This thesis explores the application of Graph Neural Networks (GNNs), a subset of Geometric Deep Learning methods, for medical image analysis and causal structure learning. Tracking the progression of pathologies in chest radiography poses several challenges in anatomical motion estimation and image registration as this task requires spatially aligning the sequential X-rays and modelling temporal dynamics in change detection. The first part of this thesis proposes a novel approach for change detection in sequential Chest X-ray (CXR) scans using GNNs. The proposed model CheXRelNet utilizes local and global information in CXRs by incorporating intra-image and inter-image anatomical information and showcases an increased downstream performance for predicting the change direction for a pair of CXRs. The second part of the thesis focuses on using GNNs for causal structure learning. The proposed method introduces the concept of intervention on graphs and attempts to relate belief propagation in Bayesian Networks (BN) to message passing in GNNs. Specifically, the proposed method leverages the downstream prediction accuracy of a GNN-based model to infer the correctness of Directed Acyclic Graph (DAG) structures given observational data. Our experimental results do not reveal any correlation between the downstream prediction accuracy of GNNs and structural correctness and hence indicate the harms of directly relating message passing in GNNs to belief propagation in BNs. Overall, this thesis demonstrates the potential of GNNs in medical image analysis and highlights the challenges and limitations of applying GNNs to causal structure learning. / Master of Science / Graphs are a powerful way to represent different real-world data such as interactions between patient observations, co-morbidities, treatments, and relationships between different parts of the human anatomy. They are also a simple and intuitive way of representing causeand- effect relationships between related entities. Graph Neural Networks (GNNs) are neural networks that model such graph-structured data. In this thesis, we explore the applicability of GNNs in analyzing chest radiography and in learning causal relationships. In the first part of this thesis, we propose a method for monitoring disease progression over time in sequential chest X-rays (CXRs). This proposed model CheXRelNet focuses on the interactions within different regions of a CXR and temporal interactions between the same region compared in two CXRs taken at different times for a given patient and accurately predicts the disease progression trend. In the second part of the thesis, we explore if GNNs can be used for identifying causal relationships between covariates. We design a method that uses GNNs for ranking different graph structures based on how well the structures explain the observed data.

Dans ce mémoire par articles, nous nous intéressons à l’apprentissage de modèles causaux à partir de données. L’intérêt de cette entreprise est d’obtenir une meilleure compréhension des données et de pouvoir prédire l’effet qu’aura un changement sur certaines variables d’un système étudié. Comme la découverte de liens causaux est fondamentale en sciences, les méthodes permettant l’apprentissage de modèles causaux peuvent avoir des applications dans une pléthore de domaines scientifiques, dont la génomique, la biologie et l’économie. Nous présentons deux nouvelles méthodes qui ont la particularité d’être des méthodes non-linéaires d’apprentissage de modèles causaux qui sont posées sous forme d’un problème d’optimisation continue sous contrainte. Auparavant, les méthodes d’apprentissage de mo- dèles causaux abordaient le problème de recherche de graphes en utilisant des stratégies de recherche voraces. Récemment, l’introduction d’une contrainte d’acyclicité a permis d’abor- der le problème différemment. Dans un premier article, nous présentons une de ces méthodes: GraN-DAG. Sous cer- taines hypothèses, GraN-DAG permet d’apprendre des graphes causaux à partir de données observationnelles. Depuis la publication du premier article, plusieurs méthodes alternatives ont été proposées par la communauté pour apprendre des graphes causaux en posant aussi le problème sous forme d’optimisation continue avec contrainte. Cependant, aucune de ces méthodes ne supportent les données interventionnelles. Pourtant, les interventions réduisent le problème d’identifiabilité et permettent donc l’utilisation d’architectures neuronales plus expressives. Dans le second article, nous présentons une autre méthode, DCDI, qui a la particularité de pouvoir utiliser des données avec différents types d’interventions. Comme le problème d’identifiabilité est moins important, une des deux instanciations de DCDI est un approximateur de densité universel. Pour les deux méthodes proposées, nous montrons que ces méthodes ont de très bonnes performances sur des données synthétiques et réelles comparativement aux méthodes traditionelles. / In this thesis by articles, we study the learning of causal models from data. The goal of this entreprise is to gain a better understanding of data and to be able to predict the effect of a change on some variables of a given system. Since discovering causal relationships is fundamental in science, causal structure learning methods have applications in many fields that range from genomics, biology, and economy. We present two new methods that have the particularity of being non-linear methods learning causal models casted as a continuous optimization problem subject to a constraint. Previously, causal strutural methods addressed this search problem by using greedy search heuristics. Recently, a new continuous acyclity constraint has allowed to address the problem differently. In the first article, we present one of these non-linear method: GraN-DAG. Under some assumptions, GraN-DAG can learn a causal graph from observational data. Since the publi- cation of this first article, several alternatives methods have been proposed by the community by using the same continuous-constrained optimization formulation. However, none of these methods support interventional data. Nevertheless, interventions reduce the identifiability problem and allow the use of more expressive neural architectures. In the second article, we present another method, DCDI, that has the particularity to leverage data with several kinds of interventions. Since the identifiabiliy issue is less severe, one of the two instantia- tions of DCDI is a universal density approximator. For both methods, we show that these methods have really good performances on synthetic and real-world tasks comparatively to other classical methods.