 34Afaör
(6)
With dist, fair and Acc being defined in Section For the three regressions, the resulting coelficients of determination R2 are 0.96, 0.99 and 0.97. This shows that the performance of COMMOD along the three considered dimensions almost exclusively depends on the performance of the initial model f, as well as on COMMOD's hyperparameters. The impact of other sources of possible stochasticity, e.g. due to the initialization of the neural network, remains therefore limited, thus confirming the stability of our method.
7 Conclusion
In this work, we introduced COMMOD, a novel model update technique that manages to enforce fairness and accuracy while making less, and more interpretable, changes to the original biased classifier. Additionally, we also provided theoretical results for this new optimization problem. Future works include researching the Controlled Model Debiasing task in non-linear settings, and further exploring the tradeoffs between the different hyperparamcters to propose automated selection strategies.
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A Overview of post-processin approaches
In order to better have an overview of existing post-processing approaches, we decided to summarize (part of) them into the following table.
No Sensitive at test time
Model agnostic
Metric optimized
Minimizes changes
Paper
MNB Calders & Verwer 2010
(NB)
X
DP
X
Leaf Relabeling Kamiran el al,
2010
(C4.5)
DP
X
ROC (Kamiran et al. 2012
x
DP
X
EO post-processing (Hardt et al.
2016
x
EO
X
Information Withholding Pleiss el al.
2017
x
EO
X
TGD post-processing
(Lohia et al.
2019)
X
DP
X
MultiaccuracyBoost
(Kim et al. 2019
x
other
X
CFBC Chzhen et al. 2019
EO
Wass-1 post-processing (Jiang al.
2020
DP
Wass-
Penalized LogReg (Jangg et al.
2020
(LogReg)
DP
FST Wei et al.
2020
DP, EO
RNF Du al.
2021
x (NN)
DP, EO
FCGP Nguyen et al.
2021
DP
FairP Poirrtojnttion Alghamndi et al. 2022
DP, EO
FRAPPÉ. Tifrea et al.
2023
DP, EO
LPP (sensitiveuuawwrr)
Xian & Zhao 2024
DP, EO
LPP (sensitivo-aware)
[ian & Zhao 2024
DP, EO
COMMOD (Ours)
DP, EO
Table 2: Comparison between post-processing methods. NB stands for Naive Bayes, and NN for Neural Networks.
From the table above, we can observe that our method is one the few that simultaneously model- agnostic, does require the sensitive variable during inference, and explicitly minimizes the difference between the black-box scores and the edited ones.
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B Proofs of results in Section 4
In this section, present the proofs for the propositions and lemmas stated in the paper. Additionally, we offer some context for certain lemmas from Menon & Williamson (2018), which remain necessary within our new framework of Equation
B.1 Tayes-Optings Classifier (Result 1)
Building on the results proposed in the paper, we first analyze the Bayes- Optreal Classifier of Equation IT
To facilitate this analysis, draw upon the work of Menon & Williamson (2018), who demonstrated that by translating the components of the optimization problem into cost-sensitive framework, the problem becomes analytically equivalent but more tractable to solve.
B.1.1 A cost-sensitive view of fairness Menon & Williamson (2018).
For any randomized classifier g: X' [0, 1| + [0, 1] that post-process the prediction a classifier f: X + [0, 1]
we can write FN P(Y 0 S 1) and FPR(g: D) P(Y 1 0), where we recall that
y= 1=
If we want to study for example Demographic Parity, can refers and compute the following quantity to mcasure fairness:
f (g) FFRK: (1 R(g()))))
(7)
Then, we can translates this quantity into & cost-sensitive risks.
Lemma B.1 (Lemma in Menon & Williamson (2018). Pick any random classifier g. Then, for ony (0, 20), ik= -
DI 2 T (g k) k,
where CSpat (g: D, c) c)- FNR(F: - FFFg)(( Further, we con also rewrite the desired "symmetrised" fairness constraint as
min(Rfair (g), Reaer (1 (0g)) g)) 2 T + (s, [K, 1-.1-h k],
for a suitable choice of e.
B.1.2 A cost-sensitive view of minimal changes (Ours).
In the paper, we propose then to find an equivalence the extra (compared to the usual optimization problem in fairness) constraint we have in our new optimization problem. To achieve this, we present. Lemma 4.1 whose proof is provided below.
Lemma
of Section 4.1 By law of total probability we have:
P + Y) P + 1) 1) P # + 0)
Since we are in a binary classification sctting, i.c. 8 E {0,,1) we can define
c P 1 1- c- P 0).
Hence,
p( +8 p( +8 811==) +8 + FN (1- Sp CSmilg D' ,'''"'
.c') <p.
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B.1.3 Bayes- Optimal- Classifier.
Finally, we can rewrite in Lagrangian version the cost-sensitive problem and solve it analytically.
Lemma B.2. Pick any distributions D, D,D,D" fairness measure DI and constraint number of changes. Pick any c, T.P E (0,1). 1). Then, fajrr Aratio E CR,,, E (0,1) with
min CS(g;D,c)
s.1. min(Rfairlus (g): R (1 g)) 2
(8)
p( * S Sp
is equivalent
min g
C YaiirCiSaal DJ Aratio (g; D ,c),)
Proof (Lemma B.2 By Lomma B.1 and Lemma 4.1 we have that
min( fair (g), R (1 - g)) 2 e CSaal (g; D2 E 1k R),
p(L + 9) S + CSaa (f:D" ,0) p. Consoquently, for Å1 22, As 2 0, the corresponding Lagrangian version will be min CS c) + A1 (CSbal D, - k)) (C (g; D,ē) k) Aa D ,0²) p).
Letting ffarr a1 x2 and Aratio as shows the results.
Lemma B.3. Pick any randomised classifier g. Then, for anyy cost porameter E (0,
CS(g: c) = -1-11)) + Exl(c - (XX))((X))))
where nxx) P(Y 1|X x) and क P(Y 1)
Proof (Lemma B33 For the case of accuracy and fairness constraints the proof is in Lemma of Menon & Williamson (0018) For what concerns the constraint similarity between the black-box predictions Y7 and the one coming from the post-processed classifier g(X), FPR and FNR refers to Y and no more to S. Hence, in the same spirit of the above mentioned proofs,
CS(g: D' c*) (1 cm)m"" " Exii o(X)) cc
= - =1'-c")T xxx''=-'l'' Exl(c* -1"(("))
where - P(SS 1|X = x) and प* = P(L
After introduced all these lemma and definitions, we are now able to provide the proof of Lemma 4.2 stated in the paper and that provides the definition of the Bayes-Optimal Classifier.
Proof (Lemma 4.2 By Lemma
B.3 measures of accuracy, fairness and minimal changes are CS (1 c)m क + Exl(c-
CSfair (1 - c) Ex xx (X)(g-()(
OSratio = -1 c²)= + Ex[(c* 17" (X)))
Then, ignoring constants not dependent. from g, the overall objective becomes
min Ros(g: D min CS(g; D) ASair (g; D, CSati D" c²) min Ex((n(x) - c Aratio((((2) 2) "Aaair (x) (()](()))
min -in (X)9(X))
Thus, at optimality, when s" s²(x) # Sopt = (x)) > OI. When 5"(x: 0, any choice of Jopt admissible.
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B.2 Fairness Level Under Maximum Change Constraint (Result 2)
Proof of Proposition Without loss of generality, let suppose that P-Rule(S) = C. 211 Pio
Then, by doing
changes with Ka: we get a new value of P-Rulé' that given by
+ P-Rule (g) C' Tio(f) (K aa)
Further, if we compute the derivative with respect to alpha of P-Rulé get
P-Rule (g) = c2 - - 71((f)
(9)
da
(71((f) (K a))²
and we observe that P- (g) (g) is either everywhere decreasing or increasing. Hence,
{
- P-Rulee (g) if no(f) -11(f)
max P-Rule" 05a5K
( P-Rulee (g) otherwise
Finally, the same reasoning applies to the case where the starting value of the P- P-Rule (f) is 7))
C "ial)
Proof of Proposilion Writing out the sum,
DM(x) ATPR ATPR 7z APPR 8(K - x)) (ATPR + AFPR 5K) + (6 - (6)--)a
Thus (M( is an affine (linear) function of with slope 5 7
If - y > 0, the slope positive, so DMaum()) is increasing in x and its minimum on [0, K] occurs at x (all flips to FPR-adjustmmnt).
If 5 7 O, the slope negative, so DMaum (z) ) docrcasing in and its minimum occurs x (all flips IPR-adjustment)
If 7, the function constant and any allocation [0, K] yields the same DM.
In all cases, "extreme" Iilocation-putinng all K flips into the single most effective action- minimizes the sum-based Disparate Mistreatment.
C Implementation details
C.1 COMMOD Algorithm
In this section we give more detailed walk-through of our end-to-end training procedure for COMMOD, well a compact pseudocode listing.
Discussion. At each training step, for minibatch of examples (xi, Vi. 8:) we first convert the biased model's output probability f(z;) into logits
flgit (Ix)) = (xx)((((11
We then concatenate (or otherwise condition on) both x; and fiogie as input to small rescaling network Tag: which produces a scalar multiplier r(z;). The corrected score
g(x;) r(x;) (xo
is fed both the final classification loss Ly (against yc) and to adversary h that predicts the sensitive attribute si, giving Lg. In addition regularize to stay close to 1 via.
(r(xs) ( 1|
and add a concept- penalty Lconcepts. All four terms are weighted and summed, and we backpropagate through and h jointly.
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Algorithm COMMOD Training (simplified pseudocode)
Require:
Pretrained biased model f, rescaler adversary h, data ((Ti, Mi. 84 9:)}. {úi f(x;) are proba- bilities, Vi E {0, 1} are true labels}.
1: for each epoch do
for each minibatch (ar y, s, 9) do Slogit (11 Ø))
r()(z)
or flogit)
6:
(optional) Warm-up adversary: update h on (g,
7:
Compute losses:
Cy, Ls, Cration (optional concept losses)
Combine into total loss & (with weights and epoch gates)
Update parameters of r (and any concept modules) by backpropagating V. 10: end for
11: end for
C.2 Loss and Hyperparameters
As with any deep learning-basee method, fine-tuning hyperparameters has been crucial for our COMMOD algorithm. Specifically, we adjusted the weights of the terms in the loss function using the hyperparameters Accuracy, presented
Afiir Aratios and Aconcepts- To explore the entire Pareto frontier of Fairness in this paper, we performed a grid search over these hyperparameters. For implementation purposes, we occasionally found it easier to decompose the concept loss feoncepts into the sum of sparsity loss and diversity loss, cach controlled by separate hyperparameters. The range of values we tested remained consistent across different dalasets, with Afair & 10, Aratio S 0.5, and Acnncopts S
C.3 Quartiles definition
In the paper, we referred several times the quartiles of fairness and accuracy. We used them in order compare the methods in the region of the Pareto for which they have approximately the same levels of fairness and accuracy. These quartiles have been computed the AdvDebias method and their values are shown in the tables below.
C.4 Law School Dataset
C.4.1 Demographic Parity.
We recall that in order measure Demographic Parity we used the P-Rule (the higher, the better). The value of the point (fairness, accuracy) of the black-boo box model (Logistic Regression) is (0.2764, 0.7970).
Quartile
Fairness range
Accuracy range
Q1
[0, 0.5587)
[0, 0.6709) (0.6709, 0.7294) (0. (0.7294, 0. 0.7500) [0.7550, 1]
Q2
[0.5587, 0.7212)
Q3
[0.7212, 0.8719)
Q4
[0.8719, 1]
Table 3: Fairness (Demographic Parity) and Accuracy Quartiles Law School dataset.
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C.4.2 Equalizing Odds.
We recall that in order to measure Equalizing Odds we used the Disporate Mistreabment (the lower, the better). The value of the point (fairness, accuracy) of the black-box model (Logistic Regression) is (0.4935, 0.7970).
Quartile
Fairness range
Accuracy range
Q1
(0.3429, 1]
[0, 0.7230) (0. (0.7230, 0. 0.7458)
Q2
(0.2415, 0.3429
Q3
(0.1503, 0.2415
[0. 00.458, 0.7577)
Q4
[0, 0.1503]
[0.7577,
Table 4: Fairness (Equalizing Odds) and Accuracy Quartiles on Law School dataset.
C.5 COMPAS Dataset
C.5.1
Demographic Parity
We recall that in order to measure Demographic Parity used the P-Rule (the higher, the better). The value of the point (fairness, accuracy) of the black-box model (Logistic Regression) is (0.6310, 0.6580).
Quartile
Fairness range
Accuracy range
Q1
[0 0.7345)
[0, 0.6242)
Q2
[0. 0343,,, 0.7695)
0..224, 0.6391)
Q3
(0.7695, 0.8058)
(0.6391, 0.6537)
Q4
[0.8058,
[0.6537, 1]
Table Fairness (Demographic Parity) and Accuracy Quartiles on COMPAS dataset.
C.5.2 Equalizing Odds.
We recall that in order to measure Equalizing Odds we used the Disparate Mistreatment (the lower, the better). The value of the point (fairness, accuracy) of the black-box model (Logistic Regression) is (0.2828, 0.6580).
Quartile
Fairness range
Accuracy range
Q1
(0.2198, 1]
[0, 0.6242) [0.6242, 0. 0.6391)
Q2
(0.2079, 0.2198
Q3
(0.1869, 0.2079)
(0. (0.6391, 0.6537)
Q4
[0, 0.1869]
[0.6537,
Table 6: Fairness (Equalizing Odds) and Accuracy Quartiles on COMPAS dataset.
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D Additional Experiments and Further Results
D.1 Experiment 1: robustness over segment definition
To ensure that the results of Experiment are robust to the choice of the segment definitions for accuracy and fairness, we propose this section reproduce the experiment with other segment definitions. To define these segments, we thus propose, take the quartile values of the results achieved by LPP (Definition 2) and ROC (Definition 3), instead of AdvDebias.
D.1.1 Definition 2.
The quartiles values obtained through the result of LPP the following
Quartile
Fairness range
Accuracy range
Q1
[0, 0.4709]
[0, 0.7459) (0.7459, 0.7541) [0.7541, 0.7723) [0.7723, 1]
Q2
(0.4709, 0.5918
Q3
(0.5918, 0.7763]
Q4
[0.7763, 1.0]
Table 7: Fairness (DP) and Accuracy Quartiles (Definition 2) on Law School dataset.
Using this values, then plot. the analogue of Fig.
LAW SCHOOL
Q1 Fairness
Q2 Fairness
0.40
o Changes
0.30
COMMOD (Ours)
0.20
LPP
Oracle (ROC)
0.10
Oracle (LPP)
Zhang
FRAPPE
Q3 Fairness
Q4 Fairness
0.40
% Changes
0.30
0.20
0.00-
Accuracy
Accuracy
Figure 5: Experiment 1 results, with Definition 2 for Accuracy and Fairness segments
D.1.2 Definition 3.
The quartiles values obtained through the results of ROC are the following Using this values, we can then plot the analogue of Fig.
D.2 Accuracy and Fairness Performance
As traditionally done for bias mitigation methods, we evaluate the efficacy of COMMOD to preserve accuracy when enforcing fairness through the so-called Pareto plot. Figure 7 shows the accuracy and fairness scores
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Quartile
Fairness range
Accuracy range
Q1
[0, 0.3247]
[0, 0.7033)
Q2
(0.3247, 0.4127|
[0. (0.7,33, 0.755
Q3
(0.4127, 0.5695]
[0. (0.7559, 0. 0.7793)
Q4
[0.5695,
[0.7793, 1]
Table 8: Fairness (DP) and Accuracy Quartiles (Definition 3) on Law School dataset.
LAW SCHOOL
Q1 Fairness
Q2 Fairness
0.40-
% Changes
0.30
COMMOD (Ours)
0.20
LPP
Oracle (ROC)
0.10
Oracle (LPP)
Zhang
FRAPPE
0.00
Q3 Fairness
Q4 Fairness
0.40-
% Changes
0.30
200
0.20-
0.00
0.60
0.65
0.70
0.75
0.50
0.65
0.70 Accuracy
0.75
0.50
Accuracy
Figure 6: Experiment 1 results, with Definition 3 for Accuracy and Fairness segments
achieved by all methods on Law School and Compas datasets (each dot represents one run). In terms of direct competitors, we observe that COMMOD outperforms LPP (resp. FRAPPE) on the Law School dataset (resp. Compas) and achieves similar results in the Compas dataset (resp. Law School). Further, we show here that even by adding the Minimal Changes and Interpretability constraints in Equation 4 COMMOD achieves almost similar results on all datasets as the in-processing method AdeDebias. Finally, as expected, Oracle (and also by ROC in Compas) generally outperform all methods. Hence, COMMOD remains competitive algorithm in terms of fairness and accuracy, regardless of its other benefits, addressed in the next sections.
D.3 Intuition behind linear self-explainable model.
One might question why we chose to introduce explainability into our method through linear architecture that learns concepts as linear combinations of the input features. Typically, using a linear model instead of more complex one can lead to decrease in model performance. However, the rationale behind our choice is clarified through the following experiment, where evaluate different architectures for the network that learns the multiplicative ratio. From the plot above, we observe that the linear architecture performs similarly to more complex models. This obsorvation aligns with the findings in Tifrea et al. (2023). where a similar conclusion was drawn regarding their additive term, which is conceptually similar to our multiplicative ratio. Based on these insights, we decided to design the architecture of the ratio as a one hidden-layer linear network. In this design, the hidden layer acts as a bottleneck that represents the concepts, and the output layer computes the ratio as a linear combination of these concepts.
Additionally, maintaining linearity between the concepts and the output ratio allows to easily determine
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LAW SCHOOL
COMPAS
0.80
0.66
0.78
0.65
0.75
0.64
Accuracy
0.73
Accuracy
0.63
0.70
0.62
0.68
0.61
0.65
Adveetian (Zhang atal. 20181
0.60
Addirbias
COMMOD 10urs
COMMOn (Ours)
0.63
RDC Kayminnn an 2012)
IPP Otinn et 2024)
0.59
soc (Kamimen 2012
IKnn mtall 2024)
Drecia Olan al. 25241
Grade (Kan al, 2024)
0.60
FRAFFE (Tirea 2024)
FRAFFÉ (iffrea 20241
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
P-Rule
P-Rule
LAW SCHOOL
COMPAS
0.80
0.66
0.78
0.65
0.76
Accuracy
0.74
Accuracy
0.64
0.72
0.63
0.70
0.62
0.68
AdsDesiss IZhang at ai, 20181
AdrDabias (2hang et 2018)
COMMOD (Dusi
0.61
COMMoO (Durs)
0.66
RoC Kamman etai. 20121
ROC (Kamirn dt 2013)
LPP Olan eta., 20241
UP 1X et al, 2024)
Dracie Dlan al, 2024)
Orace (Xian es 2024)
0.64
FRAPPE Miheea 2024)
0.60
RAMPE (TPtee erai. 20241
0.5
0.4
0.3
0.2
0.1
0.3
0.2
0.2
0.2
0.1
0.1
Disparate Mistreatment (DM)
Disparate Mistreatment (DM)
Figure 7: Fairness (x-axis) vs Accuracy (y-axis) trade-offs on Law School and Compas datasets for Demo- graphic Parity (top) and Equalized Odds (bottom).
the direction (positive or negative) in which each concept influences the ratio's value. This design choice enhances both the interpretability and transparency of the model.
D.4 Benefits of MSE Loss
In this section, we propose visualization in support to the MSE loss we chose to keep as similar possible the edited scores with the ones outputted by the black-box algorithm. To do so, we used a "calibration" plot on edited scores vs black-box scores for our COMMOD algorithm and for AdvDebias
similar levels of (fairness, accuracy). From such a plot, one can observe that the curve of COMMOD more stick to the dashed line, representing when probabilities are not changed all by the editing. On the other hand, we observe that in AduDebias even if we do not change prediction label, the probabilities are more scattered in the area of the dashed line. This behavior is beneficial for our motivation. When you want to edit model for fairness, you usually want to do changes that flip labels (and hence that modifies the values of your fairness definition) and keep the other instances at the same confidence they were before.
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Law School datasct for Published in Transactions on Machine Learning Research (06/2025)
SCHOOL
0.75
Accuracy
0.70
0.65
0.30
0.40
0.50
0.60
0.70
0.50
0.90
1.00
P-Rule
Figure 8: Fairness vs Accuracy trade-off on Law School for different ratio architectures. Each dot corresponds to one model run.
LAW SCHOOL
LAW SCHOOL
1.0
yex
0.8-
Edited probabiiitiss
Scores AdvDebias
0.4
0.2
Senstive
Senstive
1.0
0.2
1.0
Biased probabilities
Scores Black-Box (Logistic Regression)
Figure Calibration plot (predicted probabilitics black-box probabilities) Demographic Parity.
D.5 Posthoc vs self explainable
As final experiment, we aim to demonstrate the need for approach specifically designed for Controlled Model Debiasing such COMMOD. For this purpose, we build the previous experiment and show that the combination of FRAPPE (which minimizes the number of changes) and a post-hoc interpretability tool leads to less efficient models in terms of debiasing; in other words, that adding interpretability in a post-hoc way comes at higher cost for fairness. We train FRAPPE and COMMOD on the Law School dataset such that their scores in terms accuracy, fairness and number of changes are comparable. We then train decision tree model FRAPPE's additive output, and show Figure I0 the final P-Rule obtained by COMMOD and this built competitor. We observe that, regardless of the tree's depth, controlling the debiasing by introducing interpretability in post-hoc way heavily degrades fairness, contrary to COMMOD.
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0.85
0.80
max depti=None
X
Fairness
0.75
0.70
0.65
0.60
FRAPPE CART
COMMOD
2
6 Depth
Figure 10: Comparison of fairness levels of FRAPPE+CART (trained on the additive term) with the one of a selfexxpainable model for different levels of depth
27


Reviews:
[{"review_id": "UpCCGBT5gX", "reviewer": "Reviewer_kgV6", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength:\n+ The introduction of \"Controlled Model Debiasing\" as a formal objective is novel, addressing the practical need for minimally invasive updates to deployed models.\n+ The paper provides strong theoretical backing, including a fairness-aware Bayes-optimal classifier and an analysis of fairness-improvement bounds under a change constraint.\n+ Unlike many fairness approaches, COMMOD does not require access to sensitive features at inference, enhancing applicability.\n+ The concept-based architecture with sparsity and diversity regularization makes COMMOD’s decision changes explainable.\n\nWeakness:\n- While Controlled Model Debiasing presents a valuable and less-explored idea, its proposed solution, COMMOD, is very similar to existing fairness methods—especially those that adjust model outputs to meet fairness goals. The use of a multiplicative factor to adjust logits can be seen as a nuanced variation of established post-hoc calibration or output perturbation techniques, which makes its originality questionable. Additionally, the paper does not address how COMMOD would handle successive updates over time—an important consideration in practical deployment where fairness constraints or data distributions may evolve. If one were to apply COMMOD iteratively (e.g., to enforce new or evolving fairness standards), the multiplicative update mechanism may compound and unintentionally drift significantly from the original model's calibration, leading to degraded predictive performance or unstable decision boundaries.\n- Although the use of the concept is motivated by the desire to provide interpretable model updates, the interpretability of the learned concepts in COMMOD remains questionable. In the current setup, concepts are formed as sparse linear combinations of input features with constraints on diversity and sparsity. However, there is no guarantee that these learned combinations align with human-understandable semantics or domain-relevant groupings. As a result, even if a concept contributes significantly to a model update, it may be difficult for a practitioner or domain expert to interpret the meaning or implication of the change, especially in high-dimensional or non-tabular domains.\n- The theoretical results presented in Section 4 provide formal grounding for the feasibility of minimal and fair model updates under certain assumptions, including the derivation of a fairness-aware Bayes-optimal classifier. However, these results remain largely detached from the actual algorithmic design of COMMOD. The analysis presumes access to full knowledge of joint distributions (e.g., over features, labels, and sensitive attributes), which is impractical in real-world applications. Moreover, the Bayes-optimal formulation does not inform the specific architectural choices, training dynamics, or constraint integration in COMMOD. Similarly, the theoretical bounds on fairness change (P-rule improvement) offer little actionable guidance on hyperparameter tuning or trade-off navigation. In essence, while the theory helps justify the problem's tractability, it does not substantially aid or guide the design decisions behind the proposed method, nor does it provide predictive or diagnostic tools to practitioners applying COMMOD.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces a novel problem setting called Controlled Model Debiasing, which focuses on modifying a previously trained, potentially biased model into a fairer one by making minimal and interpretable changes. The authors propose a model-agnostic algorithm, COMMOD (COncept-based Minimal MOdel Debiasing), which applies a multiplicative update to a model’s prediction logits. COMMOD combines adversarial learning for fairness enforcement with a concept-based interpretable architecture to provide traceable and sparse explanations for prediction changes. The paper provides theoretical results (e.g., a Bayes-optimal classifier under fairness and change constraints), and empirical evaluations on two standard fairness datasets, comparing COMMOD against existing state-of-the-art methods across multiple fairness metrics and interpretability criteria.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Could the authors comment on the potential of COMMOD in handling successive updates over time?\n\nCould the authors conduct more extensive qualitative analysis, user studies, or grounding in domain knowledge to validate that these concepts offer practically meaningful interpretability?", "broader_impact_concerns": "No", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ig9OYZTezA", "reviewer": "Reviewer_fDJu", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths:**\n\nS1. The paper is mostly well-written and well-presented. It’s also addressing an important problem.\n\nS2. The authors provide theoretical guarantees—both a fairness-aware Bayes-optimal classifier result and analysis of how many label changes are needed to improve demographic parity. \n\nS3. The proposed method, COMMOD, has practical properties such as not needing the sensitive feature at the test time and being model agnostic.  \n\n**Weaknesses:**\n\nW1. The authors do not fully motivate the importance of the two desiderata they introduce in CMD. Why are they important, what trade-offs would they introduce and what problems would they solve? These are occasionally mentioned throughout the paper, but having them in the introduction would help.\n\nW2. Could the author clarify their contribution to the theoretical guarantees for the minimal update problem? It seems to be mostly from (Menon & Williamson, 2018) and the establishment of the equivalence between the two settings seems very straightforward.\n\nW3. I struggle to make sense of the constraint (\\hat{Y^f} \\neq \\hat{Y}) \\leq p. What ‘p’ exactly and why it's taking that range of values? is this a population risk?\n\nW4. Why the theoretical results in section 4.2 are only analyzed for the DP metric. Some discussions or insights on EO would be nice. \n\nW5. The authors can do a better job in introducing some notations and giving them a little intuition, such as D*, c*, K^s_A. \n\nW6. Can the author elaborate on the connection between the penalty term in 5.1 and Eq 1.  Te The L_2 penalty approximates prediction similarity but does not directly control the probability of label flips (p in Eq 1). \n\nW7. My main concern about the experiments is that the results appear based on a single train/test split—no confidence intervals or seed variance are provided. \n\nW8. By assuming the sensitive attribute taking a binary value, both the theoretical guarantees, as well as the experimental results (with the two small datasets) are limiting.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces the concept of Controlled Model Debiasing, which aims to update an already-trained, biased model with minimal and interpretable changes to ensure fairness. The authors propose COMMOD, a model-agnostic algorithm that integrates an adversarial framework to mitigate bias and learns sparse, linear “concepts” that clarify how updates from the old model are made. Theoretical guarantees regarding a fairness-aware Bayes-optimal classifier and the trade-off between fairness and the extent of model changes are provided. Experiments on standard datasets (Law School, Compas) demonstrate that COMMOD achieves performance comparable to state-of-the-art debiasing methods but with fewer prediction changes and clearer global explanations of how and why changes occur.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "please refer to the weaknesses.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "XMZOVXC2By", "reviewer": "Reviewer_7L1a", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Main Strengths:\n\n- The problem of making classifiers more fair is relevant, especial in some particular application;\n\n- The paper since the very beginning states its main two intuitions, namely that a postprocessed classifier should be similar to the initial model (i.e., minimal changes) and the differences should be easy to explain;\n\n- Using the decision tree to explain the differences is smart and intuitively interesting. Great to have in the paper and I would give more visibility to it, instead of including it as final concept.\n\n\n### Main Weaknesses:\n\n- The minimal update in Eq 1 is based on the accuracy metric, which essentially relies on thresholding some scores/probabilities at 0.5 to obtain hard predictions. However, the model is based on logistic regression, which makes probabilities (and are also used in Ea 3). Because it's a threshold-based metric, accuracy does not account for small changes in probabilities, which might be the effect of making a model more fair. Wouldn't a metric that accounts for probabilities (e.g., calibration metrics, ranking-based metrics) more suitable for the task?\n\n- Section 5.3 explains the final construction of the model, i.e. how to setup the optimization problem to learn. I find this section very disconnected from the previous ones, and I am not sure how the previous paragraphs fit into the final model. For example, Eq. 1 and 2? How about the explainability of the difference? This part introduces the loss function, which is not considered in most of the paper.\n\n- Eq. 3 uses logits but how to estimate them is unclear; Similarly, r(X) is modeled as a Neural Network but it's unclear (1) what type of NN, (2) what's the target value, (3) how the network is trained;\n\n- Sec 5.1 mentions the need for a penalization term, which measures the distance between two distributions. The paper proposes a simple L2 norm, which is obviously defined over a dot product. I wonder what's the utility of defining L_ratio with the norm M, if eventually the only norm used is the L2. This feels just like overgeneralizing.\n\n- The experiments look interesting and results seem promising. However, a couple of points for improvement: 1) Most experiments do not show standard deviations or confidence intervals, and the setup section does not report any repetition of experiments, which makes me conclude that only one iteration is used. Therefore, results might only be good because of random noise; 2) Tables can help visualize the superiority of the proposed approach, as they summarize properly the comparison; 3) Figure 4 plots the F1 score, while initially only the accuracy is measured. Why such a change in performance metric? What's the advantage of measuring F1 or Accuracy, especially when using models that produce scores/probabilities?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper tackles the challenge of postprocessing a model with the goal of increasing its fairness. The approach is formally a supervised learning task which relies on two insights: The differences between new fair model and existing one should be (1) interpretable and (2) minimal. The paper introduces a novel algorithm, COMMOD, which is model-agnostic, does not require sensitive attribute at test time, and makes minimal and interpretable changes between biased and debiased predictions. Experimentally, COMMOD achieves comparable performance to state-of-the-art debiasing methods.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "No", "audience_explanation": "", "requested_changes": "See weaknesses.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)