Titre de la thèse: A Bayesian approach for periodic components estimation for chronobiological signals
Résumé de la thèse: The toxicity and efficacy of more than 30 anticancer agents presents very high variations, depending on the dosing time. Therefore the biologists studying the circadian rhythm require a very precise method for estimating the Periodic Components (PC) vector of chronobiological signals. Moreover, in recent developments not only the dominant period or the PC vector present a crucial interest, but also their stability or variability. In cancer treatment experiments the recorded signals corresponding to different phases of treatment are short, from seven days for the synchronization segment to two or three days for the after treatment segment. When studying the stability of the dominant period we have to consider very short length signals relative to the prior knowledge of the dominant period, placed in the circadian domain. The classical approaches, based on Fourier Transform (FT) methods are inefficient (i.e. lack of precision) considering the particularities of the data (i.e. the short length). Another particularity of the signals considered in such experiments is the level of noise: such signals are very noisy and establishing the periodic components that are associated with the biological phenomena and distinguish them from the ones associated with the noise is a difficult task. In this thesis we propose a new method for the estimation of the PC vector of biomedical signals, using the biological prior informations and considering a model that accounts for the noise. The experiments developed in the cancer treatment context are recording signals expressing a limited number of periods. This is a prior information that can be translated as the sparsity of the PC vector. The proposed method considers the PC vector estimation as an Inverse Problem (IP) using the general Bayesian inference in order to infer all the unknowns of our model, i.e. the PC vector but also the hyperparameters. The sparsity prior information is modelled using a sparsity enforcing prior law. In this thesis we propose a Student-t distribution, viewed as the marginal distribution of a bivariate Normal - Inverse Gamma distribution. In fact, when the equality between the shape and scale parameters corresponding to the Inverse Gamma distribution is not imposed, the marginal of the Normal-Inverse Gamma distribution is a generalization of the Student-t distribution. We build a general Infinite Gaussian Scale Mixture (IGSM) hierarchical model where we also assign prior distributions for the hyperparameters. The expression of the joint posterior law of the unknown PC vector and the hyperparameters is obtained via the Bayes rule and then the unknowns are estimated via Joint Maximum A Posteriori (JMAP) or Posterior Mean (PM). For the PM estimator, the expression of the posterior distribution is approximated by a separable one, via Variational Bayesian Approximation (VBA), using the Kullback-Leibler (KL) divergence. Two possibilities are considered: an approximation with partially separable distributions and an approximation with a fully separable one. The algorithms are presented in detail and are compared with the ones corresponding to the Gaussian model. We examine the practical convergency of the algorithms and give simulation results to compare their performances. Finally we show simulation results on synthetic and real data in cancer treatment applications. The real data considered in this thesis examines the rest-activity patterns and gene expressions of KI/KI Per2::luc mouse, aged 10 weeks, singly housed in RT-BIO. Keywords : Periodic Components (PC) vector estimation, Sparsity enforcing, Bayesian parameter estimation, Variational Bayesian Approximation (VBA), Kullback-Leibler (KL) divergence, Infinite Gaussian Scale Mixture (IGSM), Normal - Inverse Gamma, Inverse problem, Joint Maximum A Posteriori (JMAP), Posterior Mean (PM), Chronobiology, Circadian rhythm, Cancer treatment.. Citation: Mircea Dumitru. A Bayesian approach for periodic components estimation for chronobiological signals. Probability [math.PR]. Université Paris-Saclay, 2016. English. <NNT : 2016SACLS104>. <tel-01318048> @phdthesis{dumitru:tel-01318048, TITLE = {{A Bayesian approach for periodic components estimation for chronobiological signals}}, AUTHOR = {Dumitru, Mircea}, URL = {https://tel.archives-ouvertes.fr/tel-01318048}, NUMBER = {2016SACLS104}, SCHOOL = {{Universit{\'e} Paris-Saclay}}, YEAR = {2016}, MONTH = Mar, KEYWORDS = {Bayesian approach ; Sparsity enforcing ; Chronobiology ; Hierarchical model ; Periodic Components vector estimation ; Inverse problem ; Approches bay{\'e}siennes ; Renforcement de parcimonie ; Chronobiologie ; Mod{\`e}le hi{\'e}rarchique ; Estimation de composantes p{\'e}riodiques ; Probl{\`e}mes inverses}, TYPE = {Theses}, PDF = {https://tel.archives-ouvertes.fr/tel-01318048/file/76211_DUMITRU_2016_diffusion.pdf}, HAL_ID = {tel-01318048}, HAL_VERSION = {v1}, }

Titre de post-doc: Diffusion des méthodes bayésiennes du GPI en reconstruction tomographique au sein de Toolkits open-source (encadré par Ali Mohammad-Djafari et Nicolas Gac )

Contexte & mission du post-doc: Le GPI développe depuis plusieurs années des méthodes bayésiennes originales pour la reconstruction tomographique appliquées au contrôle non destructif ou à l’imagerie médicale. Pour faire bénéficier aux divers domaines applicatifs de ses avancées au niveau méthodologique, le GPI a notamment dû relever le défi du traitement des données réelles de grande taille avec la mise en œuvre de la parallélisation sur serveur multi-GPU. Le GPI souhaite à présent une diffusion plus large de ses développements méthodologiques et logiciels, vers les toolkits open source ouverts aux diverses communautés de la reconstruction tomographique.La participation du GPI à l‘effort commun de développements logiciels libres a un triple but : (i) rendre accessible ses méthodes bayésiennes originales à une plus large communauté d’utilisateurs, (ii) gagner en visibilité (référencement notamment des méthodes dans les publications), et (iii) catalyser les collaborations avec d’autres acteurs académiques ou industriels du domaine.’objectif de ce post-doc est d’intégrer les méthodes bayésiennes de reconstruction tomographique à la toolbox ASTRA et de contribuer à les améliorer. Il s’agit donc d’un double défi : (i) de mise en œuvre logiciel, en faisant le lien entre le logiciel interne au GPI préexistant et la toolbox ASTRA, et (ii) de développements méthodologiques.

Keywords : Periodic Components (PC) vector estimation, Sparsity enforcing, Bayesian parameter estimation, Variational Bayesian Approximation (VBA), Kullback-Leibler (KL) divergence, Infinite Gaussian Scale Mixture (IGSM), Normal - Inverse Gamma, Inverse problem, Joint Maximum A Posteriori (JMAP), Posterior Mean (PM), Chronobiology, Circadian rhythm, Cancer treatment.

Citation: Mircea Dumitru. A Bayesian approach for periodic components estimation for chronobiological signals. Probability [math.PR]. Université Paris-Saclay, 2016. English. .

@phdthesis{dumitru:tel-01318048, TITLE = {{A Bayesian approach for periodic components estimation for chronobiological signals}}, AUTHOR = {Dumitru, Mircea}, URL = {https://tel.archives-ouvertes.fr/tel-01318048}, NUMBER = {2016SACLS104}, SCHOOL = {{Universit{\'e} Paris-Saclay}}, YEAR = {2016}, MONTH = Mar, KEYWORDS = {Bayesian approach ; Sparsity enforcing ; Chronobiology ; Hierarchical model ; Periodic Components vector estimation ; Inverse problem ; Approches bay{\'e}siennes ; Renforcement de parcimonie ; Chronobiologie ; Mod{\`e}le hi{\'e}rarchique ; Estimation de composantes p{\'e}riodiques ; Probl{\`e}mes inverses}, TYPE = {Theses}, PDF = {https://tel.archives-ouvertes.fr/tel-01318048/file/76211_DUMITRU_2016_di...}, HAL_ID = {tel-01318048}, HAL_VERSION = {v1}, }