Bayesian networks can be used to model the respiratory system. Their structure indicate how risk factors, symptoms, and diseases are related and the Conditional Probability Tables enable predictions about a patient’s need for hospitalization. Numerous structure learning algorithms exist for discerning the structure of a Bayesian network, but none can guarantee to find the perfect structure. Employing multiple algorithms can discover relationships between variables that might otherwise remain hidden when relying on a single algorithm. The Maximum Likelihood Estimator is the predominant algorithm for learning the Conditional Probability Tables. However, it faces challenges due to the data fragmentation problem, which can compromise its predictions. Failing to hospitalize patients who require specialized medical care could lead to severe consequences. Therefore, in this thesis, the use of an XGBoost model for learning is proposed as a novel and better method since it does not suffer from data fragmentation. A Bayesian network is constructed combining several structure learning algorithms, and the predictive performance of the Maximum Likelihood Estimator and XGBoost are compared. XGBoost achieved a maximum accuracy of 86.0% compared to the Maximum Likelihood Estimator, which attained an accuracy of 81.5% in predicting future patient hospitalization. In this way, the predictive performance of Bayesian networks has been enhanced. / Bayesianska nätverk kan användas för att modellera andningssystemet. Deras struktur visar hur riskfaktorer, symtom och sjukdomar är relaterade, och de villkorliga sannolikhetstabellerna möjliggör prognoser om en patients behov av sjukhusvård. Det finns många strukturlärningsalgoritmer för att urskilja strukturen i ett bayesianskt nätverk, men ingen kan garantera att hitta den perfekta strukturen. Genom att använda flera algoritmer kan man upptäcka relationer mellan variabler som annars kan förbli dolda när man bara förlitar sig på en enda algoritm. Maximum Likelihood Estimator är den dominerande algoritmen för att lära sig de villkorliga sannolikhetstabellerna. Men den står inför utmaningar på grund av datafragmenteringsproblemet, vilket kan äventyra dess prognoser. Att inte lägga in patienter som behöver specialiserad medicinsk vård kan leda till allvarliga konsekvenser. Därför föreslås i denna avhandling användningen av en XGBoost-modell för inlärning som en ny och bättre metod eftersom den inte lider av datafragmentering. Ett bayesianskt nätverk byggs genom att kombinera flera strukturlärningsalgoritmer, och den prediktiva prestandan för Maximum Likelihood Estimator och XGBoost jämförs. XGBoost uppnådde en maximal noggrannhet på 86,0% jämfört med Maximum Likelihood Estimator, som uppnådde en noggrannhet på 81,5% för att förutsäga framtida patientinläggning. På detta sätt har den prediktiva prestandan för bayesianska nätverk förbättrats.

Extracting knowledge and providing insights into complex mechanisms underlying noisy high-dimensional data sets is of utmost importance in many scientific domains. Statistical modeling has become ubiquitous in the analysis of high dimensional functional data in search of better understanding of cognition mechanisms, in the exploration of large-scale gene regulatory networks in hope of developing drugs for lethal diseases, and in prediction of volatility in stock market in hope of beating the market. Statistical analysis in these high-dimensional data sets is possible only if an estimation procedure exploits hidden structures underlying data. This thesis develops flexible estimation procedures with provable theoretical guarantees for uncovering unknown hidden structures underlying data generating process. Of particular interest are procedures that can be used on high dimensional data sets where the number of samples n is much smaller than the ambient dimension p. Learning in high-dimensions is difficult due to the curse of dimensionality, however, the special problem structure makes inference possible. Due to its importance for scientific discovery, we put emphasis on consistent structure recovery throughout the thesis. Particular focus is given to two important problems, semi-parametric estimation of networks and feature selection in multi-task learning.

L’omniprésente utilisation des plongements de mot dans le traitement des langues naturellesest la preuve de leur utilité et de leur capacité d’adaptation a une multitude de tâches. Ce-pendant, leur nature continue est une importante limite en terme de calculs, de stockage enmémoire et d’interprétation. Dans ce travail de recherche, nous proposons une méthode pourapprendre directement des plongements de mot discrets. Notre modèle est une adaptationd’une nouvelle méthode de recherche pour base de données avec des techniques dernier crien traitement des langues naturelles comme les Transformers et les LSTM. En plus d’obtenirdes plongements nécessitant une fraction des ressources informatiques nécéssaire à leur sto-ckage et leur traitement, nos expérimentations suggèrent fortement que nos représentationsapprennent des unités de bases pour le sens dans l’espace latent qui sont analogues à desmorphèmes. Nous appelons ces unités dessememes, qui, de l’anglaissemantic morphemes,veut dire morphèmes sémantiques. Nous montrons que notre modèle a un grand potentielde généralisation et qu’il produit des représentations latentes montrant de fortes relationssémantiques et conceptuelles entre les mots apparentés. / The ubiquitous use of word embeddings in Natural Language Processing is proof of theirusefulness and adaptivity to a multitude of tasks. However, their continuous nature is pro-hibitive in terms of computation, storage and interpretation. In this work, we propose amethod of learning discrete word embeddings directly. The model is an adaptation of anovel database searching method using state of the art natural language processing tech-niques like Transformers and LSTM. On top of obtaining embeddings requiring a fractionof the resources to store and process, our experiments strongly suggest that our representa-tions learn basic units of meaning in latent space akin to lexical morphemes. We call theseunitssememes, i.e., semantic morphemes. We demonstrate that our model has a greatgeneralization potential and outputs representation showing strong semantic and conceptualrelations between related words.

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.

The goal of the diploma work is to demonstrate the possibilities of montessori education elements implementation into the education of the children with autism spectrum disorders in the preparatory form of the special elementary school. This is performed on the basis of the theoretical knowledge gained by the specific material study and by using the methods of the inspiring practice. The theoretical part has three chapters. It deals with the subject of the persons with mental disorder and is mainly focused on the children with the autism spectrum disorders. It describes the autism spectrum disorders, their etiology, diagnosis and the intervention options for people with the autism spectrum disorders. It is dedicated also to the education of children and pupils with the autism spectrum disorders and the mental disorder within the preparatory form of the special elementary school. It introduces in great detail the montessori pedagogy and its elements. The empirical part states the definition of the research inquiry. It also describes an example of the inspiring practice how the class setting, education outline concept and education materials using the elements of the montessori pedagogy into the education of the children with the autism spectrum disorders in the preparatory form of the special...

<p>Graphs are a natural choice for understanding the associations between variables, and assuming a probabilistic embedding for the graph structure leads to a variety of graphical models that enable us to understand these associations even further. In the realm of high-dimensional data, where the number of associations between interacting variables is far greater than the available number of data points, the goal is to infer a sparse graph. In this thesis, we make contributions in the domain of Bayesian graphical models, where our prior belief on the graph structure, encoded via uncertainty on the model parameters, enables the estimation of sparse graphs.</p> <p><br></p> <p>We begin with the Gaussian Graphical Model (GGM) in Chapter 2, one of the simplest and most famous graphical models, where the joint distribution of interacting variables is assumed to be Gaussian. In GGMs, the conditional independence among variables is encoded in the inverse of the covariance matrix, also known as the precision matrix. Under a Bayesian framework, we propose a novel prior--penalty dual called the `graphical horseshoe-like' prior and penalty, to estimate precision matrix. We also establish the posterior convergence of the precision matrix estimate and the frequentist consistency of the maximum a posteriori (MAP) estimator.</p> <p><br></p> <p>In Chapter 3, we develop a general framework based on local linear approximation for MAP estimation of the precision matrix in GGMs. This general framework holds true for any graphical prior, where the element-wise priors can be written as a Laplace scale mixture. As an application of the framework, we perform MAP estimation of the precision matrix under the graphical horseshoe penalty.</p> <p><br></p> <p>In Chapter 4, we focus on graphical models where the joint distribution of interacting variables cannot be assumed Gaussian. Motivated by the quantile graphical models, where the Gaussian likelihood assumption is relaxed, we draw inspiration from the domain of precision medicine, where personalized inference is crucial to tailor individual-specific treatment plans. With an aim to infer Directed Acyclic Graphs (DAGs), we propose a novel quantile DAG learning framework, where the DAGs depend on individual-specific covariates, making personalized inference possible. We demonstrate the potential of this framework in the regime of precision medicine by applying it to infer protein-protein interaction networks in Lung adenocarcinoma and Lung squamous cell carcinoma.</p> <p><br></p> <p>Finally, we conclude this thesis in Chapter 5, by developing a novel framework to compute the marginal likelihood in a GGM, addressing a longstanding open problem. Under this framework, we can compute the marginal likelihood for a broad class of priors on the precision matrix, where the element-wise priors on the diagonal entries can be written as gamma or scale mixtures of gamma random variables and those on the off-diagonal terms can be represented as normal or scale mixtures of normal. This result paves new roads for model selection using Bayes factors and tuning of prior hyper-parameters.</p>

Dans les annales de l'Intelligence Artificielle (IA), la quête incessante pour émuler la cognition humaine dans les machines a sous-tendu l'évolution technologique, repoussant les limites du potentiel humain et des capacités de résolution de problèmes. L'intégration de l'IA a catalysé des progrès remarquables, pénétrant divers domaines et redéfinissant des industries. Cependant, un défi demeure imperturbable : l'obstacle de la généralisation hors de la distribution (OOD). Alors que l'IA triomphe avec des données familières, elle échoue avec des données en dehors de son domaine d'entraînement. En santé, en finance et au-delà, les limitations de l'IA entravent l'adaptation à des scénarios nouveaux. Cette lacune découle de l'écart entre les schémas appris et les caractéristiques causales et invariantes sous-jacentes, entravant l'adaptabilité à des scénarios inexplorés. Cette thèse franchit des étapes significatives pour aborder cette question en innovant et en exploitant des méthodes issues de l'apprentissage de structure causale et de représentation. Le parcours commence par un algorithme novateur d'apprentissage de structure, les ``Reusable Factor Graphs'', qui tire parti des biais inductifs issus de la causalité et de la cognition humaine pour une meilleure généralisation. Ensuite, en explorant l'apprentissage de représentation causale, nous découvrons des représentations désenchevêtrées centrées sur les objets en utilisant une supervision faible basée sur une connaissance partielle de la structure causale des données. Ces connaissances se conjuguent pour préconiser l'apprentissage conjoint de la structure causale et de la représentation. L'architecture proposée, les ``Reusable Slotwise Mechanisms'' (RSM), relie théorie et pratique, démontrant une promesse réelle à travers ses représentations centrées sur les objets et ses mécanismes causaux réutilisables. Cette fusion offre une solution potentielle pour surmonter les limitations de la généralisation OOD en IA. / In the annals of Artificial Intelligence (AI), an enduring quest to emulate human cognition in machines has underpinned technological evolution, driving the boundaries of human potential and problem-solving capabilities. The integration of AI has catalyzed remarkable progress, infiltrating various domains and redefining industries. Yet, a challenge remains unshaken: the hurdle of out-of-distribution (OOD) generalization. While AI triumphs with familiar data, it falters with data outside its training realm. In healthcare, finance, and beyond, AI's limitations hinder adaptation to novel scenarios. This deficiency arises from the gap between learned patterns and underlying causal and invariant features, hindering adaptability to uncharted scenarios. This thesis takes significant steps toward tackling this issue by innovating and leveraging methods from causal structure and representation learning. The journey begins with an innovative structure learning algorithm, Reusable Factor Graphs, leveraging inductive biases from causality and human cognition for improved generalization. Next, delving into causal representation learning, we uncover object-centric disentangled representations using weak supervision from partial knowledge of the causal structure of data. These insights synergize in advocating joint learning of causal structure and representation. The proposed Reusable Slotwise Mechanisms (RSM) architecture bridges theory and practice, demonstrating real-world promise through its object-centric representations and reusable causal mechanisms. This fusion offers a potential solution for tackling OOD generalization limitations in AI.