ASA 2022 Apprentissage Statistiques et Applications
Mercredi 22 juin au Vendredi 24 juin 2022
Mercredi 22 juin au Vendredi 24 juin 2022
- Speakers : Stéphanie Allasonnière (Université de Paris), Oumaima Ben Mrad (Université de Sfax et LMA de Poitiers), Christophe Biernacki (Université de Lille), Azzouz Dermoune (Université de Lille), Yohann Foucher (Université de Nantes), Léo Grill (Orange et LMA de Poitiers), Salima Helali (Université d'Angers), François Husson (Institut Agro Rennes-Angers), Grégory Nuel (Sorbonne université), Amine Ounajim (CHU et LMA de Poitiers), Arnaud Poinas (LMA de Poitiers).
Programme
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Mercredi 22 Juin 2022
- Pause déjeuner 12h10--13h50 -- Hôtel Altéora - Avenue du Futuroscope, 86961 Chasseneuil du Poitou Chairman (Yousri Slaoui)
- Solym Manou-Abi, 14h30--15h10.
- Pause café 15h20--15h50.
- Salima Helali, 16h00--16h40
- Arnaud Poinas 16h45--17h25
- Dinner 20h00 -- Restaurant le Bis: 4 Rue Saint-Nicolas, 86000 Poitiers
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Jeudi 23 Juin 2022
Chairman (Solym Manou-Abi)
- Azzouz Dermoune, 0915--09h55.
- Oumaima Ben Mrad, 10h00-10h40.
- Pause café 10h45--11h15.
- Léo Grill 11h20--12h00.
- Pause déjeuner 12h10--13h50 -- Hôtel Altéora - Avenue du Futuroscope, 86961 Chasseneuil du Poitou Chairman (Grégory Nuel)
- Christophe Biernacki, 14h00--14h40.
- François Husson, 14h45-15h25.
- Pause café 15h30--15h45.
Chairman (Christophe Biernacki)
- Yohann Foucher 16h00--16h40.
- Grégory Nuel 16h45--17h30.
- Stéphanie Allasonnière 17h35--18h15.
- Dinner 20h30 -- Restaurant le Bis: 4 Rue Saint-Nicolas, 86000 Poitiers
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Vendredi 24 Juin 2022
- Soutenance de la thèse d'Amine Ounajim, 09h45--11h45.
- Pause déjeuner 12h30--14h00 -- Restaurant Plaza - Avenue du Futuroscope, 86360 Chasseneuil-du-Poitou
- Jocelyne Attab (LMA, Université de Poitiers)
Pour me contacter
Université de Poitiers
Laboratoire de Mathématiques et Applications
UMR 6086 du CNRS
86962 Futuroscope Chasseneuil, France
Téléphone: (+33) (0)5 49 49 68 77
Fax: (+33) (0)5 49 49 69 01
Mail: Yousri"point"Slaoui "AT" math "point"univ "-"poitiers "point" fr
Chairman (Stéphanie Allasonnière )
Titres et résumés
Mercredi 22 juin 2022
Abstract: We are interested in this talk by a stochastic model for the dynamic of water borne infections
diseases such as the typhoid fever. We motivate the construction with a linear birth and
death process with immigration together with the parameter estimation in a given framework.
Abstract : We investigate the problem of survival copula based models with data subject to dependent censoring. In this context, we propose to adapt the Marshall-Olkin model and to study some main characteristics of the associated copula in the application to survival data. We also introduce the estimators for the marginal distributions and the copula, and in the meantime, show their asymptotic normality under appropriate conditions. We finally assess the finite-sample performance for our approach with a small simulation study on synthetic data, and with an application on real data.
Résumé: Après quelques rappels sur les processus ponctuels, nous présenterons dans cet exposé une classe de processus ponctuels spatiaux sur R^d utilisés pour modéliser des données au caractère répulsif, appelés processus ponctuels déterminantaux. Nous nous intéresserons en particulier à l'estimation paramétrique par maximum de vraisemblance des ces processus ponctuels. Bien qu'une expression explicite de leur vraisemblance ne soit connue, elle n'est malheureusement pas calculable numériquement. Nous verrons alors une méthode d'approximation de cette vraisemblance et nous illustrerons ensuite ses performances par des simulations.
Jeudi 23 juin 2022
Résumé: Lorsque nous adaptons des données à un modèle, nous devons minimiser une fonction objectif f.
Souvent on utilise le minimum global de f pour estimer le paramètre du modèle et pour faire la prévision.
Ici nous allons considérer le cas où f a plusieurs minimums locaux.
A titre d'exemple, nous proposons d'ajuster les infections quotidiennes de COVID-19 en Chine en utilisant un modèle gaussien.
La fonction objectif est donnée par la norme l1 et dépend de quatre paramètres
(le nombre des observations, l'amplitude, l'emplacement de l'amplitude et la largeur).
En faisant varier l'initialisation et le nombre de redémarrage
de l'algorithme du simplexe de Nelder-Mead, nous montrons que notre fonction objectif possède de nombreux minimums locaux.
On montre numériquement que le minimum global est un mauvais estimateur et qu'aucun minimum
n'est capable seul de donner une bonne estimation de l'amplitude et de l'emplacement.
Le choix de la norme l1 revient à supposer que les erreurs entre le modèle et les infections quotidiennes
suivent la la loi de Laplace. Chaque minimum local est une estimation du paramètre d'échelle de cette loi et ceci nous permet
d'associer à chaque minimum local un intervalle de confiance pour les infections futures.
Abstract : The aim of this presentation is to complet the work of Diaz and Pariguan (2009) by constructing the centered q-Gaussian distribution with variance σ². In addition, the notion of entropy of Shannon and quantile will be generalized. However, we highlight the relation of convergence of the centered q-Gaussian distribution with variance σ² to the Uniform distribution on [-σ, σ] and to the Gaussian distribution on the real line when q tends to 0 and 1 respectively. Finally an estimation of the parameters q and σ² will be achieved by following the E-M algorithm.
Titre: Utilisation d'un Réseau de Neurones Bayésien en tant qu'Acteur dans l'Apprentissage Renforcé Profond
Résumé: L'apprentissage renforcé s'est beaucoup développé, et trouve de nombreuses applications. En parallèle les méthodes bayésiennes sont de plus en plus étudiées, notamment pour l'apprentissage profond. Ces méthodes permettent de palier à des problèmes tels que le surapprentissage et la transparence des modèles. L'utilisation d'un acteur basé sur un réseau de neurones bayésien, dans le cadre des méthodes d'acteur-critique, permet d'apporter un fondement théorique ainsi qu'une nouvelle approche algorithmique. Une étude numérique est présentée, elle montre l'intérêt de l'utilisation de ces méthodes dans l'apprentissage renforcé profond.
Abstract: Frequency of missing data increases with the growing size of modern datasets, making this topic important in the research agenda of statisticians. First, we introduce the MCAR mechanism for mixed data (quantitative and categorical) mixture models and illustrate it on a biological data set. Second, as a more theoretical but important step in the talk, we discuss the impact of missing values on the EM algorithm for Gaussian mixtures in the MAR situation. We exhibit the fact that the quite familiar degeneracy problem is aggravated during the EM runs, leading to dangerously slow and also more frequent events than with complete data. Finally, we discuss the impact of missing not at random values (MNAR mechanism) on the partition estimation provided from mixtures (Gaussian or not). In particular we defend the advantage to embed the missingness mechanism directly within the clustering modeling step. A new MNAR model is introduced, discussed and experimented on a medical data set.
Résumé: Les jeux de données sont de plus en plus souvent issus de plusieurs sources d'information et sont de plus en plus volumineux. Avant de se lancer dans une modélisation ou une étude statistique, il est indispensable de visualiser ces données. On peut notamment voir quelle est l'information commune et l'information spécifique apportée par chaque source d'information. L'analyse factorielle multiple, qui est une extension de l'ACP au cas où les données sont structurées en groupes de variables (chaque groupe correspondant à une source d'information), répond à cet objectif de visualisation et de comparaison d'information.
Nous verrons dans cet exposé des exemples de jeux de données analysés par l'AFM ainsi que les problématiques associées, puis nous donnerons les principes de l'AFM et insisterons sur les interprétations des résultats.
Abstract: Controlling for confounding bias is crucial in causal inference. Distinct methods are currently employed to estimate marginal confounder-adjusted effects. The G-computation (GC) is one of these methods, but it is its use is much less frequent than methods based on propensity scores. We conducted several simulations-based studies to explore its performances in the context of a binary treatment, a binary outcome and baseline confounders.
Firstly, we compared different sets of covariates (those causing the outcome, those causing the treatment allocation, those causing both the outcome and the treatment allocation, and all the covariates) and four methods: GC, inverse probability of treatment weighting (IPW), full matching and targeted maximum likelihood estimator (TMLE). The results suggested that considering all the covariates causing the outcome led to the lowest bias and variance, particularly for g-computation. (Le Borgne et al, Sci Rep 2021)
Secondly, we aimed to combine machine learning and G-computation. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. (Chatton et al, Sci Rep 2020)
Thirdly, we studied the robustness of GC, IPW, truncated IPW, TMLE and truncated TMLE in case of near-violation of the positivity. We tested different level of extrapolation issue. The near-violation of the positivity impacted all methods, but we reported a higher robustness of GC and TMLE-based methods. Truncation helped in limiting the bias in near-violation situations, but at the cost of bias in normal conditions. (Léger et al, Biom J. 2022)
Regarding these results, we propose an R package RISCA to encourage the use of the GC and we are working to further propose a super learner for causal inference in the context of time-to-event outcomes.
References
Le Borgne F, Chatton A, Léger M, Lenain R, Foucher Y. G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes. Sci Rep. 2021 Jan 14;11(1):1435.
Chatton A, Le Borgne F, Leyrat C, Gillaizeau F, Rousseau C, Barbin L, Laplaud D, Léger M, Giraudeau B, Foucher Y. G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study. Sci Rep. 2020 Jun 8;10(1):9219.
Léger M, Chatton A, Pirrachio M, Lasocki S, Foucher Y. Causal inference in case of near-violation of positivity: comparison of methods. Biometrical Journal. 2022 Jan 7. Online ahead of print.
Le Borgne F, Chatton A, Léger M, Lenain R, Foucher Y. G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes. Sci Rep. 2021 Jan 14;11(1):1435.
Chatton A, Le Borgne F, Leyrat C, Gillaizeau F, Rousseau C, Barbin L, Laplaud D, Léger M, Giraudeau B, Foucher Y. G-computation, propensity score-based methods, and targeted maximum likelihood estimator for causal inference with different covariates sets: a comparative simulation study. Sci Rep. 2020 Jun 8;10(1):9219.
Léger M, Chatton A, Pirrachio M, Lasocki S, Foucher Y. Causal inference in case of near-violation of positivity: comparison of methods. Biometrical Journal. 2022 Jan 7. Online ahead of print.
Abstract: We all know that correlation is not causality, and that cofounding factors can easily mislead us to spurious conclusions. Even when all cofounding factors are observed, we know that many causal DAGs (Directed Acyclic Graphs) structures can lead to the same likelihood; this is the so-called Markov equivalence. In simple cases, we can reduce the Markov equivalence class to a single DAG structure by using intervention experiments like clinical randomized trial. But in complex situations, even intervention experiments might not allow to infer with certainty all causal relationships. Moreover, in practice, we are often confronted to mixture of observation and intervention experiments. In this talk, we start by presenting the notion of PDAG (Partially Directed Acyclic Graphs) as a representation of the Markov equivalence class of a DAG. We will start by PDAG in the presence of observation experiments only, and then generalize to a mixture of observation and intervention experiments. We will then see how it is possible to compute the likelihood of a PDAG assuming that the underlying variables are connected to each other through generalized linear models (e.g. linear regression, logistic regression, survival, etc.). Finally, we will explain how it is possible to use the BIC criterion and MCMC (Markov Chain Monte-Carlo) in order to explore the PDAG space and derive a posterior distribution.
Titre: Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder
Abstract: n this work, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder (VAE). Our approach combines the proposal of 1) a new VAE model, the latent space of which is modeled as a Riemannian manifold and which combines both Riemannian metric learning and normalizing flows and 2) a new generation scheme which produces more meaningful samples especially in the context of small data sets. The method is tested through a wide experimental study where its robustness to data sets, classifiers and training samples size is stressed. It is also validated on a medical imaging classification task on the challenging ADNI database where a small number of 3D brain magnetic resonance images (MRIs) are considered and augmented using the proposed VAE framework. In each case, the proposed method allows for a significant and reliable gain in the classification metrics. For instance, balanced accuracy jumps from 66.3% to 74.3% for a state-of-the-art convolutional neural network classifier trained with 50 MRIs of cognitively normal (CN) and 50 Alzheimer disease (AD) patients and from 77.7% to 86.3% when trained with 243 CN and 210 AD while improving greatly sensitivity and specificity metrics.
Vendredi 24 juin 2022
Title: Mixture of random time-varying coefficient models and mixture of longitudinal factor analysers and their application to chronic pain after spinal surgery multidimensional evaluation
Abstract: Multivariate longitudinal data play an essential role in various fields of research, including the medical and behavioral sciences. They allow researchers to test multiple hypotheses, such as the identification of variation over time in a clinical variable. The robustness of the inferences obtained from the analysis of longitudinal data leads to an increasing complexity of statistical processing methods. This complexity arises from the structure of longitudinal data and their statistical properties including intra-individual time dependence. Another degree of complexity may arise from potential heterogeneity due to the existence of several latent subpopulations in the data. Currently, the literature recognizes that pain has a complex longitudinal aspect. It has also been shown that the correlations between the different dimensions of pain become stronger over time. This may be due to the long-term accumulation of biopsychosocial burdens generated by chronic pain and to alterations in brain mechanisms linking pain to emotion. Moreover, the socio-cultural and emotional character of chronic pain makes its evaluation complex since each patient is impacted by the sensory, emotional and functional component differently. The first objective of this thesis is to demonstrate empirically the existence of different latent groups of chronic pain patients through the application of a mixture of mixed-effects model. We show that the quality of life is impacted differently by the sensory, emotional and functional components of pain for each latent group. This provides a rationale for the need for a heterogeneous, patient-specific assessment. The second objective is to propose a new non-parametric model formulated as a time-varying mixture of time-varying coefficient models including random effects processes. We propose a modified EM algorithm to estimate the model parameters. This model allows us to study the evolution over time of the coefficients associating patient quality of life with the other components of chronic pain for each latent group. The third and final objective of the thesis is to propose a new factorial model to analyze heterogeneous multivariate longitudinal data. The proposed model is a mixture of longitudinal factor analysis models that allows summarizing several longitudinal indicators into one or more latent variables, which differ between the mixture components. An EM algorithm has been proposed to estimate the model. Methods to ensure the comparability of the latent factors were discussed. The goal of this model is to extract latent and multidimensional indicators that depend on both the time of measurement in the patient's pathway and the intrinsic characteristics of the patients. The ultimate goal being to shift the assessment of pain to a multidimensional, time-varying and patient-specific assessment based on the patient's biopsychosocial characteristics.
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