ED Mathématiques et Informatique
Asymptotic Expansions of probabilities for Finite Range Random Walks on Infinite Trees
by Guillaume CHEVALIER (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 10h00 - Salle 109 IMAG, UMR 5149, Université de Montpellier, Place Eugène Bataillon, 34090 Montpellier
in front of the jury composed of
- Vincent KOZIARZ - Professeur des universités - Université de Bordeaux - Directeur de these
- Sébastien GOUEZEL - Directeur de recherche - CNRS - IRMAR - Institut de recherche mathématique de Rennes - Rapporteur
- Çağrı SERT - Assistant professor - University of Warwick - Warwick Mathematics Institute - Rapporteur
- Bernard BERCU - Professeur des universités - Institut Mathématique de Bordeaux - Examinateur
- Jean-François QUINT - Directeur de recherche - CNRS - Institut Montpellierain Alexander Grothendieck - CoDirecteur de these
- Anna ERSCHLER - Directrice de recherche - CNRS - DMA ENS Paris - Sorbonne Université - Examinateur
- Jérémie BRIEUSSEL - Maître de conférences - Institut Montpelliérain Alexander Grothendieck, Université de Montpellier - Examinateur
Given a finite-range random walk on an infinite tree with bounded valence, what is the asymptotic behaviour, as the number of steps goes to infinity, of the sequence of probabilities that the random walk is at a given vertex? In this Thesis, we answer this question by providing an asymptotic expansion to any order for the sequence of probabilities mentioned above. We will work under the assumption that each vertex of the tree has valence greater than or equal to three, and we will assume that the tree is endowed with a cofinite action of an automorphism group preserving the step distribution. A classical example is the finite-range random walk in a free group. The method used to answer the question above is introduced in Chapter I, in the case of a nearest-neighbour random walk in a regular tree. Furthermore, for nearest-neighbour random walks, we give a description of the asymptotic behaviour as the number of steps goes to infinity, of the sequences of probabilities, that such a random walk, in a regular tree of valence at least three, is in a geodesic ray or in a horocycle, after n steps. In Chapter II, we address the question posed by extending the results established in Chapter I. Finally, Chapter III presents a collection of Tauberian theorems used throughout the text to derive our asymptotic expansions.
ED Sciences Physiques et de l'Ingénieur
Contributions to conformal prediction for computer vision-based decision making in agriculture.
by Paul MELKI (Laboratoire de l'Intégration du Matériau au Système)
The defense will take place at 9h00 - Amphithéâtre JP Dom 351 Cours de la Libération Bâtiment A31, Laboratoire IMS 33400 Talence
in front of the jury composed of
- Jean-Pierre DA COSTA - Professeur - Université de Bordeaux - Directeur de these
- Sébastien DESTERCKE - Directeur de recherche - Université de Technologie de Compiègne - Rapporteur
- David ROUSSEAU - Professeur - Université d'Angers - Rapporteur
- Anne RUIZ-GAZEN - Professeure - Toulouse School of Economics - Examinateur
- Lionel BOMBRUN - Maître de conférences - Université de Bordeaux - CoDirecteur de these
The agricultural sector is currently facing numerous challenges and structural changes accentuated by demographics, climate change, environmental impact, consumption patterns, competitiveness, among others. To address these challenges, digital technologies are emerging as one of the main levers. In recent years, the ability to acquire large databases, increased computing capabilities, and key theoretical advances have enabled the rise of new learning methods based on deep neural networks. However, as these models began to be deployed in real-world safety-critical use cases, it became clear that they exhibit a significant gap between their performance "in the lab", and their predictive quality "in the real world." This same observation was made during the development of an autonomous spraying system, which must detect and spray herbicide in real time, only where and when needed. Such a system must be reliable and trustworthy, as any untreated weed can multiply rapidly and cause extensive damage to crops, with important losses incurred by the farmers. This use case is a perfect instance of the problem of decision-making under uncertainty. In order to develop more reliable methods to assess the quality of learning models and provide valid guarantees on the quality of predictions and decisions produced by the system, as well as to exploit the multitude of auxiliary data describing environmental and geographical features associated with images, we turn to conformal prediction as a holistic approach to address these issues. In this context, this thesis offers several contributions. (1) First, we propose a novel nonconformity score function, the Penalized Inverse Probability (PIP), and its regularized version (RePIP), and demonstrate how it can jointly optimize the two measures of the usefulness of a conformal predictor, namely efficiency and informativeness. (2) Turning to the practical problem at hand, we integrate the conformal predictor into a complete pipeline that transforms images into spraying decisions and show how it can guarantee at least 100(1-α)% coverage of weeds, where α is the user-defined error tolerance, across three experimental setups emulating real-world scenarios ranging from the simplest (controlled environment) to the most complex (brutal distribution shift). (3) Finally, focusing on metadata, we propose a conceptual framework to model the influence of exogenous factors described by these auxiliary variables on the conformal prediction procedure and propose a new, simple and elegant method based on quantile regression to obtain group-conditional coverage results for observations sharing the same environmental and geographical characteristics. (4) Finally, we develop a new methodology to disentangle the representations learned by the neural network from the influence of exogenous factors described by the auxiliary data so as to learn group-invariant representations, and study its impact on the group-conditional conformal approach.
ED Sociétés, Politique, Santé Publique
Mother-adolescent conflict: a dynamic approach and links with the dyadic relational context and adolescent well-being
by Fiona DUBOST (Laboratoire de Psychologie)
The defense will take place at 13h30 - Amphi Sigalas 3 TER place de la Victoire Batiment C 33 000 BORDEAUX
in front of the jury composed of
- Lyda LANNEGRAND - Professeure des universités - Université de Bordeaux - Directeur de these
- Grégoire ZIMMERMANN - Professeur des universités - Université de Lausanne - Rapporteur
- Claire SAFONT-MOTTAY - Professeure des universités - Université Toulouse Jean Jaurès - Rapporteur
- Baptiste BARBOT - Professeur - Université catholique de Louvain - Examinateur
Adolescence is a period of significant reshaping of the relationship between parent and child, marked by an average increase in the number of conflicts. These conflicts can play a constructive role in the adolescent's autonomy and socio-emotional development. Studies that consider the plurality of conflict characteristics (i.e., frequency, topics, severity, management, emotional impact) and aspects of rigidity/flexibility in the experience of conflict help to clarify why some adolescents seem to benefit from conflict for their psychosocial adjustment and socio-emotional development, while others do not. Nevertheless, few studies attempt to explain and understand these inter-individual differences. To do so, it is necessary to consider the relational context in which conflicts occur, especially regarding attachment security and parenting. This work has three main objectives. Objective 1 aims to study the links between the dyadic relational context with the mother (i.e., regarding attachment security and parenting) and the characteristics of mother-adolescent conflicts perceived by adolescents. Objective 2 aims to examine the aspects of rigidity and flexibility in conflict, considering the intra-individual variability of management styles and emotional incidence, and to study the links between the dyadic relational context and this intra-individual variability. Objective 3 aims to analyze the associations between the dyadic relational context, conflicts, and adolescent well-being. Our study took place in two steps: (1) an initial questionnaire measuring adolescents' attachment security to their mother and mother's parenting perceived by adolescents; (2) a daily diary in four sequences of seven consecutive days, each six weeks apart, measuring daily interactions and possible mother-adolescent conflicts. Our initial sample consisted of 297 adolescents (M age = 14.1, SD = 0.6) (54% girls) who completed the initial questionnaire. Of these, 154 adolescents responded at least once to the daily diary (67% girls). Using a person-centred approach, we identified three attachment security profiles (i.e., inhibiting relationship, secure relationship, hyperactive relationship) and three parenting profiles (i.e., need-supportive, need-thwarting, intermediate). Among the main findings, we observe that adolescents with a need-thwarting parenting profile were also those who had the most daily conflicts with their mother and seemed to experience more negative emotional incidence during their conflicts than other adolescents. In contrast, adolescents with a need-supportive parenting profile had the least negative emotional incidence. Using dynamic systems theory, we have shown that some adolescents display a form of rigidity in their emotional experience and/or conflict management, while others display a form of stability and others a form of flexibility. Furthermore, by considering several characteristics of conflict, we observed differences between adolescents in terms of well-being. Our results contribute to our understanding of mother-adolescent conflict by illustrating the importance of considering more than just the frequency of conflict, but also the plurality of conflict characteristics. Moreover, considering adolescents' perceptions of parenting can help explain interindividual differences in adolescents' experiences of conflict with their mother.