François Hu

Agathe Fernandes Machado, Arthur Charpentier, Emmanuel Flachaire et al.

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to ensure alignment between predicted probabilities and actual outcomes. However, when score heterogeneity deviates from the underlying data probability distribution, traditional calibration metrics lose reliability, failing to align score distribution with actual probabilities. In this study, we highlight approaches that prioritize optimizing the alignment between predicted scores and true probability distributions over minimizing traditional performance or calibration metrics. When employing tree-based models such as Random Forest and XGBoost, our analysis emphasizes the flexibility these models offer in tuning hyperparameters to minimize the Kullback-Leibler (KL) divergence between predicted and true distributions. Through extensive empirical analysis across 10 UCI datasets and simulations, we demonstrate that optimizing tree-based models based on KL divergence yields superior alignment between predicted scores and actual probabilities without significant performance loss. In real-world scenarios, the reference probability is determined a priori as a Beta distribution estimated through maximum likelihood. Conversely, minimizing traditional calibration metrics may lead to suboptimal results, characterized by notable performance declines and inferior KL values. Our findings reveal limitations in traditional calibration metrics, which could undermine the reliability of predictive models for critical decision-making.

François Hu, Philipp Ratz, Arthur Charpentier

Algorithmic Fairness is an established field in machine learning that aims to reduce biases in data. Recent advances have proposed various methods to ensure fairness in a univariate environment, where the goal is to de-bias a single task. However, extending fairness to a multi-task setting, where more than one objective is optimised using a shared representation, remains underexplored. To bridge this gap, we develop a method that extends the definition of Strong Demographic Parity to multi-task learning using multi-marginal Wasserstein barycenters. Our approach provides a closed form solution for the optimal fair multi-task predictor including both regression and binary classification tasks. We develop a data-driven estimation procedure for the solution and run numerical experiments on both synthetic and real datasets. The empirical results highlight the practical value of our post-processing methodology in promoting fair decision-making.

Arthur Charpentier, François Hu, Philipp Ratz

The insurance industry is heavily reliant on predictions of risks based on characteristics of potential customers. Although the use of said models is common, researchers have long pointed out that such practices perpetuate discrimination based on sensitive features such as gender or race. Given that such discrimination can often be attributed to historical data biases, an elimination or at least mitigation is desirable. With the shift from more traditional models to machine-learning based predictions, calls for greater mitigation have grown anew, as simply excluding sensitive variables in the pricing process can be shown to be ineffective. In this article, we first investigate why predictions are a necessity within the industry and why correcting biases is not as straightforward as simply identifying a sensitive variable. We then propose to ease the biases through the use of Wasserstein barycenters instead of simple scaling. To demonstrate the effects and effectiveness of the approach we employ it on real data and discuss its implications.

Philipp Ratz, François Hu, Arthur Charpentier

Ensuring trust and accountability in Artificial Intelligence systems demands explainability of its outcomes. Despite significant progress in Explainable AI, human biases still taint a substantial portion of its training data, raising concerns about unfairness or discriminatory tendencies. Current approaches in the field of Algorithmic Fairness focus on mitigating such biases in the outcomes of a model, but few attempts have been made to try to explain \emph{why} a model is biased. To bridge this gap between the two fields, we propose a comprehensive approach that uses optimal transport theory to uncover the causes of discrimination in Machine Learning applications, with a particular emphasis on image classification. We leverage Wasserstein barycenters to achieve fair predictions and introduce an extension to pinpoint bias-associated regions. This allows us to derive a cohesive system which uses the enforced fairness to measure each features influence \emph{on} the bias. Taking advantage of this interplay of enforcing and explaining fairness, our method hold significant implications for the development of trustworthy and unbiased AI systems, fostering transparency, accountability, and fairness in critical decision-making scenarios across diverse domains.

François Hu, Philipp Ratz, Arthur Charpentier

In the standard use case of Algorithmic Fairness, the goal is to eliminate the relationship between a sensitive variable and a corresponding score. Throughout recent years, the scientific community has developed a host of definitions and tools to solve this task, which work well in many practical applications. However, the applicability and effectivity of these tools and definitions becomes less straightfoward in the case of multiple sensitive attributes. To tackle this issue, we propose a sequential framework, which allows to progressively achieve fairness across a set of sensitive features. We accomplish this by leveraging multi-marginal Wasserstein barycenters, which extends the standard notion of Strong Demographic Parity to the case with multiple sensitive characteristics. This method also provides a closed-form solution for the optimal, sequentially fair predictor, permitting a clear interpretation of inter-sensitive feature correlations. Our approach seamlessly extends to approximate fairness, enveloping a framework accommodating the trade-off between risk and unfairness. This extension permits a targeted prioritization of fairness improvements for a specific attribute within a set of sensitive attributes, allowing for a case specific adaptation. A data-driven estimation procedure for the derived solution is developed, and comprehensive numerical experiments are conducted on both synthetic and real datasets. Our empirical findings decisively underscore the practical efficacy of our post-processing approach in fostering fair decision-making.

Agathe Fernandes Machado, Suzie Grondin, Philipp Ratz et al.

Algorithmic fairness has received considerable attention due to the failures of various predictive AI systems that have been found to be unfairly biased against subgroups of the population. Many approaches have been proposed to mitigate such biases in predictive systems, however, they often struggle to provide accurate estimates and transparent correction mechanisms in the case where multiple sensitive variables, such as a combination of gender and race, are involved. This paper introduces a new open source Python package, EquiPy, which provides a easy-to-use and model agnostic toolbox for efficiently achieving fairness across multiple sensitive variables. It also offers comprehensive graphic utilities to enable the user to interpret the influence of each sensitive variable within a global context. EquiPy makes use of theoretical results that allow the complexity arising from the use of multiple variables to be broken down into easier-to-solve sub-problems. We demonstrate the ease of use for both mitigation and interpretation on publicly available data derived from the US Census and provide sample code for its use.

François HU, Philipp Ratz, Arthur Charpentier

Algorithmic fairness has gained prominence due to societal and regulatory concerns about biases in Machine Learning models. Common group fairness metrics like Equalized Odds for classification or Demographic Parity for both classification and regression are widely used and a host of computationally advantageous post-processing methods have been developed around them. However, these metrics often limit users from incorporating domain knowledge. Despite meeting traditional fairness criteria, they can obscure issues related to intersectional fairness and even replicate unwanted intra-group biases in the resulting fair solution. To avoid this narrow perspective, we extend the concept of Demographic Parity to incorporate distributional properties in the predictions, allowing expert knowledge to be used in the fair solution. We illustrate the use of this new metric through a practical example of wages, and develop a parametric method that efficiently addresses practical challenges like limited training data and constraints on total spending, offering a robust solution for real-life applications.

Bertille Tierny, Arthur Charpentier, François Hu

Linear models are widely used in high-stakes decision-making due to their simplicity and interpretability. Yet when fairness constraints such as demographic parity are introduced, their effects on model coefficients, and thus on how predictive bias is distributed across features, remain opaque. Existing approaches on linear models often rely on strong and unrealistic assumptions, or overlook the explicit role of the sensitive attribute, limiting their practical utility for fairness assessment. We extend the work of (Chzhen and Schreuder, 2022) and (Fukuchi and Sakuma, 2023) by proposing a post-processing framework that can be applied on top of any linear model to decompose the resulting bias into direct (sensitive-attribute) and indirect (correlated-features) components. Our method analytically characterizes how demographic parity reshapes each model coefficient, including those of both sensitive and non-sensitive features. This enables a transparent, feature-level interpretation of fairness interventions and reveals how bias may persist or shift through correlated variables. Our framework requires no retraining and provides actionable insights for model auditing and mitigation. Experiments on both synthetic and real-world datasets demonstrate that our method captures fairness dynamics missed by prior work, offering a practical and interpretable tool for responsible deployment of linear models.

Agathe Fernandes Machado, François Hu, Philipp Ratz et al.

Driven by an increasing prevalence of trackers, ever more IoT sensors, and the declining cost of computing power, geospatial information has come to play a pivotal role in contemporary predictive models. While enhancing prognostic performance, geospatial data also has the potential to perpetuate many historical socio-economic patterns, raising concerns about a resurgence of biases and exclusionary practices, with their disproportionate impacts on society. Addressing this, our paper emphasizes the crucial need to identify and rectify such biases and calibration errors in predictive models, particularly as algorithms become more intricate and less interpretable. The increasing granularity of geospatial information further introduces ethical concerns, as choosing different geographical scales may exacerbate disparities akin to redlining and exclusionary zoning. To address these issues, we propose a toolkit for identifying and mitigating biases arising from geospatial data. Extending classical fairness definitions, we incorporate an ordinal regression case with spatial attributes, deviating from the binary classification focus. This extension allows us to gauge disparities stemming from data aggregation levels and advocates for a less interfering correction approach. Illustrating our methodology using a Parisian real estate dataset, we showcase practical applications and scrutinize the implications of choosing geographical aggregation levels for fairness and calibration measures.

Agathe Fernandes Machado, Arthur Charpentier, Emmanuel Flachaire et al.

The assessment of binary classifier performance traditionally centers on discriminative ability using metrics, such as accuracy. However, these metrics often disregard the model's inherent uncertainty, especially when dealing with sensitive decision-making domains, such as finance or healthcare. Given that model-predicted scores are commonly seen as event probabilities, calibration is crucial for accurate interpretation. In our study, we analyze the sensitivity of various calibration measures to score distortions and introduce a refined metric, the Local Calibration Score. Comparing recalibration methods, we advocate for local regressions, emphasizing their dual role as effective recalibration tools and facilitators of smoother visualizations. We apply these findings in a real-world scenario using Random Forest classifier and regressor to predict credit default while simultaneously measuring calibration during performance optimization.

Arthur Charpentier, Agathe Fernandes Machado, Olivier Côté et al.

Many fairness goals are defined at a population level that misaligns with siloed data collection, which remains unsharable due to privacy regulations. Horizontal federated learning (FL) enables collaborative modeling across clients with aligned features without sharing raw data. We study federated auditing of demographic parity through score distributions, measuring disparity as a Wasserstein--Frechet variance between sensitive-group score laws, and expressing the population metric in federated form that makes explicit how silo-specific selection drives local-global mismatch. For the squared Wasserstein distance, we prove an ANOVA-style decomposition that separates (i) selection-induced mixture effects from (ii) cross-silo heterogeneity, yielding tight bounds linking local and global metrics. We then propose a one-shot, communication-efficient protocol in which each silo shares only group counts and a quantile summary of its local score distributions, enabling the server to estimate global disparity and its decomposition, with $O(1/k)$ discretization bias ($k$ quantiles) and finite-sample guarantees. Experiments on synthetic data and COMPAS show that a few dozen quantiles suffice to recover global disparity and diagnose its sources.

Romuald Elie, Caroline Hillairet, François Hu et al.

This paper addresses significant obstacles that arise from the widespread use of machine learning models in the insurance industry, with a specific focus on promoting fairness. The initial challenge lies in effectively leveraging unlabeled data in insurance while reducing the labeling effort and emphasizing data relevance through active learning techniques. The paper explores various active learning sampling methodologies and evaluates their impact on both synthetic and real insurance datasets. This analysis highlights the difficulty of achieving fair model inferences, as machine learning models may replicate biases and discrimination found in the underlying data. To tackle these interconnected challenges, the paper introduces an innovative fair active learning method. The proposed approach samples informative and fair instances, achieving a good balance between model predictive performance and fairness, as confirmed by numerical experiments on insurance datasets.