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.

Exploration des Techniques de Transfert d’Apprentissage sur des Données Climatiques

L’été avance. Florent, qui est en stage depuis presque 4 mois, va faire un exposé demain au séminaire d’été des étudiants, sur le thème “Exploration des Techniques de Transfert d’Apprentissage sur des Données Climatiques”

Le transfert d’apprentissage (ou Transfer Learning) représente une avancée notable dans le domaine de l’intelligence artificielle. Cette technique repose sur l’idée que lorsqu’un modèle est bien entraîné et performant dans un contexte donné, on peut utiliser ce savoir-faire dans un autre contexte, différent mais lié, pour améliorer la modélisation, notamment lorsqu’on dispose de peu d’informations sur ce dernier. Cependant, les performances des modèles de transfert d’apprentissage varient, et le choix de transférer la connaissance n’est pas toujours optimal. La principale difficulté réside dans la capacité à garantir les performances du transfert afin de justifier ce choix. Cette approche pourrait s’avérer particulièrement précieuse dans le contexte de l’analyse des données climatiques. En effet, les modèles utilisés dans divers secteurs pourraient bénéficier des techniques avancées de transfert d’apprentissage pour améliorer la précision des prévisions et optimiser les stratégies d’adaptation et d’atténuation du changement climatique. De plus, le transfert d’apprentissage permet de réutiliser des modèles existants, réduisant ainsi les coûts temporels et écologiques liés à l’entraînement de nouveaux modèles. Cette méthode pourrait rendre l’analyse climatique plus efficace et durable, tout en économisant des ressources précieuses.

Pour l’anecdote, il y a presque 5 ans, je donnais un exposé sur Paris “The Challenge of Predictive Models (for Rare Events)” (les slides sont toujours en ligne). Mes centres d’intérêt n’ont pas trop évolués,


Some updates about the insurance datasets package (CASdataset)

Ten years ago, Computational Actuarial Science with R was published. With Christophe Dutang, we created at the same time an R package, collecting datasets used in the book. It was mainly to give access to the datasets to reproduce the applications, since functions used in the different chapters were coming from other R packages. Then, we started adding more and more datasets, not used in the book, but that could be used by researchers and students. We are quite happy to see that those datasets are now considered as a benchmark in actuarial and insurance litterature (and also outside the community, actually).

The maintenance was a bit complicated since it was not possible to be hosted by the CRAN (Comprehensive R Archive Network), so it was either on Christophe’s github repo, or on a dedicated website at UQAM. Christophe’s repo

is under construction (or major refreshing, with Ewen Gallic), and several vignettes will be added, created by ). Actually, we encourage colleagues, or students, who used datasets from the package to share some codes, we can now host the application. And there is also the following repository,

Hence, the dataset has now an official DOI, which makes it easier to cite doi:10.57745/P0KHAG. And  the following bib file can be obtained,

author = {Dutang, Christophe and Charpentier, Arthur},
publisher = {Recherche Data Gouv},
title = {{Insurance dataset}},
year = {2024},
version = {V1},
doi = {10.57745/P0KHAG},
url = {}

Talk at the 27th International Congress on Insurance: Mathematics and Economics

On Wednesday morning, I will be chairing our session “Discrimination-free Insurance Pricing” at the Insurance: Mathematics & Insurance Conference, in Chicago. With Olivier Côté, Lydia Gabric and Hong Beng Lim, we will be four speaker, just before lunch time. My talk will be a mix of recent work on quantifying and mitigating discrimination in scores (in insurance). Slides are available online.


Talk on collaborative insurance, unfairness and discrimination

Monday, I will be giving a short course at the workshop on Decentralized Insurance and Risk Sharing (SAC 161), in Chicago

  • Decentralized Finance and Blockchain: Implications for the Insurance Industry, by Marco Mirabella
  • Decentralized risk sharing: definitions, properties, and characterizations, by Jan Dhaene
  • Collaborative insurance, unfairness, and discrimination, by Arthur Charpentier
  • Decentralized insurance: bridging the gap between industry practice and academic theory, by Runhuan Feng

My slides are available online.

In this course, we will get back to mathematical properties of risk sharing on networks, with reciprocal contrats. We will discuss conditions about stochastic dominance, proving that policyholers might have interest in sharing risks with “friends”.
Then, we will try to adress fairness issues, for such risk sharing mechanisms. If fairness has been recently intensively studied, either through group or individual fairness, there are yet not much litterature about fairness on networks. It is important to adress those issues, since perceived discrimination is usually associated with networks. We will see why the topology of the network is important, both to design peer-to-peer schemes to share risks, but also to see if perceived discrimination is associated with global disparate treatement.

Insurance, Biases, Discrimination and Fairness

Insurance, Biases, Discrimination and Fairness was published a few weeks ago. I still plan to spend some time this summer on the R package, including data and some functions…

This book offers an introduction to the technical foundations of discrimination and equity issues in insurance models, catering to undergraduates, postgraduates, and practitioners. It is a self-contained resource, accessible to those with a basic understanding of probability and statistics. Designed as both a reference guide and a means to develop fairer models, the book acknowledges the complexity and ambiguity surrounding the question of discrimination in insurance. In insurance, proposing differentiated premiums that accurately reflect policyholders’ true risk—termed “actuarial fairness” or “legitimate discrimination”—is economically and ethically motivated. However, such segmentation can appear discriminatory from a legal perspective. By intertwining real-life examples with academic models, the book incorporates diverse perspectives from philosophy, social sciences, economics, mathematics, and computer science. Although discrimination has long been a subject of inquiry in economics and philosophy, it has gained renewed prominence in the context of “big data,” with an abundance of proxy variables capturing sensitive attributes, and “artificial intelligence” or specifically “machine learning” techniques, which often involve less interpretable black box algorithms.

The book distinguishes between models and data to enhance our comprehension of why a model may appear unfair. It reminds us that while a model may not be inherently good or bad, it is never neutral and often represents a formalization of a world seen through potentially biased data. Furthermore, the book equips actuaries with technical tools to quantify and mitigate potential discrimination, featuring dedicated chapters that delve into these methods.

Samuel が横浜に到着

After defending his PhD last week, Samuel just arrived in 横浜市, at the International Joint Conference on Neural Networks (IJCNN’24), that will take place at the IEEE World Congress on Computational Intelligence (WCCI).

He will present our recent work on 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.

Contribution of machine learning in modeling rare values and imbalanced data

This morning (Montréal time), Samuel Stocksieker defended his PhD thesis entitled “contribution of machine learning in modeling rare values and imbalanced data“. Cécile Capponi, Marianne Clausel, Julie Josse, Frédéric Planchet and  Anne Sabourin, Christian-Yann Robert and Stéphane Loisel were in the jury,

the work is structured around major axes: Imbalanced Features and Imbalanced Regression. The first axis addresses the issue of feature imbalance, that is, when it concerns the attributes and not the variable to be explained. The first solution involves adjusting the distribution of a continuous covariate relative to a given target distribution. It proposes to combine weighted resampling and synthetic data generators. This strategy notably allows to deal with selection bias: when the distribution of the covariate in the training sample is significantly different from that of the population. A second solution is proposed in the context of multi-supervised learning, particularly with autoencoders. It relies on a new metric aimed at balancing the influence of variables during learning and is applicable not only to supervised and unsupervised models, but also to generative models such as variational autoencoders. The second part deals with the issue of regression from imbalanced data. Various preprocessing solutions, including synthetic data generation, are proposed. Initially, we propose to explore the initial data space by introducing new generators and methodologies to address the specific case of regression. We then propose to immerse the data in a latent space in order to provide a more conducive framework for synthetic data generation.

Generalized Oversampling for Learning from Imbalanced datasets and Associated Theory

Our paper, Generalized Oversampling for Learning from Imbalanced datasets and Associated Theory: Application in Regression, written with Samuel Stocksieker and Denys Pommeret, has been accepted for publication in TMLR (Transactions on Machine Learning Research)

In supervised learning, it is quite frequent to be confronted with real imbalanced datasets. This situation leads to a learning difficulty for standard algorithms. Research and solutions in imbalanced learning have mainly focused on classification tasks. Despite its importance, very few solutions exist for imbalanced regression. In this paper, we propose a data augmentation procedure, the GOLIATH algorithm, based on kernel density estimates and especially dedicated to the problem of imbalanced data. This general approach encompasses two large families of synthetic oversampling: those based on perturbations, such as Gaussian Noise, and those based on interpolations, such as SMOTE. It also provides an explicit form of such machine learning algorithms. New synthetic data generators are deduced. We apply GOLIATH in imbalanced regression combining such generator procedures with a new wild-bootstrap resampling technique for the target values. We evaluate the performance of the GOLIATH algorithm in imbalanced regression where we compare our approach with state-of-the-art techniques.