We develop a family of Bayesian algorithms built around Gaussian processes for various problems posed by sensor networks. We firstly introduce an iterative Gaussian process for multi-sensor inference problems, and show how our algorithm is able to cope with data that may be noisy, missing, delayed and/or correlated. Our algorithm can also effectively manage data that features changepoints, such as sensor faults. Extensions to our algorithm allow us to tackle some of the decision problems faced in sensor networks, including observation scheduling. Along these lines, we also propose a general method of global optimisation, Gaussian process global optimisation (GPGO), and demonstrate how it may be used for sensor placement. Our algorithms operate within a complete Bayesian probabilistic framework. As such, we show how the hyperparameters of our system can be marginalised by use of Bayesian quadrature, a principled method of approximate integration. Similar techniques also allow us to produce full posterior distributions for any hyperparameters of interest, such as the location of changepoints. We frame the selection of the positions of the hyperparameter samples required by Bayesian quadrature as a decision problem, with the aim of minimising the uncertainty we possess about the values of the integrals we are approximating. Taking this approach, we have developed sampling for Bayesian quadrature (SBQ), a principled competitor to Monte Carlo methods. We conclude by testing our proposals on real weather sensor networks. We further benchmark GPGO on a wide range of canonical test problems, over which it achieves a significant improvement on its competitors. Finally, the efficacy of SBQ is demonstrated in the context of both prediction and optimisation.

<div>Researchers and scientists across various areas face the perennial challenge of selecting experimental conditions or inputs for computer simulations in order to achieve promising results.</div><div> The aim of conducting these experiments could be to study the production of a material that has great applicability.</div><div> One might also be interested in accurately modeling and analyzing a simulation of a physical process through a high-fidelity computer code.</div><div> The presence of noise in the experimental observations or simulator outputs, called aleatory uncertainty, is usually accompanied by limited amount of data due to budget constraints.</div><div> This gives rise to what is known as epistemic uncertainty. </div><div> This problem of designing of experiments with limited number of allowable experiments or simulations under aleatory and epistemic uncertainty needs to be treated in a Bayesian way.</div><div> The aim of this thesis is to extend the state-of-the-art in Bayesian optimal design of experiments where one can optimize and infer statistics of the expensive experimental observation(s) or simulation output(s) under uncertainty.</div>

Les problèmes aux valeurs et fonctions propres surviennent fréquemment dans la théorie et dans les applications des processus stochastiques. Cependant quelques-uns seulement admettent une solution explicite; la résolution est alors généralement obtenue par la théorie généralisée de Sturm-Liouville pour les opérateurs différentiels. Les problèmes plus généraux ne peuvent pas être résolus sous une forme fermée et le sujet de cette thèse est l'analyse spectrale asymptotique des processus gaussiens fractionnaires et ses applications. Dans la première partie, nous développons une méthodologie pour l'analyse spectrale des opérateurs de covariance de type fractionnaire, correspondant à une famille importante de processus, incluant le processus fractionnaire d'Ornstein-Uhlenbeck, le mouvement brownien fractionnaire intégré et le mouvement brownien fractionnaire mixte. Nous obtenons des approximations asymptotiques du second ordre pour les valeurs propres et les fonctions propres. Au chapitre 2, nous considérons le problème aux valeurs et fonctions propres pour l'opérateur de covariance des ponts gaussiens. Nous montrons comment l'asymptotique spectrale d'un pont peut être dérivée de celle de son processus de base, en prenant comme exemple le cas du pont brownien fractionnaire. Dans la dernière partie, nous considérons trois applications représentatives de la théorie développée: le problème de filtrage des signaux gaussiens fractionnaires dans le bruit blanc, le problème de grande déviation pour le processus d'Ornstein-Uhlenbeck gouverné par un mouvement brownien fractionnaire mixte et probabilités des petites boules pour les processus gaussiens fractionnaires. / Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do are usually solved by reduction to the generalized Sturm-Liouville theory for differential operators.The more general eigenproblems are not solvable in closed form and the subject of this thesis is the asymptotic spectral analysis of the fractional Gaussian processes and its applications.In the first part, we develop methodology for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes that includes the fractional Ornstein-Uhlenbeck process, the integrated fractional Brownian motion and the mixed fractional Brownian motion. We obtain accurate second order asymptotic approximations for both the eigenvalues and the eigenfunctions. In Chapter 2 we consider the covariance eigenproblem for Gaussian bridges. We show how the spectral asymptotics of a bridge can bederived from that of its base process, considering, as an example, the case of the fractional Brownian bridge. In the final part we consider three representative applications of the developed theory: filtering problem of fractional Gaussian signals in white noise, large deviation properties of the maximum likelihood drift parameter estimator for the Ornstein-Uhlenbeck process driven by mixed fractional Brownian motion and small ball probabilities for the fractional Gaussian processes.

A navegação autônoma é um dos problemas fundamentais na área da robótica móvel. Algoritmos capazes de conduzir um robô até o seu destino de maneira segura e eficiente são um pré-requisito para que robôs móveis possam executar as mais diversas tarefas que são atribuídas a eles com sucesso. Dependendo da complexidade do ambiente e da tarefa que deve ser executada, a programação de algoritmos de navegação não é um problema de solução trivial. Esta tese trata do desenvolvimento de sistemas de navegação autônoma baseados em técnicas de aprendizado supervisionado. Mais especificamente, foram abordados dois problemas distintos: a navegação de robôs/- veículos em ambientes urbanos e a navegação de robôs em ambientes não estruturados. No primeiro caso, o robô/veículo deve evitar obstáculos e se manter na via navegável, a partir de exemplos fornecidos por um motorista humano. No segundo caso, o robô deve identificar e evitar áreas irregulares (maior vibração), reduzindo o consumo de energia. Nesse caso, o aprendizado foi realizado a partir de informações obtidas por sensores. Em ambos os casos, algoritmos de aprendizado supervisionado foram capazes de permitir que os robôs navegassem de maneira segura e eficiente durante os testes experimentais realizados / Autonomous navigation is a fundamental problem in the field of mobile robotics. Algorithms capable of driving a robot to its destination safely and efficiently are a prerequisite for mobile robots to successfully perform different tasks that may be assigned to them. Depending on the complexity of the environment and the task to be executed, programming of navigation algorithms is not a trivial problem. This thesis approaches the development of autonomous navigation systems based on supervised learning techniques. More specifically, two distinct problems have been addressed: a robot/vehicle navigation in urban environments and robot navigation in unstructured environments. In the first case, the robot/vehicle must avoid obstacles and keep itself in the road based on examples provided by a human driver. In the second case, the robot should identify and avoid unstructured areas (higher vibration), reducing energy consumption. In this case, learning was based on information obtained by sensors. In either case, supervised learning algorithms have been capable of allowing the robots to navigate in a safe and efficient manner during the experimental tests

Audiobook reading has traditionally been used for educational purposes but has in recent times grown into a popular alternative to the more traditional means of consuming literature. In order to differentiate themselves from other players in the market, but also provide their users enjoyable literature, several audiobook companies have lately directed their efforts on producing own content. Creating highly rated content is, however, no easy task and one reoccurring challenge is how to make a bestselling story. In an attempt to identify latent features shared by successful audiobooks and evaluate proposed methods for literary quantification, this thesis employs an array of frameworks from the field of Statistics, Machine Learning and Natural Language Processing on data and literature provided by Storytel - Sweden’s largest audiobook company. We analyze and identify important features from a collection of 3077 Swedish books concerning their promotional and literary success. By considering features from the aspects Metadata, Theme, Plot, Style and Readability, we found that popular books are typically published as a book series, cover 1-3 central topics, write about, e.g., daughter-mother relationships and human closeness but that they also hold, on average, a higher proportion of verbs and a lower degree of short words. Despite successfully identifying these, but also other factors, we recognized that none of our models predicted “bestseller” adequately and that future work may desire to study additional factors, employ other models or even use different metrics to define and measure popularity. From our evaluation of the literary quantification methods, namely topic modeling and narrative approximation, we found that these methods are, in general, suitable for Swedish texts but that they require further improvement and experimentation to be successfully deployed for Swedish literature. For topic modeling, we recognized that the sole use of nouns provided more interpretable topics and that the inclusion of character names tended to pollute the topics. We also identified and discussed the possible problem of word inflections when modeling topics for more morphologically complex languages, and that additional preprocessing treatments such as word lemmatization or post-training text normalization may improve the quality and interpretability of topics. For the narrative approximation, we discovered that the method currently suffers from three shortcomings: (1) unreliable sentence segmentation, (2) unsatisfactory dictionary-based sentiment analysis and (3) the possible loss of sentiment information induced by translations. Despite only examining a handful of literary work, we further found that books written initially in Swedish had narratives that were more cross-language consistent compared to books written in English and then translated to Swedish.

Machine learning algorithms has its applications in almost all areas of our daily lives. This is mainly due to its ability to learn complex patterns and insights from massive datasets. With the increase in the data at a high rate, it is becoming necessary that the algorithms are resource-efficient and scalable. Gaussian processes are one of the efficient techniques in non linear modelling, but has limited practical applications due to its computational complexity. This thesis studies how parallelism techniques can be applied to optimize performance of Gaussian process regression and empirically assesses parallel learning of a sequential GP and a distributed Gaussian Process Regression algorithm with Random Projection approximation implemented in SPARK framework. These techniques were tested on the dataset provided by Volvo Cars. From the experiments, it is shown that training the GP model with 45k records or 219 ≈106 data points takes less than 30 minutes on a spark cluster with 8 nodes. With sufficient computing resources these algorithms can handle arbitrarily large datasets. / Maskininlärningsalgoritmer har sina applikationer inom nästan alla områden i vårt dagliga liv. Detta beror främst på dess förmåga att lära sig komplexa mönster och insikter från massiva datamängder. Med ökningen av data i en hög takt, blir det nödvändigt att algoritmerna är resurseffektiva och skalbara. Gaussiska processer är en av de effektiva teknikerna i icke-linjär modellering, men har begränsade praktiska tillämpningar på grund av dess beräkningskomplexitet. Den här uppsatsen studerar hur parallellismtekniker kan användas för att optimera prestanda för Gaussisk processregression och utvärderar parallellt inlärning av en sekventiell GP och distribuerad Gaussian Process Regression algoritm med Random Projection approximation implementerad i SPARK ramverk. Dessa tekniker testades på en datamängd från Volvo Cars. Från experimenten visas att det krävs mindre än 30 minuter att träna GP-modellen med 45k poster eller 219 ≈106 datapunkter på ett Spark-kluster med 8 noder. Med tillräckliga datoressurser kan dessa algoritmer hantera godtyckligt stora datamängder.

Nous étudions le comportement asymptotique de statistiques ou fonctionnelles liées à des processus à longue mémoire saisonnière. Nous nous concentrons sur les lignes de Donsker et sur le processus empirique. Les suites considérées sont de la forme $G(X_n)$ où $(X_n)$ est un processus gaussien ou linéaire. Nous montrons que les résultats que Taqqu et Dobrushin ont obtenus pour des processus à longue mémoire dont la covariance est à variation régulière à l'infini peuvent être en défaut en présence d'effets saisonniers. Les différences portent aussi bien sur le coefficient de normalisation que sur la nature du processus limite. Notamment nous montrons que la limite du processus empirique bi-indexé, bien que restant dégénérée, n'est plus déterminée par le degré de Hermite de la fonction de répartition des données. En particulier, lorsque ce degré est égal à 1, la limite n'est plus nécessairement gaussienne. Par exemple on peut obtenir une combinaison de processus de Rosenblatt indépendants. Ces résultats sont appliqués à quelques problèmes statistiques comme le comportement asymptotique des U-statistiques, l'estimation de la densité et la détection de rupture.

Le développement des véhicules autonomes a reçu une attention croissant ces dernières années, notamment les secteurs de la défense et de l'industrie automobile. L'intérêt pour l'industrie automobile est motivé par la conception de véhicules sûrs et confortables. Une raison commune derrière la plupart des accidents de la circulation est due au manque de vigilance du conducteur sur la route. Cette thèse se trouve dans le problématique de l'estimation des risques de collision pour un véhicule dans les secondes qui suivent en condition de circulation urbaines. Les systèmes actuellement disponibles dans le commerce sont pour la plupart conçus pour prévenir les collisions avant, arrières, ou latérales. Ces systèmes sont généralement équipés d'un capteur de type radar, à l'arrière, à l'avant ou sur les côtés pour mesurer la vitesse et la distance aux obstacles. Les algorithmes pour déterminer le risque de collision sont fondés sur des variantes du TTC (time-to-collision en anglais). Cependant, un véhicule peut se trouver dans des situations où les routes ne sont pas droites et l'hypothèse que le mouvement est linéaire ne tient pas pour le calcul du TTC. Dans ces situations, le risque est souvent sous-estimé. De plus, les instances où les routes ne sont pas tout droit se trouve assez souvent dans les environnement urbain ; par exemple, les rond point ou les intersections. Un argument de cette thèse est que, savoir simplement qu'il y ait un objet à une certaine position et à une instance spécifique dans le temps ne suffit pas à évaluer sa sécurité dans le futur. Un système capable de comprendre les comportements de déplacement du véhicule est indispensable. En plus, les contraintes environnementales doivent être prises en considération. Le cas le plus simple du mouvement « libre » est d'abord traité. Dans cette situation il n'ya pas de contraintes environnementales ou de comportement explicite. Ensuite, les contraintes environnementales des routes sur trafic urbain et le comportement des conducteurs des véhicules sont introduits et pris en compte explicitement. Cette thèse propose un modèle probabiliste pour les trajectoires des véhicules fondé sur le processus gaussien (GP). Son avantage est le pouvoir d'exprimer le mouvement dans le futur indépendamment de la discrétisation d'espace et d'état. Les comportements des conducteurs sont modélisés avec une variante du modèle de Markov caché. La combinaison de ces deux modèles donne un modèle probabiliste de l'évolution complète du véhicule dans le temps. En plus, une méthode générale pour l'évaluation probabiliste des risques de collision est présentée, où différentes valeurs de risque, chacun avec sa propre sémantique.

Localization of Drosophila embryos in images is a fundamental step in an automatic computational system for the exploration of gene-gene interaction on Drosophila. Contour extraction of embryonic images is challenging due to many variations in embryonic images. In the thesis work, we develop a localization framework based on the analysis of connected components of edge pixels in a scale space. We propose criteria to select optimal scales for embryonic localization. Furthermore, we propose a scale mapping strategy to compress the range of a scale space in order to improve the efficiency of the localization framework. The effectiveness of the proposed framework and the scale mapping strategy are validated in our experiments.

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised classification tasks. In this thesis, we propose new algorithms for solving semi-supervised binary classification problem using GP regression (GPR) models. The algorithms are closely related to semi-supervised classification based on support vector regression (SVR) and maximum margin clustering. The proposed algorithms are simple and easy to implement. Also, the hyper-parameters are estimated without resorting to expensive cross-validation technique. The algorithm based on sparse GPR model gives a sparse solution directly unlike the SVR based algorithm. Use of sparse GPR model helps in making the proposed algorithm scalable. The results of experiments on synthetic and real-world datasets demonstrate the efficacy of proposed sparse GP based algorithm for semi-supervised classification.