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Extensions multivariées de modélisation de la mortalité
No full textOver the past two centuries, life expectancy around the globe has increased considerably. While the long-term trend is fairly regular, the improvement in longevity can be broken down into several phases in the short term, which can most often be linked to medical progress and the reduction in specific causes of mortality. The year 2020 marks a turning point due to the scale of the Covid-19 pandemic and its consequences. Its direct and indirect effects on the economy and healthcare systems will also be felt through other major causes of death. To understand and anticipate mortality-related risks, it is becoming increasingly necessary for reinsurance players to reason and model in terms of causes of death. However, this type of modeling poses specific challenges. By its very nature, it involves multivariate models, whose complexity exceeds that of conventional actuary tools. In this thesis, we propose several avenues for extending mortality modeling to a multivariate framework. These are presented in the form of research articles. The first study deals with technical aspects of multivariate distributions within generalized linear models. When the explanatory variables are categorical, we propose new estimators for the multinomial, negative multinomial and Dirichlet distributions in the form of closed formulas, which notably enable considerable savings in computation time. These estimators are used in the second study to propose a new method for estimating the parameters of mortality models. This method extends the existing framework for all-cause mortality, and enables all mortality modeling issues to be addressed in a single step, particularly by cause-of-death. The third axis concerns mortality forecasts. We study neural networks specifically adapted to time series. Based on concrete use cases, we show that these models are sufficiently flexible and robust to offer a credible alternative to conventional models.Au cours des deux derniers siècles, l’espérance de vie tout autour du globe a connu un accroissement considérable. Si la tendance sur le long terme est plutôt régulière, l’amélioration de la longévité peut être décomposée sur le court-terme en plusieurs phases, que l’on peut relier le plus souvent aux progrès médicaux et à la diminution de causes de mortalité particulières. L’année 2020 marque un tournant du fait de l’ampleur de la pandémie Covid-19 et de ses conséquences. Ses effets directs et indirects sur l’économie et les systèmes de santé se manifestent également au travers des autres causes majeures de décès. Pour comprendre et anticiper les risques liés à la mortalité, il devient de plus en plus nécessaire pour les acteurs de la réassurance de raisonner et modéliser en termes de causes de décès. Ce type de modélisation pose néanmoins des défis spécifiques, issues de la nature multivariée des modèles, dont la complexité dépasse celle des outils classiques de l’actuaire. Nous proposons dans cette thèse plusieurs axes pour étendre la modélisation de la mortalité à un cadre multivarié. Ces axes sont abordés sous forme d’articles de recherche. La première étude porte sur des aspects techniques des distributions multivariées au sein de modèles linéaires généralisés. Lorsque les variables explicatives sont catégorielles, nous proposons de nouveaux estimateurs pour les distributions multinomiale, multinomiale négative et de Dirichlet sous forme de formules fermées, qui permettent notamment un gain considérable en temps de calcul. Ces estimateurs sont utilisés dans la seconde étude pour proposer une nouvelle méthode d’estimation des paramètres de modèles de mortalité. Cette méthode prolonge le cadre existant pour la mortalité toute cause, et permet de traiter toutes les problématiques de modélisation de mortalité en une seule étape, en particulier par cause de décès. Le troisième axe porte sur les projections de mortalité. Nous étudions des réseaux de neurones spécifiquement adaptés aux séries temporelles. Nous montrons par des exemples concrets auxquels peut faire face l’actuaire que ces modèles sont suffisamment flexibles et robustes, offrant une alternative crédible aux modèles classiques
Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence
No full textInternational audienceWe prove a sharp quantitative version for the stability of the Sobolev inequality with explicit constants. Moreover, the constants have the correct behavior in the limit of large dimensions, which allows us to deduce an optimal quantitative stability estimate for the Gaussian log-Sobolev inequality with an explicit dimension-free constant. Our proofs rely on several ingredients such as competing symmetries, a flow based on continuous Steiner symmetrization that interpolates continuously between a function and its symmetric decreasing rearrangement, and refined estimates on the Sobolev functional in the neighborhood of the optimal Aubin-Talenti functions
Les déterminants des distances domicile-travail : cas des aires urbaines françaises métropolitaines.
No full textWe estimate urban form effects on commuting distances within French urban areas using cross-sectional analysis (1999, 2007 and 2014). A stronger concentration of jobs relative to population within urban areas appears to significantly influence commuting distances. However, our estimates suggest relatively weak effects. Average distances between residence location and workplace would decrease by 10% whether jobs and population were equally distributed within urban areas. Our results show that commuting distances depend on many parameters that differ with spatial distribution of jobs within urban areas (density, demographics and public transport).Nous estimons les effets des formes urbaines sur les distances domicile-travail au sein des aires urbaines françaises par une analyse en coupe (1999, 2007 et 2014). La plus grande concentration géographique des emplois par rapport à la population au sein des aires urbaines semble influencer significativement les distances domicile-travail. Cependant, nos estimations suggèrent des effets relativement faibles. Les distances moyennes entre lieu de résidence et lieu d’emploi diminueraient de 10% si la répartition spatiale des emplois était identique à celle de la population au sein des aires urbaines. Nos résultats montrent que les distances domicile-travail dépendent de nombreux paramètres autres que la répartition spatiale des emplois au sein des aires urbaines (densité, démographie et transports en communs)
A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting
No full textInternational audienceCapturing complex temporal patterns and relationships within multivariate data streams is a difficult task. We propose the Temporal Kolmogorov-Arnold Transformer (TKAT), a novel attention-based architecture designed to address this task using Temporal Kolmogorov-Arnold Networks (TKANs). Inspired by the Temporal Fusion Transformer (TFT), TKAT emerges as a powerful encoder-decoder model tailored to handle tasks in which the observed part of the features is more important than the a priori known part. This new architecture combined the theoretical foundation of the Kolmogorov-Arnold representation with the power of transformers. TKAT aims to simplify the complex dependencies inherent in time series, making them more "interpretable". The use of transformer architecture in this framework allows us to capture long-range dependencies through self-attention mechanisms
A Gated Residual Kolmogorov-Arnold Networks for Mixtures of Experts
No full textInternational audienceThis paper introduces KAMoE, a novel Mixture of Experts (MoE) framework based on Gated Residual KolmogorovArnold Networks (GRKAN). We propose GRKAN as an alternative to the traditional gating function, aiming to enhance efficiency and interpretability in MoE modeling. Through extensive experiments on digital asset markets and real estate valuation, wedemonstrate that KAMoE consistently outperforms traditional MoE architectures across various tasks and model types. Our results show that GRKAN exhibits superior performance compared to standard Gating Residual Networks, particularly in LSTMbased models for sequential tasks. We also provide insights into the trade-offs between model complexity and performance gains in MoE and KAMoE architectures
TKAN: Temporal Kolmogorov-Arnold Networks
No full textInternational audienceRecurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies in sequential data. Inspired by the Kolmogorov-Arnold Networks (KANs) a promising alternatives to Multi-Layer Perceptrons (MLPs), we proposed a new neural networks architecture inspired by KAN and the LSTM, the Temporal Kolomogorov-Arnold Networks (TKANs). TKANs combined the strenght of both networks, it is composed of Recurring Kolmogorov-Arnold Networks (RKANs) Layers embedding memory management. This innovation enables us to perform multi-step time series forecasting with enhanced accuracy and efficiency. By addressing the limitations of traditional models in handling complex sequential patterns, the TKAN architecture offers significant potential for advancements in fields requiring more than one step ahead forecastin
Normativité de l’évaluation économique en santé : méthodes, pratiques et discours
No full textThe aim of my research is to support the development of economic evaluation methods by initiating a dialogue between economics and philosophy. The use of these methods needs to be strengthened because they improve the consistency of public decisions, increase transparency and encourage the emergence of public debate. This dialogue can be implemented in three ways, which structure the manuscript. First, economics can address a number of normative issues raised by the allocation of public resources by mathematically formalising the relevant ethical frameworks and translating these ethical frameworks into evaluation tools. Our research seeks to demonstrate that economic evaluation can consider other social justice models than the utilitarian one, in particular liberal-egalitarian justice models that propose an equitable distribution of the chosen distribendua (well-being, capabilities, resources).Second, philosophy can assist evaluators when they encounter moral dilemmas that economics alone cannot address, requiring other approaches such as philosophy. Philosophy makes it possible to examine the opposing positions in such dilemmas and to identify the particular values that underpin them. Thanks to this analytical work, it is possible to construct a common language, to facilitate the public discussions needed to resolve these dilemmas. Thirdly, philosophy examines the economic calculation methods themselves in order to identify the ‘’visions of the world‘’ that underlie them. To this end, we are using the method of historical epistemology to study the discourses surrounding health economic evaluation and the evolution of thess discourses. This method is fruitful in encouraging evaluators to adopt a reflexive stance, i.e. one that is aware of the history of the ideas in which they operate and conscious of the normative biases on which their tools are based.Mes travaux de recherche visent à soutenir l’utilisation des méthodes d’évaluation économique, en mettant en œuvre un dialogue entre économie et philosophie. L’utilisation de ces méthodes doit être renforcée car elles permettent d’améliorer la cohérence des décisions publiques, de renforcer la transparence sur les considérants de ces décisions et de favoriser l’émergence de débats publics. Ce dialogue peut être mis en œuvre de trois façons, qui structurent le manuscrit.En premier lieu, les sciences économiques permettent de répondre à un ensemble de questions normatives que pose l’allocation des ressources publiques en formalisant mathématiquement les cadres éthiques envisageables et en traduisant ces cadres éthiques en outils d’évaluation. Nous cherchons en particulier à montrer dans nos recherches que l’évaluation économique peut tenir compte d’autres modèles que le modèle de justice utilitariste, comme les modèles de justice libérale-égalitariste qui proposent de répartir équitablement les distribuendua retenus (bien-être, capabilités, ressources).En deuxième lieu, la philosophie peut soutenir les évaluateurs lorsqu’ils se heurtent à des dilemmes moraux que les sciences économiques ne peuvent pas traiter seules. Elle permet notamment d’étudier les positions qui s’opposent face à de tels dilemmes et d’identifier les valeurs particulières qui les soutiennent. Grâce à ce travail analytique, elle rend possible la construction d’un langage commun, débarrassé de non-dits, et faciliter ainsi les discussions publiques amenées à trancher ces dilemmes. Enfin, en troisième lieu, la philosophie interroge les outils du calcul économique eux-mêmes pour identifier les « visions du monde » sur lesquelles ils reposent. Nous utilisons dans cette perspective la méthode de l’épistémologie historique pour étudier les discours autour de l’évaluation économique en santé et l’évolution de ces discours. Cette méthode est fructueuse pour favoriser une posture réflexive des évaluateurs, c’est-à-dire consciente de l’histoire des idées dans lesquelles ils s’inscrivent et consciente des partis pris normatifs sur lesquels reposent leurs outils
Recension : Paula Bialski, Middle Tech. Software Work and the Culture of Good Enough, Princeton University Press, 2024
No full textInternational audienc
Scaling limits for a population model with growth, division and cross-diffusion
No full textInternational audienceOriginally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic stochastic model, write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. Under smoothness and symmetry assumptions for the interaction kernel, we then obtain entropy estimates, which provide us with a localization limit at the macroscopic level. Finally, we perform a thorough numerical study in order to compare the three modeling scales
Standing-sphere blowup solutions for the nonlinear heat equation
No full textInternational audienceIn this paper, we construct a singular standing ring solution of the nonlinear heat in the radial case. We give rigorous proof for the existence of a ring blow-up solution in finite time. This result was predicted formally by Baruch, Fibich and Gavish [BFG10]. We also prove the stability of these dynamics among radially symmetric solutions