All posts by Arthur Charpentier

Arthur Charpentier, professor in Montréal, in Actuarial Science. Former professor-assistant at ENSAE Paristech, associate professor at Ecole Polytechnique and assistant professor in Economics at Université de Rennes 1.  Graduated from ENSAE, Master in Mathematical Economics (Paris Dauphine), PhD in Mathematics (KU Leuven), and Fellow of the French Institute of Actuaries.

Agathe at AAAI’25, Philadelphia

Agathe Fernandes Machado is currently in Philadelphia, to present our paper Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness, written with Ewen Gallic

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.

Conference at CIMAT, D2

After our poster session yesterday, and a great tacos diner yesterday, we are back to work at the “Montréal – Guanajuato Workshop on Probability and Machine Learning“. We had José Luis Luis Pérez (CIMAT), for the first plenary talk on ‘Fluctuation theory for spectrally negative Lévy processes killed by an additive functional’, Jean-Francois Renaud (UQAM), second plenary talk on ‘Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy’, Kodjo Raphaël Madou (McGill), @Jesus Contreras (CIMAT), Terry Daniel Easlick (UdeM) and finally Sandra Palau (UNAM) , is the third plenary talk on ‘Rates on Yaglom’s limit for Galton-Watson processes’.

This conference is great, perfect location, very high level, both among the presenters, but also in the audience, with always a strong participation of students present, it’s a pleasure to see! Thanks again to the organizers

Conference at CIMAT, D1

Day 1 at our conference at CIMAT, Guanajauto (Mexico), on “Probability and Machine Learning“. Everyone is here, with Alma Sarai Hernandez Torres (UNAM), first plenary talk on ‘Uniform spanning trees: theory and applications’, Benjamin Côté (Waterloo), Elliot Paquette (McGill), second plenary talk on ‘From magic squares, through random matrices, and to the multiplicative chaos’, Tulio Gaxiola (UAS), Arturo jaramillo Jaramillo (CIMAT), third plenary talk on ‘High-Frequency Statistics for Lévy Processes: A Stein’s Method Perspective’, and Sayle Sigarreta Ricardo (BUAP). Great talks, great day. After flash presentations of posters, and short break before the tacos welcome evening (with posters). A big thank you to the presenters, and to the audience, the room was full all day, with active participation !

Conference at CIMAT, D-1

Pre-conference day at CIMAT, Guanajauto (Mexico), “Probability and Machine Learning“. Finalizing the last details, with the incredible local team, financial services, etc. So far, no last-minute imponderables, fingers crossed. At lunchtime, Hélène Guérin gives a presentation at the probability seminar, and tomorrow morning, the conference begins. Thanks again to our sponsors, SCOR Foundation for Science CIMAT the probability lab of Centre de recherches mathématiques (CRM) and the actuarial science lab, Quantact.

Mathematics Colloquium at CIMAT

Wednesday afternoon, I am invited to give a talk at the Mathematics Colloquium at Centro de Investigación en Matemáticas (CIMAT). I will present an overview of recent work. The long title is Using optimal transport to mitigate unfair predictions and quantify counterfactual fairness (slides are available)

Many industries are 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  the first part of this seminar, we propose to mitigate possible discrimination (related to so call « group fairness », related to discrepancies in score distributions) 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. This part will be based on recent work with François Hu and Philipp Ratz (2310.205082309.066272306.12912 and 2306.10155). In the second part, we will focus on another aspect of discrimination usually called « counterfactual fairness », where the goal is to quantify a potential discrimination « if that person had not been Black » or « if that person had not been a woman ». The standard approach, called « ceteris paribus » (everything remains unchanged) is not sufficient to take into account indirect discrimination, and therefore, we consider a « mutates mutants » approach based on optimal transport. With multiple features, optimal transport becomes more challenging and we suggest a sequential approach based on probabilistic graphical models. This part will be based on recent work with Agathe Fernandes Machado and Ewen Gallic (2408.03425 and 2501.15549).

Continue reading Mathematics Colloquium at CIMAT

Workshop on Probability and Machine Learning, in Guanajuato, Mexico

Next week, we organize the first Montréal – Guanajuato Workshop on Probability and Machine Learning, at CIMAT, Centro de Investigación en Matemáticas.

with Arturo Jaramillo Gil (CIMAT), Saraí Hernández-Torres (UNAM), Emilien Joly (CIMAT), Sandra Palau (UNAM), Courtney Paquette (McGill), Elliot Paquette (McGill), José Luis Pérez (CIMAT), James Melbourne (CIMAT), and Jean-François Renaud (UQAM), among invited speakers.

The Centro de Investigación en Matemáticas (CIMAT), located in Guanajuato, Mexico, is a leading research institution focused on mathematics, statistics, and computer science. Part of Mexico’s National System of Public Research Centers (CONACYT), CIMAT excels in both theoretical and applied research, fostering innovation and solving complex real-world problems. Its vibrant academic environment supports advanced studies, offering master’s and doctoral programs, while promoting interdisciplinary collaboration. Housed in the picturesque city of Guanajuato, a UNESCO World Heritage Site, CIMAT attracts top researchers and students from around the globe, contributing significantly to scientific and technological advancement in Mexico and beyond.

The first goal of the workshop is to bring together researchers, and scholars from Québec and Mexico in the field of probability theory, and Machine learning. With an emphasis on both theoretical foundations and practical applications, the conference will feature research presentations from speakers who represent a range of career stages at the faculty level. This will foster the exchange of ideas and opportunities for new collaborations.

The second goal was to encourage and promote student mobility between Mexico and Québec. The workshop will feature short talks by graduate students and postdoc fellows, who will have opportunity to present their work, but also to exchange with different researchers. This will enable them to enrich their academic network, and may well open up mobility opportunities for them in the future. Yet, Dante Mata Lopez is sharing the office with the team (Agathe, Marouane), and this summer, two interns will join our team: Allison Lara Nieva, from the Universidad Nacional Autónoma de México (Agathe Fernandes Machado will be involved in the supervision) and Fabian Dominguez Lopez, from the Universidad de Guanajuato, working with Hélène Guérin and Arsène Brice Zotsa Ngoufack, who will be involved in the supervision.

Picture credit for the poster: Yuko Nishikawa (Yuko Nishikawa is a Brooklyn-based Japanese multidisciplinary artist and designer, known for her organic, dreamlike works. She grew up in the seaside town of Chigasaki (茅ヶ崎市), south of Tokyo).

Artificial Intelligence and Personalization of Insurance: Failure or Delayed Ignition?

Our joint paper, Artificial Intelligence and Personalization of Insurance: Failure or Delayed Ignition?, with Xavier Vamparys, has been published in Big Data & Society.

In insurance, there is still a significant gap between the anticipated disruption, due to big data and machine learning algorithms, and the actual implementation of behaviour-based personalization, as described by Meyers (2018). Here, we identify eight key factors that serve as fundamental obstacles to the radical transformation of insurance guarantees, aiming to closely align them with the risk profile of each policyholder. These obstacles include the collective nature of insurance, the entrenched beliefs of some insurance companies, challenges related to data collection and use for personalized pricing, limited interest from insurers in adopting new models as well as policyholders’ reluctance towards embracing connected devices. Additionally, the hurdles of explainability, insurer inertia and ethical or societal considerations further complicate the path toward achieving highly individualized insurance pricing.

Assurance, IA, biais et équité

Pour compléter mon exposé auprès de l’Association des Masters d’Actuariat, je vais poster un billet, qui reprend les slides de mon intervention, avec un peu du discours qui va avec. Tout d’abord, mille excuses, mais les slides sont en anglais. Et ce que je raconte est très librement basé sur des travaux récents qu’on a pu mener, avec pas mal de monde, dont Laurence Barry (de la chaire PARI), Marie-Pier Côté (professeure à l’université Laval, à Québec), Olivier Côté (doctorant que je co-supervise avec Marie-Pier), Agathe Fernandes Machado (doctorante à l’UQAM), Ewen Gallic, (maître de conférences, à Marseille), François Hu (ancien stagiaire postdoctoral et aujourd’hui consultant en France), Philipp Ratz (ancien stagiaire postdoctoral et aujourd’hui consultant en Suisse), ainsi qu’Ana Patron Pinerez (ancienne stagiaire qui venait de Colombie) et Mulah Moriah (doctorant en France, que j’ai suivi pendant son mémoire de fin de maîtrise).

Continue reading Assurance, IA, biais et équité

Exposé auprès des étudiants (et anciens étudiants) de l’AMA

Ce midi (heure de Montréal), je donnerais un exposé virtuel sur le thème « IA, biais et équité (en actuariat et en assurance) » (les slides sont disponibles via le lien). C’est un honneur de donner la première conférence de l’AMA, Association des Masters en Actuariat, qui sera diffusée en direct aux différentes promotions des formations de l’AMA, réunies dans leurs universités !

Comme me le disaient Chi et Samuel, “pour les anciens ou extérieurs qui veulent suivre sans être en présentiel, cela sera possible sur Briques2math“, la chaîne YouTube. Je préciserais juste que personne ne sera en présentiel, puisque je serais à Montréal, j’enseigne demain matin…

Ah oui, l’exposé sera en français… mais j’aurais des slides en anglais

KNN and K-means in Gini Prametric Spaces

With Cassandra Mussard, intern last summer, and Stéphane Mussard, we uploaded a paper entitled KNN and K-means in Gini Prametric Spaces on ArXiv.

This paper introduces innovative enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces. Unlike traditional distance metrics, Gini-based measures incorporate both value-based and rank-based information, improving robustness to noise and outliers. The main contributions of this work include: proposing a Gini-based measure that captures both rank information and value distances; presenting a Gini K-means algorithm that is proven to converge and demonstrates resilience to noisy data; and introducing a Gini KNN method that performs competitively with state-of-the-art approaches such as Hassanat’s distance in noisy environments. Experimental evaluations on 14 datasets from the UCI repository demonstrate the superior performance and efficiency of Gini-based algorithms in clustering and classification tasks. This work opens new avenues for leveraging rank-based measures in machine learning and statistical analysis.

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

Our paper, Beyond Human Intervention: Algorithmic Collusion through Multi-Agent Learning Strategies, with Suzie Grondin and Philipp Ratz is now available online

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.

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

Our recent paper, Optimal Transport on Categorical Data for Counterfactuals using Compositional Data and Dirichlet Transport, with Agathe and Ewen is now online

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.

https://freakonometrics.hypotheses.org/files/2025/01/transp2.png

See https://github.com/fer-agathe/transport-simplex for the codes