# Optimal Transport for Counterfactual Estimation: A Method for Causal Inference

For those who wish to reproduce the techniques proposed in our paper, Optimal Transport for Counterfactual Estimation: A Method for Causal Inference, Ewen Gallic has put online some nice pages, with the application mentioned in the paper (both univariate and bivariate, including confidence intervals with bootstrap), as well as simpler examples, which I use in the slides, to present the method

http://egallic.fr/Recherche/Transport_Counterfactual/

I will present this work at the Bachelier Seminar, in Paris, at the end of the week. Slides are online here.

Many problems ask a question that can be formulated as a causal question: “what would have happened if…?” For example, “would the person have had surgery if he or she had been Black?” To address this kind of questions, calculating an average treatment effect (ATE) is often uninformative, because one would like to know how much impact a variable (such as skin color) has on a specific individual, characterized by certain covariates. Trying to calculate a conditional ATE (CATE) seems more appropriate. In causal inference, the propensity score approach assumes that the treatment is influenced by x, a collection of covariates. Here, we will have the dual view: doing an intervention, or changing the treatment (even just hypothetically, in a thought experiment, for example by asking what would have happened if a person had been Black) can have an impact on the values of x. We will see here that optimal transport allows us to change certain characteristics that are influenced by the variable we are trying to quantify the effect of. We propose here a mutatis mutandis version of the CATE, which will be done simply in dimension one by saying that the CATE must be computed relative to a level of probability, associated to the proportion of x (a single covariate) in the control population, and by looking for the equivalent quantile in the test population. In higher dimension, it will be necessary to go through transport, and an application will be proposed on the impact of some variables on the probability of having an unnatural birth (the fact that the mother smokes, or that the mother is Black).

# Talk at StatQAM on Counterfactuals and Optimal Transport

Next Thursday, I will present our recent work at the StatQAM seminar, with Emmanuel Flachaire ajd Ewen Gallic, on Optimal Transport for Counterfactual Estimation: A Method for Causal Inference

Many problems ask a question that can be formulated as a causal question: “what would have happened if…?” For example, “would the person have had surgery if he or she had been Black?” To address this kind of questions, calculating an average treatment effect (ATE) is often uninformative, because one would like to know how much impact a variable (such as skin color) has on a specific individual, characterized by certain covariates. Trying to calculate a conditional ATE (CATE) seems more appropriate. In causal inference, the propensity score approach assumes that the treatment is influenced by x, a collection of covariates. Here, we will have the dual view: doing an intervention, or changing the treatment (even just hypothetically, in a thought experiment, for example by asking what would have happened if a person had been Black) can have an impact on the values of x. We will see here that optimal transport allows us to change certain characteristics that are influenced by the variable we are trying to quantify the effect of. We propose here a mutatis mutandis version of the CATE, which will be done simply in dimension one by saying that the CATE must be computed relative to a level of probability, associated to the proportion of x (a single covariate) in the control population, and by looking for the equivalent quantile in the test population. In higher dimension, it will be necessary to go through transport, and an application will be proposed on the impact of some variables on the probability of having an unnatural birth (the fact that the mother smokes, or that the mother is Black).

Slides are now online.

This Tuesday morning (7 am), I will give a talk at the ASTIN reading club, on auto-calibration. More precisely, we will look at the topic of ensuring the calibration of machine learning models for non-life pricing. Slides are available here.

# Talk on fairness and “differential pricing” in insurance

Tomorrow morning, I will give a talk on fairness, “differential pricing” and “price walking” in insurance, at the AXA Chief Actuary Meeting. Slides are available online.

I will get back on two reports published recently (that can be related to the recent EIOPA consultation)

The first one was the report by the Sweedish Finans Inspektionen, Fär lojala försäkringstagare betala mer?

and the study by the Central Bank of Ireland.

They get back on price walking, seen as a discrimination problem,

It found that pricing practices applied by insurance providers could result in unfair outcomes for some consumers in the private car and home insurance markets. These pricing practices include “price walking”, where consumers are charged higher premiums, relative to the expected cost, the longer they remain with an insurance provider. The Report indicates that the CBI considers this practice to be unfair, a point emphasised in the press release accompanying the report. The Report found that long term customers who stayed with the same insurer for 9 years or more, paid on average 14% more on private car insurance and 32% more on home insurance than the equivalent customer renewing for the first time.

They provide interesting graphs, with prices of motor insurance

as well as household insurance,

# Talk on Bayesian models in actuarial science

Tomorrow afternoon, I will give a talk on Bayesian models in actuarial science for the Casualty Actuarial and Statistical Task Force (CASTF) monthly “book club”. The long version of slides is available here, and a shorter one (without animations) there.

# Risque de sécheresse et de subsidence

Jeudi, en arrivant sur Paris, je ferai une intervention pour présenter predicting drought and subsidence risks in France, publié dans le numéro spécial Drought vulnerability, risk, and impact assessments: bridging… de NHESS (Nat. Hazards Earth Syst. Sci.), écrit avec Molly James, et Hani Ali, ainsi que le travail sur les inondations, en France, Insurance against natural catastrophes: balancing actuarial fairness and social solidarity, lors d’une discussion avec Marc Bagarry

Les slides sont en ligne.

# Journée d’étude “Genre, Algorithmes et Droit” à Aix-en-Provence

Vendredi, je participerais avec Rodolphe Bigot à la journée d’étude “Genre, Algorithmes et Droit” à Aix-en-Provence.

# Exposé à un webinaire IVADO-OBVIA sur l’équité (algorithmique) en assurance

Ce matin, je donnerais un court exposé sur le thème de l’équité (algorithmique) en assurance dans un webinaire organisé par IVADO et OBVIA. Les slides sont en ligne.

# Equité et discrimination en assurance

Mercredi 18 mai, j’interviendrai au séminaire de la chaire PARI, à Paris, dans les locaux de la CCR, pour parler d’équité et de discrimination en assurance… Les slides sont en ligne.

En poursuivant la discussion abordée dans “L’équité de l’apprentissage machine en assurance” (co-écrit avec Laurence Barry), nous présentons un aperçu des problèmes auxquels les actuaires sont confrontés lorsqu’ils traitent de la discrimination. Depuis le début de leur histoire, les assureurs sont connus pour utiliser des données pour classifier et tarifer les risques. En tant que tels, ils ont été confrontés très tôt au problème de l’équité et de la discrimination associées aux données. Cette question devient de plus en plus importante avec l’accès à des données plus granulaires et comportementales, et évolue pour refléter les technologies et les préoccupations sociétales actuelles. En examinant les débats antérieurs sur la discrimination, nous montrons que certains préjugés algorithmiques sont une version renouvelée de préjugés plus anciens, tandis que d’autres semblent inverser l’ordre précédent. Paradoxalement, alors que la pratique de l’assurance n’a pas profondément changé et que la plupart de ces biais ne sont pas nouveaux, l’ère de l’apprentissage automatique ébranle encore profondément la conception de l’équité en matière d’assurance. (Cette présentation s’appuiera également sur un rapport qui sera bientôt publié par l’Institut Louis Bachelier).

# Talk at the ASTIN-IAA Webinar on discrimination and fairness

This Wednesday, I will be giving a talk at the ASTIN-IAA webinar

Slides are available online.

# Exposé à Nanterre sur les accidents corporels

Lundi midi, je serais (physiquement) à Nanterre, au séminaire Laws, Institutions and Economics et je présenterais des travaux sur la modélisation des accidents corporels (en assurance automobile) en France. Les slides sont en ligne. Il est largement inspiré des travaux mené avec Enora Belz dans sa thèse. J’espérais avoir des données à jour, mais la signature de la convention a trainé (on va donc rester sur les données de 1997 à 2014). Ca sera l’occasion de revenir sur l’idée d’avoir des barèmes pour l’indemnisation des accidents corporels, et l’abandon récent de DataJust. Mais je ferais probablement un billet de blog sur le sujet, avec un peu de chance, avant lundi… à suivre donc…