arXiv subjects

Arthur Charpentier

Publications and source records attributed to Arthur Charpentier.

At least 37 records · Page 2Linked to original sources

arXiv2025

When Numbers Mislead Us

The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect implicit, and sometimes ideological, assumptions about what is worth quantifying. Moreover, in any analysis, what remains unmeasured can be just as significant as what is captured. When a key variable is omitted-whether by neglect, design, or ignorance-it can distort the observed relationships between other variables. This phenomenon, known as omitted variable bias, may produce misleading correlations or conceal genuine effects. In some cases, accounting for this hidden factor can completely overturn the conclusions drawn from a superficial analysis. This is precisely the mechanism behind Simpson's paradox.

stat.OT↗

arXiv2025

Disaster Risk Financing through Taxation: A Framework for Regional Participation in Collective Risk-Sharing

We consider an economy composed of different risk profile regions wishing to be hedged against a disaster risk using multi-region catastrophe insurance. Such catastrophic events inherently have a systemic component; we consider situations where the insurer faces a non-zero probability of insolvency. To protect the regions against the risk of the insurer's default, we introduce a public-private partnership between the government and the insurer. When a disaster generates losses exceeding the total capital of the insurer, the central government intervenes by implementing a taxation system to share the residual claims. In this study, we propose a theoretical framework for regional participation in collective risk-sharing through tax revenues by accounting for their disaster risk profiles and their economic status.

econ.TH↗

arXiv2025

Beyond Shapley Values: Cooperative Games for the Interpretation of Machine Learning Models

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic justifications whose relevance to feature attribution remains debatable. In this paper, we revisit cooperative game theory from an interpretability perspective and argue for a broader and more principled use of its tools. We highlight two general families of efficient allocations, the Weber and Harsanyi sets, that extend beyond Shapley values and offer richer interpretative flexibility. We present an accessible overview of these allocation schemes, clarify the distinction between value functions and aggregation rules, and introduce a three-step blueprint for constructing reliable and theoretically-grounded feature attributions. Our goal is to move beyond fixed axioms and provide the XAI community with a coherent framework to design attribution methods that are both meaningful and robust to shifting methodological trends.

stat.ML↗

arXiv2025

Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport

Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to interpret. To address this, alternative methodologies have been proposed, using causal graphs combined with iterative quantile regressions (Plečko and Meinshausen (2020)) or sequential transport (Fernandes Machado et al. (2025)) to examine fairness at the individual level, often referred to as ``counterfactual fairness.'' Despite these advancements, transporting categorical variables remains a significant challenge in practical applications with real datasets. In this paper, we propose a novel approach to address this issue. Our method involves (1) converting categorical variables into compositional data and (2) transporting these compositions within the probabilistic simplex of $\mathbb{R}^d$. We demonstrate the applicability and effectiveness of this approach through an illustration on real-world data, and discuss limitations.

cs.LG↗

arXiv2025

Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking predictive uncertainty. This work addresses that gap by proposing a novel, model-agnostic uncertainty attribution (UA) method grounded in conformal prediction (CP). By defining cooperative games where CP interval properties-such as width and bounds-serve as value functions, we systematically attribute predictive uncertainty to input features. Extending beyond the traditional Shapley values, we use the richer class of Harsanyi allocations, and in particular the proportional Shapley values, which distribute attribution proportionally to feature importance. We propose a Monte Carlo approximation method with robust statistical guarantees to address computational feasibility, significantly improving runtime efficiency. Our comprehensive experiments on synthetic benchmarks and real-world datasets demonstrate the practical utility and interpretative depth of our approach. By combining cooperative game theory and conformal prediction, we offer a rigorous, flexible toolkit for understanding and communicating predictive uncertainty in high-stakes ML applications.

cs.AI↗

arXiv2025

Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness

In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, and optimal transport. We extend "Knothe's rearrangement" and "triangular transport" to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss fairness at the individual level. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.

cs.LG↗

arXiv2025

EquiPy: Sequential Fairness using Optimal Transport in Python

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.

cs.LG↗

arXiv2025

Beyond Human Intervention: Algorithmic Collusion through Multi-Agent Learning Strategies

Collusion in market pricing is a concept associated with human actions to raise market prices through artificially limited supply. Recently, the idea of algorithmic collusion was put forward, where the human action in the pricing process is replaced by automated agents. Although experiments have shown that collusive market equilibria can be reached through such techniques, without the need for human intervention, many of the techniques developed remain susceptible to exploitation by other players, making them difficult to implement in practice. In this article, we explore a situation where an agent has a multi-objective strategy, and not only learns to unilaterally exploit market dynamics originating from other algorithmic agents, but also learns to model the behaviour of other agents directly. Our results show how common critiques about the viability of algorithmic collusion in real-life settings can be overcome through the usage of slightly more complex algorithms.

econ.TH↗

arXiv2024

Data Augmentation with Variational Autoencoder for Imbalanced Dataset

Learning from an imbalanced distribution presents a major challenge in predictive modeling, as it generally leads to a reduction in the performance of standard algorithms. Various approaches exist to address this issue, but many of them concern classification problems, with a limited focus on regression. In this paper, we introduce a novel method aimed at enhancing learning on tabular data in the Imbalanced Regression (IR) framework, which remains a significant problem. We propose to use variational autoencoders (VAE) which are known as a powerful tool for synthetic data generation, offering an interesting approach to modeling and capturing latent representations of complex distributions. However, VAEs can be inefficient when dealing with IR. Therefore, we develop a novel approach for generating data, combining VAE with a smoothed bootstrap, specifically designed to address the challenges of IR. We numerically investigate the scope of this method by comparing it against its competitors on simulations and datasets known for IR.

cs.LG↗

arXiv2024

Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model

We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity is introduced, considering stochasticity at the individual level. By letting the population size going to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model's equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an outbreak with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions, fair vaccine allocation is the optimal strategy to prevent endemicity.

q-bio.PE↗

arXiv2024

Probabilistic Scores of Classifiers, Calibration is not Enough

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.

cs.LG↗

arXiv2024

Measuring and Mitigating Biases in Motor Insurance Pricing

The non-life insurance sector operates within a highly competitive and tightly regulated framework, confronting a pivotal juncture in the formulation of pricing strategies. Insurers are compelled to harness a range of statistical methodologies and available data to construct optimal pricing structures that align with the overarching corporate strategy while accommodating the dynamics of market competition. Given the fundamental societal role played by insurance, premium rates are subject to rigorous scrutiny by regulatory authorities. These rates must conform to principles of transparency, explainability, and ethical considerations. Consequently, the act of pricing transcends mere statistical calculations and carries the weight of strategic and societal factors. These multifaceted concerns may drive insurers to establish equitable premiums, taking into account various variables. For instance, regulations mandate the provision of equitable premiums, considering factors such as policyholder gender or mutualist group dynamics in accordance with respective corporate strategies. Age-based premium fairness is also mandated. In certain insurance domains, variables such as the presence of serious illnesses or disabilities are emerging as new dimensions for evaluating fairness. Regardless of the motivating factor prompting an insurer to adopt fairer pricing strategies for a specific variable, the insurer must possess the capability to define, measure, and ultimately mitigate any ethical biases inherent in its pricing practices while upholding standards of consistency and performance. This study seeks to provide a comprehensive set of tools for these endeavors and assess their effectiveness through practical application in the context of automobile insurance.

stat.ML↗

arXiv2024

Multiarmed Bandits Problem Under the Mean-Variance Setting

The classical multi-armed bandit (MAB) problem involves a learner and a collection of K independent arms, each with its own ex ante unknown independent reward distribution. At each one of a finite number of rounds, the learner selects one arm and receives new information. The learner often faces an exploration-exploitation dilemma: exploiting the current information by playing the arm with the highest estimated reward versus exploring all arms to gather more reward information. The design objective aims to maximize the expected cumulative reward over all rounds. However, such an objective does not account for a risk-reward tradeoff, which is often a fundamental precept in many areas of applications, most notably in finance and economics. In this paper, we build upon Sani et al. (2012) and extend the classical MAB problem to a mean-variance setting. Specifically, we relax the assumptions of independent arms and bounded rewards made in Sani et al. (2012) by considering sub-Gaussian arms. We introduce the Risk Aware Lower Confidence Bound (RALCB) algorithm to solve the problem, and study some of its properties. Finally, we perform a number of numerical simulations to demonstrate that, in both independent and dependent scenarios, our suggested approach performs better than the algorithm suggested by Sani et al. (2012).

math.OC↗

arXiv2024

Boarding for ISS: Imbalanced Self-Supervised: Discovery of a Scaled Autoencoder for Mixed Tabular Datasets

The field of imbalanced self-supervised learning, especially in the context of tabular data, has not been extensively studied. Existing research has predominantly focused on image datasets. This paper aims to fill this gap by examining the specific challenges posed by data imbalance in self-supervised learning in the domain of tabular data, with a primary focus on autoencoders. Autoencoders are widely employed for learning and constructing a new representation of a dataset, particularly for dimensionality reduction. They are also often used for generative model learning, as seen in variational autoencoders. When dealing with mixed tabular data, qualitative variables are often encoded using a one-hot encoder with a standard loss function (MSE or Cross Entropy). In this paper, we analyze the drawbacks of this approach, especially when categorical variables are imbalanced. We propose a novel metric to balance learning: a Multi-Supervised Balanced MSE. This approach reduces the reconstruction error by balancing the influence of variables. Finally, we empirically demonstrate that this new metric, compared to the standard MSE: i) outperforms when the dataset is imbalanced, especially when the learning process is insufficient, and ii) provides similar results in the opposite case.

cs.LG↗

arXiv2024

From Uncertainty to Precision: Enhancing Binary Classifier Performance through Calibration

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.

cs.LG↗

arXiv2024

Geospatial Disparities: A Case Study on Real Estate Prices in Paris

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.

cs.LG↗

arXiv2024

A Sequentially Fair Mechanism for Multiple Sensitive Attributes

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.

stat.ML↗

arXiv2023

Fairness Explainability using Optimal Transport with Applications in Image Classification

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.

cs.CV↗