Cette thèse s'intéresse à des problèmes de prise de décision séquentielle dans lesquels l'acquisition d'information est une fin en soi. Plus précisément, elle cherche d'abord à savoir comment modifier le formalisme des POMDP pour exprimer des problèmes de collecte d'information et à proposer des algorithmes pour résoudre ces problèmes. Cette approche est alors étendue à des tâches d'apprentissage par renforcement consistant à apprendre activement le modèle d'un système. De plus, cette thèse propose un nouvel algorithme d'apprentissage par renforcement bayésien, lequel utilise des transitions locales optimistes pour recueillir des informations de manière efficace tout en optimisant la performance escomptée. Grâce à une analyse de l'existant, des résultats théoriques et des études empiriques, cette thèse démontre que ces problèmes peuvent être résolus de façon optimale en théorie, que les méthodes proposées sont presque optimales, et que ces méthodes donnent des résultats comparables ou meilleurs que des approches de référence. Au-delà de ces résultats concrets, cette thèse ouvre la voie (1) à une meilleure compréhension de la relation entre la collecte d'informations et les politiques optimales dans les processus de prise de décision séquentielle, et (2) à une extension des très nombreux travaux traitant du contrôle de l'état d'un système à des problèmes de collecte d'informations / The purpose of this dissertation is to study sequential decision problems where acquiring information is an end in itself. More precisely, it first covers the question of how to modify the POMDP formalism to model information-gathering problems and which algorithms to use for solving them. This idea is then extended to reinforcement learning problems where the objective is to actively learn the model of the system. Also, this dissertation proposes a novel Bayesian reinforcement learning algorithm that uses optimistic local transitions to efficiently gather information while optimizing the expected return. Through bibliographic discussions, theoretical results and empirical studies, it is shown that these information-gathering problems are optimally solvable in theory, that the proposed methods are near-optimal solutions, and that these methods offer comparable or better results than reference approaches. Beyond these specific results, this dissertation paves the way (1) for understanding the relationship between information-gathering and optimal policies in sequential decision processes, and (2) for extending the large body of work about system state control to information-gathering problems

Cette thèse propose de nouvelles méthodes d'analyse d'enregistrements cérébraux intra-crâniens (potentiels de champs locaux), qui pallie les lacunes de la méthode temps-fréquence standard d'analyse des perturbations spectrales événementielles : le calcul d'une moyenne sur les enregistrements et l'emploi de l'activité dans la période pré-stimulus. La première méthode proposée repose sur la détection de sous-ensembles d'électrodes dont l'activité présente des synchronisations cooccurrentes en un même point du plan temps-fréquence, à l'aide de modèles bayésiens de mélange gaussiens. Les sous-ensembles d'électrodes pertinents sont validés par une mesure de stabilité calculée entre les résultats obtenus sur les différents enregistrements. Pour la seconde méthode proposée, le constat qu'un bruit blanc dans le domaine temporel se transforme en bruit ricien dans le domaine de l'amplitude d'une transformée temps-fréquence a permis de mettre au point une segmentation du signal de chaque enregistrement dans chaque bande de fréquence en deux niveaux possibles, haut ou bas, à l'aide de modèles bayésiens de mélange ricien à deux composantes. À partir de ces deux niveaux, une analyse statistique permet de détecter des régions temps-fréquence plus ou moins actives. Pour développer le modèle bayésien de mélange ricien, de nouveaux algorithmes d'inférence bayésienne variationnelle ont été créés pour les distributions de Rice et de mélange ricien. Les performances des nouvelles méthodes ont été évaluées sur des données artificielles et sur des données expérimentales enregistrées sur des singes. Il ressort que les nouvelles méthodes génèrent moins de faux-positifs et sont plus robustes à l'absence de données dans la période pré-stimulus / This thesis promotes new methods to analyze intracranial cerebral signals (local field potentials), which overcome limitations of the standard time-frequency method of event-related spectral perturbations analysis: averaging over the trials and relying on the activity in the pre-stimulus period. The first proposed method is based on the detection of sub-networks of electrodes whose activity presents cooccurring synchronisations at a same point of the time-frequency plan, using bayesian gaussian mixture models. The relevant sub-networks are validated with a stability measure computed over the results obtained from different trials. For the second proposed method, the fact that a white noise in the temporal domain is transformed into a rician noise in the amplitude domain of a time-frequency transform made possible the development of a segmentation of the signal in each frequency band of each trial into two possible levels, a high one and a low one, using bayesian rician mixture models with two components. From these two levels, a statistical analysis can detect time-frequency regions more or less active. To develop the bayesian rician mixture model, new algorithms of variational bayesian inference have been created for the Rice distribution and the rician mixture distribution. Performances of the new methods have been evaluated on artificial data and experimental data recorded on monkeys. It appears that the new methods generate less false positive results and are more robust to a lack of data in the pre-stimulus period

Dans cette thèse on aborde le problème de la localisation en milieux urbains. Inférer un positionnement précis en ville est important dans nombre d’applications comme la réalité augmentée ou la robotique mobile. Or les systèmes basés sur des capteurs inertiels (IMU) sont sujets à des dérives importantes et les données GPS peuvent souffrir d’un effet de vallée qui limite leur précision. Une solution naturelle est de s’appuyer le calcul de pose de caméra en vision par ordinateur. On remarque que les bâtiments sont les repères visuels principaux de l’humain mais aussi des objets d’intérêt pour les applications de réalité augmentée. On cherche donc à partir d’une seule image à calculer la pose de la caméra par rapport à une base de données de bâtiments références connus. On décompose le problème en deux parties : trouver les références visibles dans l’image courante (reconnaissance de lieux) et calculer la pose de la caméra par rapport à eux. Les approches classiques de ces deux sous-problèmes sont mises en difficultés dans les environnements urbains à cause des forts effets perspectives, des répétitions fréquentes et de la similarité visuelle entre façades. Si des approches spécifiques à ces environnements ont été développés qui exploitent la grande régularité structurelle de tels milieux, elles souffrent encore d’un certain nombre de limitations autant pour la détection et la reconnaissance de façades que pour le calcul de pose par recalage de modèle. La méthode originale développée dans cette thèse s’inscrit dans ces approches spécifiques et vise à dépasser ces limitations en terme d’efficacité et de robustesse aux occultations, aux changements de points de vue et d’illumination. Pour cela, l’idée principale est de profiter des progrès récents de l’apprentissage profond par réseaux de neurones convolutionnels pour extraire de l’information de haut-niveau sur laquelle on peut baser des modèles géométriques. Notre approche est donc mixte Bottom-Up/Top-Down et se décompose en trois étapes clés. Nous proposons tout d’abord une méthode d’estimation de la rotation de la pose de caméra. Les 3 points de fuite principaux des images en milieux urbains, dits points de fuite de Manhattan sont détectés grâce à un réseau de neurones convolutionnels (CNN) qui fait à la fois une estimation de ces points de fuite mais aussi une segmentation de l’image relativement à eux. Une second étape de raffinement utilise ces informations et les segments de l’image dans une formulation bayésienne pour estimer efficacement et plus précisément ces points. L’estimation de la rotation de la caméra permet de rectifier les images et ainsi s’affranchir des effets de perspectives pour la recherche de la translation. Dans une seconde contribution, nous visons ainsi à détecter les façades dans ces images rectifiées et à les reconnaître parmi une base de bâtiments connus afin d’estimer une translation grossière. Dans un soucis d’efficacité, on a proposé une série d’indices basés sur des caractéristiques spécifiques aux façades (répétitions, symétrie, sémantique) qui permettent de sélectionner rapidement des candidats façades potentiels. Ensuite ceux-ci sont classifiés en façade ou non selon un nouveau descripteur CNN contextuel. Enfin la mise en correspondance des façades détectées avec les références est opérée par un recherche au plus proche voisin relativement à une métrique apprise sur ces descripteurs [...] / This thesis addresses the problem of localization in urban areas. Inferring accurate positioning in the city is important in many applications such as augmented reality or mobile robotics. However, systems based on inertial sensors (IMUs) are subject to significant drifts and GPS data can suffer from a valley effect that limits their accuracy. A natural solution is to rely on the camera pose estimation in computer vision. We notice that buildings are the main visual landmarks of human beings but also objects of interest for augmented reality applications. We therefore aim to compute the camera pose relatively to a database of known reference buildings from a single image. The problem is twofold : find the visible references in the current image (place recognition) and compute the camera pose relatively to them. Conventional approaches to these two sub-problems are challenged in urban environments due to strong perspective effects, frequent repetitions and visual similarity between facades. While specific approaches to these environments have been developed that exploit the high structural regularity of such environments, they still suffer from a number of limitations in terms of detection and recognition of facades as well as pose computation through model registration. The original method developed in this thesis is part of these specific approaches and aims to overcome these limitations in terms of effectiveness and robustness to clutter and changes of viewpoints and illumination. For do so, the main idea is to take advantage of recent advances in deep learning by convolutional neural networks to extract high-level information on which geometric models can be based. Our approach is thus mixed Bottom- Up/Top-Down and is divided into three key stages. We first propose a method to estimate the rotation of the camera pose. The 3 main vanishing points of the image of urban environnement, known as Manhattan vanishing points, are detected by a convolutional neural network (CNN) that estimates both these vanishing points and the image segmentation relative to them. A second refinement step uses this information and image segmentation in a Bayesian model to estimate these points effectively and more accurately. By estimating the camera’s rotation, the images can be rectified and thus free from perspective effects to find the translation. In a second contribution, we aim to detect the facades in these rectified images to recognize them among a database of known buildings and estimate a rough translation. For the sake of efficiency, a series of cues based on facade specific characteristics (repetitions, symmetry, semantics) have been proposed to enable the fast selection of facade proposals. Then they are classified as facade or non-facade according to a new contextual CNN descriptor. Finally, the matching of the detected facades to the references is done by a nearest neighbor search using a metric learned on these descriptors. Eventually we propose a method to refine the estimation of the translation relying on the semantic segmentation inferred by a CNN for its robustness to changes of illumination ans small deformations. If we can already estimate a rough translation from these detected facades, we choose to refine this result by relying on the se- mantic segmentation of the image inferred from a CNN for its robustness to changes of illuminations and small deformations. Since the facade is identified in the previous step, we adopt a model-based approach by registration. Since the problems of registration and segmentation are linked, a Bayesian model is proposed which enables both problems to be jointly solved. This joint processing improves the results of registration and segmentation while remaining efficient in terms of computation time. These three parts have been validated on consistent community data sets. The results show that our approach is fast and more robust to changes in shooting conditions than previous methods

Les sociétés modernes dépendent de plus en plus sur les systèmes informatiques et ainsi, il y a de plus en plus de pression sur les équipes de développement pour produire des logiciels de bonne qualité. Plusieurs compagnies utilisent des modèles de qualité, des suites de programmes qui analysent et évaluent la qualité d'autres programmes, mais la construction de modèles de qualité est difficile parce qu'il existe plusieurs questions qui n'ont pas été répondues dans la littérature. Nous avons étudié les pratiques de modélisation de la qualité auprès d'une grande entreprise et avons identifié les trois dimensions où une recherche additionnelle est désirable : Le support de la subjectivité de la qualité, les techniques pour faire le suivi de la qualité lors de l'évolution des logiciels, et la composition de la qualité entre différents niveaux d'abstraction. Concernant la subjectivité, nous avons proposé l'utilisation de modèles bayésiens parce qu'ils sont capables de traiter des données ambiguës. Nous avons appliqué nos modèles au problème de la détection des défauts de conception. Dans une étude de deux logiciels libres, nous avons trouvé que notre approche est supérieure aux techniques décrites dans l'état de l'art, qui sont basées sur des règles. Pour supporter l'évolution des logiciels, nous avons considéré que les scores produits par un modèle de qualité sont des signaux qui peuvent être analysés en utilisant des techniques d'exploration de données pour identifier des patrons d'évolution de la qualité. Nous avons étudié comment les défauts de conception apparaissent et disparaissent des logiciels. Un logiciel est typiquement conçu comme une hiérarchie de composants, mais les modèles de qualité ne tiennent pas compte de cette organisation. Dans la dernière partie de la dissertation, nous présentons un modèle de qualité à deux niveaux. Ces modèles ont trois parties: un modèle au niveau du composant, un modèle qui évalue l'importance de chacun des composants, et un autre qui évalue la qualité d'un composé en combinant la qualité de ses composants. L'approche a été testée sur la prédiction de classes à fort changement à partir de la qualité des méthodes. Nous avons trouvé que nos modèles à deux niveaux permettent une meilleure identification des classes à fort changement. Pour terminer, nous avons appliqué nos modèles à deux niveaux pour l'évaluation de la navigabilité des sites web à partir de la qualité des pages. Nos modèles étaient capables de distinguer entre des sites de très bonne qualité et des sites choisis aléatoirement. Au cours de la dissertation, nous présentons non seulement des problèmes théoriques et leurs solutions, mais nous avons également mené des expériences pour démontrer les avantages et les limitations de nos solutions. Nos résultats indiquent qu'on peut espérer améliorer l'état de l'art dans les trois dimensions présentées. En particulier, notre travail sur la composition de la qualité et la modélisation de l'importance est le premier à cibler ce problème. Nous croyons que nos modèles à deux niveaux sont un point de départ intéressant pour des travaux de recherche plus approfondis. / As society becomes ever more dependent on computer systems, there is more and more pressure on development teams to produce high-quality software. Many companies therefore rely on quality models, program suites that analyse and evaluate the quality of other programs, but building good quality models is hard as there are many questions concerning quality modelling that have yet to be adequately addressed in the literature. We analysed quality modelling practices in a large organisation and identified three dimensions where research is needed: proper support of the subjective notion of quality, techniques to track the quality of evolving software, and the composition of quality judgments from different abstraction levels. To tackle subjectivity, we propose using Bayesian models as these can deal with uncertain data. We applied our models to the problem of anti-pattern detection. In a study of two open-source systems, we found that our approach was superior to state of the art rule-based techniques. To support software evolution, we consider scores produced by quality models as signals and the use of signal data-mining techniques to identify patterns in the evolution of quality. We studied how anti-patterns are introduced and removed from systems. Software is typically written using a hierarchy of components, yet quality models do not explicitly consider this hierarchy. As the last part of our dissertation, we present two level quality models. These are composed of three parts: a component-level model, a second model to evaluate the importance of each component, and a container-level model to combine the contribution of components with container attributes. This approach was tested on the prediction of class-level changes based on the quality and importance of its components: methods. It was shown to be more useful than single-level, traditional approaches. To finish, we reapplied this two-level methodology to the problem of assessing web site navigability. Our models could successfully distinguish award-winning sites from average sites picked at random. Throughout the dissertation, we present not only theoretical problems and solutions, but we performed experiments to illustrate the pros and cons of our solutions. Our results show that there are considerable improvements to be had in all three proposed dimensions. In particular, our work on quality composition and importance modelling is the first that focuses on this particular problem. We believe that our general two-level models are only a starting point for more in-depth research.

Given current rates of anthropogenic environmental change, combined with the increasing lethal and non-lethal mortality threat that human activities pose, there is a vital need to understand wildlife movement and behaviour in human-dominated landscapes to help inform conservation efforts and wildlife management. As long-term monitoring of wildlife populations using Global Positioning System (GPS) telemetry increases, there are new opportunities to quantify change in wildlife movement and behaviour. The objective of this PhD research is to develop novel methodological approaches for quantifying change in spatial-temporal patterns of wildlife movement and habitat by leveraging long time series of GPS telemetry and remotely sensed data. Analyses were focused on the habitat and movement of individuals in the threatened grizzly bear (Ursus arctos) population of Alberta, Canada, which occupies a human-dominated and heterogeneous landscape. Using methods in functional data analysis, a multivariate regionalization approach was developed that effectively summarizes complex spatial-temporal patterns associated with landscape disturbance, as well as recovery, which is often left unaccounted in studies quantifying patterns associated with disturbance. Next, the quasi-experimental framework afforded by a hunting moratorium was used to compare the influence of lethal (i.e., hunting) and non-lethal (i.e., anthropogenic disturbance) human-induced risk on antipredator behaviour of an apex predator, the grizzly bear. In support of the predation risk allocation hypothesis, male bears significantly decrease risky daytime behaviours by 122% during periods of high lethal human-induced risk. Rapid behavioural restoration occurred following the end of the hunt, characterized by diel bimodal movement patterns which may promote coexistence of large predators in human-dominated landscapes. A multi-scale approach using hierarchical Bayesian models, combined with post hoc trend tests and change point detection, was developed to test the influence of landscape disturbance and conditions on grizzly bear home range and movement selection over time. The results, representing the first longitudinal empirical analysis of grizzly bear habitat selection, revealed selection for habitat security at broad scales and for resource availability and habitat permeability at finer spatial scales, which has influenced potential landscape connectivity over time. Finally, combining approaches in movement ecology and conservation physiology, a body condition index was used to characterize how the physiological condition (i.e., internal state) of grizzly bears influences behavioral patterns due to costs and benefits associated with risk avoidance and resource acquisition. The results demonstrated individuals in poorer condition were more likely to engage in risky behaviour associated with anthropogenic disturbance, which highlights complex challenges for carnivore conservation and management of human-carnivore conflict. In summary, this dissertation contributes 1) a multivariate regionalization approach for quantifying spatial-temporal patterns of landscape disturbance and recovery applicable across diverse natural systems, 2) support for the growing theory that apex predators modify behavioural patterns to account for temporal overlap with lethal and non-lethal human-induced risk associated with humans, 3) an integrated approach for considering multi-scale spatial-temporal change in patterns of wildlife habitat selection and landscape connectivity associated with landscape change, 4) a cross-disciplinary framework for considering the impacts of the internal state on behavioural patterns and risk tolerance. / Graduate

Hierarchical Bayesian Models and Matrix factorization methods provide an unsupervised way to learn latent components of data from the grouped or sequence data. For example, in document data, latent component corn-responds to topic with each topic as a distribution over a note vocabulary of words. For many applications, there exist sparse relationships between the domain entities and the latent components of the data. Traditional approaches for topic modelling do not take into account these sparsity considerations. Modelling these sparse relationships helps in extracting relevant information leading to improvements in topic accuracy and scalable solution. In our thesis, we explore these sparsity relationships for di errant applications such as text segmentation, topical analysis and entity resolution in dyadic data through the Bayesian and Matrix tri-factorization approaches, propos-in scalable solutions. In our rest work, we address the problem of segmentation of a collection of sequence data such as documents using probabilistic models. Existing state-of-the-art Hierarchical Bayesian Models are connected to the notion of Complete Exchangeability or Markov Exchangeability. Bayesian Nonpareil-metric Models based on the notion of Markov Exchangeability such as HDP-HMM and Sticky HDP-HMM, allow very restricted permutations of latent variables in grouped data (topics in documents), which in turn lead to com-mutational challenges for inference. At the other extreme, models based on Complete Exchangeability such as HDP allow arbitrary permutations within each group or document, and inference is significantly more tractable as a result, but segmentation is not meaningful using such models. To over-come these problems, we explored a new notion of exchangeability called Block Exchangeability that lies between Markov Exchangeability and Com-plate Exchangeability for which segmentation is meaningful, but inference is computationally less expensive than both Markov and Complete Exchange-ability. Parametrically, Block Exchangeability contains sparser number of transition parameters, linear in number of states compared to the quadratic order for Markov Exchangeability that is still less than that for Complete Exchangeability and for which parameters are on the order of the number of documents. For this, we propose a nonparametric Block Exchangeable model (BEM) based on the new notion of Block Exchangeability, which we have shown to be a superclass of Complete Exchangeability and subclass of Markov Exchangeability. We propose a scalable inference algorithm for BEM to infer the topics for words and segment boundaries associated with topics for a document using the collapsed Gibbs Sampling procedure. Empirical results show that BEM outperforms state-of-the-art nonparametric models in terms of scalability and generalization ability and shows nearly the same segmentation quality on News dataset, Product review dataset and on a Synthetic dataset. Interestingly, we can tune the scalability by varying the block size through a parameter in our model for a small trade-o with segmentation quality. In addition to exploring the association between documents and words, we also explore the sparse relationships for dyadic data, where associations between one pair of domain entities such as (documents, words) and as-associations between another pair such as (documents, users) are completely observed. We motivate the analysis of such dyadic data introducing an additional discrete dimension, which we call topics, and explore sparse relation-ships between the domain entities and the topic, such as of user-topic and document-topic respectively. In our second work, for this problem of sparse topical analysis of dyadic data, we propose a formulation using sparse matrix tri-factorization. This formulation requires sparsity constraints, not only on the individual factor matrices, but also on the product of two of the factors. To the best of our knowledge, this problem of sparse matrix tri-factorization has not been stud-ide before. We propose a solution that introduces a surrogate for the product of factors and enforces sparsity on this surrogate as well as on the individual factors through L1-regularization. The resulting optimization problem is e - cogently solvable in an alternating minimization framework over sub-problems involving individual factors using the well-known FISTA algorithm. For the sub-problems that are constrained, we use a projected variant of the FISTA algorithm. We also show that our formulation leads to independent sub-problems towards solving a factor matrix, thereby supporting parallel implementation leading to a scalable solution. We perform experiments over bibliographic and product review data to show that the proposed framework based on sparse tri-factorization formulation results in better generalization ability and factorization accuracy compared to baselines that use sparse bi-factorization. Even though the second work performs sparse topical analysis for dyadic data, ending sparse topical associations for the users, the user references with di errant names could belong to the same entity and those with same names could belong to different entities. The problem of entity resolution is widely studied in the research community, where the goal is to identify real users associated with the user references in the documents. Finally, we focus on the problem of entity resolution in dyadic data, where associations between one pair of domain entities such as documents-words and associations between another pair such as documents-users are ob.-served, an example of which includes bibliographic data. In our nil work, for this problem of entity resolution in bibliographic data, we propose a Bayesian nonparametric `Sparse entity resolution model' (SERM) exploring the sparse relationships between the grouped data involving grouping of the documents, and the topics/author entities in the group. Further, we also exploit the sparseness between an author entity and the associated author aliases. Grouping of the documents is achieved with the stick breaking prior for the Dirichlet processes (DP). To achieve sparseness, we propose a solution that introduces separate Indian Bu et process (IBP) priors over topics and the author entities for the groups and k-NN mechanism for selecting author aliases for the author entities. We propose a scalable inference for SERM by appropriately combining partially collapsed Gibbs sampling scheme in Focussed topic model (FTM), the inference scheme used for parametric IBP prior and the k-NN mechanism. We perform experiments over bibliographic datasets, Cite seer and Rexa, to show that the proposed SERM model imp-proves the accuracy of entity resolution by ending relevant author entities through modelling sparse relationships and is scalable, when compared to the state-of-the-art baseline

Le sentiment d’agentivité est défini comme le sentiment de contrôler nos actions, et à travers elles, les évènements du monde extérieur. Cet ensemble phénoménologique dépend de notre capacité d’apprendre les contingences entre nos actions et leurs résultats, et un algorithme classique pour modéliser cela vient du domaine de l’apprentissage par renforcement. Dans cette thèse, nous avons utilisé l’approche de modélisation cognitive pour étudier l’interaction entre agentivité et apprentissage par renforcement. Tout d’abord, les participants réalisant une tâche d’apprentissage par renforcement tendent à avoir plus d’agentivité. Cet effet est logique, étant donné que l’apprentissage par renforcement consiste à associer une action volontaire et sa conséquence. Mais nous avons aussi découvert que l’agentivité influence l’apprentissage de deux manières. Le mode par défaut pour apprendre des contingences action-conséquence est que nos actions ont toujours un pouvoir causal. De plus, simplement choisir une action change l’apprentissage de sa conséquence. En conclusion, l’agentivité et l’apprentissage par renforcement, deux piliers de la psychologie humaine, sont fortement liés. Contrairement à des ordinateurs, les humains veulent être en contrôle, et faire les bons choix, ce qui biaise notre aquisition d’information. / Sense of agency or subjective control can be defined by the feeling that we control our actions, and through them effects in the outside world. This cluster of experiences depend on the ability to learn action-outcome contingencies and a more classical algorithm to model this originates in the field of human reinforcementlearning. In this PhD thesis, we used the cognitive modeling approach to investigate further the interaction between perceived control and reinforcement learning. First, we saw that participants undergoing a reinforcement-learning task experienced higher agency; this influence of reinforcement learning on agency comes as no surprise, because reinforcement learning relies on linking a voluntary action and its outcome. But our results also suggest that agency influences reinforcement learning in two ways. We found that people learn actionoutcome contingencies based on a default assumption: their actions make a difference to the world. Finally, we also found that the mere fact of choosing freely shapes the learning processes following that decision. Our general conclusion is that agency and reinforcement learning, two fundamental fields of human psychology, are deeply intertwined. Contrary to machines, humans do care about being in control, or about making the right choice, and this results in integrating information in a one-sided way.

Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.

Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.

La classe des modèles à chaîne de Markov cachée (HMM, Hidden Markov Models) permet, entre autres, de modéliser des données financières. Par exemple, dans ce type de modèle, la distribution du rendement sur un actif financier est exprimée en fonction d'une variable non-observée, une chaîne de Markov, qui représente la volatilité de l'actif. Notons que les dynamiques de cette volatilité sont difficiles à reproduire, car la volatilité est très persistante dans le temps. Les HMM ont la particularité de permettre une variation de la volatilité selon les états de la chaîne de Markov. Historiquement, ces modèles ont été estimés avec un nombre faible de régimes (états), car le nombre de paramètres à estimer explose rapidement avec le nombre de régimes et l'optimisation devient vite difficile. Pour résoudre ce problème une nouvelle sous-classe de modèles à chaîne de Markov cachée, dite à haute dimension, a vu le jour grâce aux modèles dits factoriels et à de nouvelles méthodes de paramétrisation de la matrice de transition. L'objectif de cette thèse est d'étendre cette classe de modèles avec de nouvelles approches plus générales et de montrer leurs applications dans le domaine financier. Dans sa première partie, cette thèse formalise la classe des modèles factoriels à chaîne de Markov cachée et étudie les propriétés théoriques de cette classe de modèles. Dans ces modèles, la dynamique de la volatilité dépend d'une chaîne de Markov latente de haute dimension qui est construite en multipliant des chaînes de Markov de dimension plus faible, appelées composantes. Cette classe englobe les modèles factoriels à chaîne de Markov cachée précédemment proposés dont les composantes sont de dimension deux. Le modèle MDSV (Multifractal Discrete Stochastic Volatility) est introduit afin de pouvoir considérer des composantes de dimension supérieure à deux, généralisant ainsi les modèles factoriels existants. La paramétrisation particulière de ce modèle lui offre suffisamment de flexibilité pour reproduire différentes allures de décroissance de la fonction d'autocorrélation, comme celles qui sont observées sur les données financières. Un cadre est également proposé pour modéliser séparément ou simultanément les données de rendements financiers et de variances réalisées. Une analyse empirique sur 31 séries d'indices financiers montre que le modèle MDSV présente de meilleures performances en termes d'estimation et de prévision par rapport au modèle realized EGARCH. La modélisation par l'entremise des modèles factoriels à chaîne de Markov cachée nécessite qu'on définisse le nombre N de composantes à multiplier et cela suppose qu'il n'existe pas d'incertitude lié à ce nombre. La seconde partie de cette thèse propose, à travers une approche bayésienne, le modèle iFHMV (infinite Factorial Hidden Markov Volatility) qui autorise les données à déterminer le nombre de composantes nécessaires à leur modélisation. En s'inspirant du processus du buffet indien (IBP, Indian Buffet Process), un algorithme est proposé pour estimer ce modèle, sur les données de rendements financiers. Une analyse empirique sur les données de deux indices financiers et de deux actions permet de remarquer que le modèle iFHMV intègre l'incertitude liée au nombre de composantes pour les estimations et les prévisions. Cela lui permet de produire de meilleures prévisions par rapport à des modèles de référence. / Hidden Markov Models (HMMs) are popular tools to interpret, model and forecast financial data. In these models, the return dynamics on a financial asset evolve according to a non-observed variable, a Markov chain, which generally represents the volatility of the asset. This volatility is notoriously difficult to reproduce with statistical models as it is very persistent in time. HMMs allow the volatility to vary according to the states of a Markov chain. Historically, these models are estimated with a very small number of regimes (states), because the number of parameters to be estimated grows quickly with the number of regimes and the optimization becomes difficult. The objective of this thesis is to propose a general framework to construct HMMs with a richer state space and a higher level of volatility persistence. In the first part, this thesis studies a general class of high-dimensional HMMs, called factorial HMMs, and derives its theoretical properties. In these models, the volatility is linked to a high-dimensional Markov chain built by multiplying lower-dimensional Markov chains, called components. We discuss how previously proposed models based on two-dimensional components adhere to the factorial HMM framework. Furthermore, we propose a new process---the Multifractal Discrete Stochastic Volatility (MDSV) process---which generalizes existing factorial HMMs to dimensions larger than two. The particular parametrization of the MDSV model allows for enough flexibility to reproduce different decay rates of the autocorrelation function, akin to those observed on financial data. A framework is also proposed to model financial log-returns and realized variances, either separately or jointly. An empirical analysis on 31 financial indices reveals that the MDSV model outperforms the realized EGARCH model in terms of fitting and forecasting performance. Our MDSV model requires us to pre-specify the number of components and assumes that there is no uncertainty on that number. In the second part of the thesis, we propose the infinite Factorial Hidden Markov Volatility (iFHMV) model as part of a Bayesian framework to let the data drive the selection of the number of components and take into account the uncertainty related to the number of components in the fitting and forecasting procedure. We also develop an algorithm inspired by the Indian Buffet Process (IBP) to estimate the iFHMV model on financial log-returns. Empirical analyses on two financial indices and two stocks show that the iFHMV model outperforms popular benchmarks in terms of forecasting performance.