Global ETD Search

61	[en] APPROXIMATE NEAREST NEIGHBOR SEARCH FOR THE KULLBACK-LEIBLER DIVERGENCE / [pt] BUSCA APROXIMADA DE VIZINHOS MAIS PRÓXIMOS PARA DIVERGÊNCIA DE KULLBACK-LEIBLER 19 March 2018 (has links) [pt] Em uma série de aplicações, os pontos de dados podem ser representados como distribuições de probabilidade. Por exemplo, os documentos podem ser representados como modelos de tópicos, as imagens podem ser representadas como histogramas e também a música pode ser representada como uma distribuição de probabilidade. Neste trabalho, abordamos o problema do Vizinho Próximo Aproximado onde os pontos são distribuições de probabilidade e a função de distância é a divergência de Kullback-Leibler (KL). Mostramos como acelerar as estruturas de dados existentes, como a Bregman Ball Tree, em teoria, colocando a divergência KL como um produto interno. No lado prático, investigamos o uso de duas técnicas de indexação muito populares: Índice Invertido e Locality Sensitive Hashing. Os experimentos realizados em 6 conjuntos de dados do mundo real mostraram que o Índice Invertido é melhor do que LSH e Bregman Ball Tree, em termos de consultas por segundo e precisão. / [en] In a number of applications, data points can be represented as probability distributions. For instance, documents can be represented as topic models, images can be represented as histograms and also music can be represented as a probability distribution. In this work, we address the problem of the Approximate Nearest Neighbor where the points are probability distributions and the distance function is the Kullback-Leibler (KL) divergence. We show how to accelerate existing data structures such as the Bregman Ball Tree, by posing the KL divergence as an inner product embedding. On the practical side we investigated the use of two, very popular, indexing techniques: Inverted Index and Locality Sensitive Hashing. Experiments performed on 6 real world data-sets showed the Inverted Index performs better than LSH and Bregman Ball Tree, in terms of queries per second and precision. [pt] DIVERGENCIA KULLBACK-LEIBER [pt] ARVORES DE BREGMAN [pt] HASH SENSIVEL A LOCALIDADE [pt] INDICES INVERTIDOS [pt] BUSCA DE VIZINHOS MAIS PROXIMOS [en] KULLBACK-LEIBLER DIVERGENCE [en] BREGMAN BALL TREE [en] LOCALITY SENSITIVE HASHING [en] INVERTED INDEX [en] NEAREST NEIGHBOR SEARCH
62	Studies on two specific inverse problems from imaging and finance Rückert, Nadja 20 July 2012 (has links) (PDF) This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial diﬀerential equation. The option prices are only available as discrete noisy observations so that the main diﬃculty is the ill-posedness of the numerical diﬀerentiation. Finite diﬀerence schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these diﬃculties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial diﬀerential equation and evaluate the performance of the ﬁnite diﬀerence schemes and the new algorithm for synthetic and real option prices. Tikhonov-Regularisierung Kullback-Leibler Totale Variation Poissonverteilte Daten Bildverarbeitung Wahl des Regularisierungsparameters Diskrepanzprinzip L-Kurve Quasi-Optimalitätskriterium PET Black-Scholes-Modell Volatilität Dupire Call-Option Regularisierung durch Diskretisierung Parameter Identifikationsalgorithmus Tikhonov-Regularization Kullback-Leibler Total Variation Poisson distributed data discrepancy principle L-curve method quasi-optimality criterion PET Black-Scholes model volatility Dupire call option regularization by discretization imaging finance ddc:515 ddc:519 Tichonov-Regularisierung Black-Scholes-Modell Volatilität Regularisierungsverfahren Poisson-Verteilung Bildverarbeitung Call-Option Parameter <Mathematik>
63	Studies on two specific inverse problems from imaging and finance Rückert, Nadja 16 July 2012 (has links) This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regularization. After a general consideration of Tikhonov-type regularization for data corrupted by Poisson noise, we examine the methods for choosing the regularization parameter numerically on the basis of two test images and real PET data. In Part II we consider the estimation of the volatility function from observed call option prices with the explicit formula which has been derived by Dupire using the Black-Scholes partial diﬀerential equation. The option prices are only available as discrete noisy observations so that the main diﬃculty is the ill-posedness of the numerical diﬀerentiation. Finite diﬀerence schemes, as regularization by discretization of the inverse and ill-posed problem, do not overcome these diﬃculties when they are used to evaluate the partial derivatives. Therefore we construct an alternative algorithm based on the weak formulation of the dual Black-Scholes partial diﬀerential equation and evaluate the performance of the ﬁnite diﬀerence schemes and the new algorithm for synthetic and real option prices. info:eu-repo/classification/ddc/515 ddc:515 info:eu-repo/classification/ddc/519 ddc:519
64	Stratégies optimistes en apprentissage par renforcement Filippi, Sarah 24 November 2010 (has links) (PDF) Cette thèse traite de méthodes « model-based » pour résoudre des problèmes d'apprentissage par renforcement. On considère un agent confronté à une suite de décisions et un environnement dont l'état varie selon les décisions prises par l'agent. Ce dernier reçoit tout au long de l'interaction des récompenses qui dépendent à la fois de l'action prise et de l'état de l'environnement. L'agent ne connaît pas le modèle d'interaction et a pour but de maximiser la somme des récompenses reçues à long terme. Nous considérons différents modèles d'interactions : les processus de décisions markoviens, les processus de décisions markoviens partiellement observés et les modèles de bandits. Pour ces différents modèles, nous proposons des algorithmes qui consistent à construire à chaque instant un ensemble de modèles permettant d'expliquer au mieux l'interaction entre l'agent et l'environnement. Les méthodes dites « model-based » que nous élaborons se veulent performantes tant en pratique que d'un point de vue théorique. La performance théorique des algorithmes est calculée en terme de regret qui mesure la différence entre la somme des récompenses reçues par un agent qui connaîtrait à l'avance le modèle d'interaction et celle des récompenses cumulées par l'algorithme. En particulier, ces algorithmes garantissent un bon équilibre entre l'acquisition de nouvelles connaissances sur la réaction de l'environnement (exploration) et le choix d'actions qui semblent mener à de fortes récompenses (exploitation). Nous proposons deux types de méthodes différentes pour contrôler ce compromis entre exploration et exploitation. Le premier algorithme proposé dans cette thèse consiste à suivre successivement une stratégie d'exploration, durant laquelle le modèle d'interaction est estimé, puis une stratégie d'exploitation. La durée de la phase d'exploration est contrôlée de manière adaptative ce qui permet d'obtenir un regret logarithmique dans un processus de décision markovien paramétrique même si l'état de l'environnement n'est que partiellement observé. Ce type de modèle est motivé par une application d'intérêt en radio cognitive qu'est l'accès opportuniste à un réseau de communication par un utilisateur secondaire. Les deux autres algorithmes proposés suivent des stratégies optimistes : l'agent choisit les actions optimales pour le meilleur des modèles possibles parmi l'ensemble des modèles vraisemblables. Nous construisons et analysons un tel algorithme pour un modèle de bandit paramétrique dans un cas de modèles linéaires généralisés permettant ainsi de considérer des applications telles que la gestion de publicité sur internet. Nous proposons également d'utiliser la divergence de Kullback-Leibler pour la construction de l'ensemble des modèles vraisemblables dans des algorithmes optimistes pour des processus de décision markoviens à espaces d'états et d'actions finis. L'utilisation de cette métrique améliore significativement le comportement de des algorithmes optimistes en pratique. De plus, une analyse du regret de chacun des algorithmes permet de garantir des performances théoriques similaires aux meilleurs algorithmes de l'état de l'art. [MATH] Mathematics Apprentissage statistique Apprentissage par renforcement Processus de Décisions Markovien Bandit Analyse du Regret Algorithmes model-based optimistes Divergence de Kullback-Leibler
65	Computational Bayesian techniques applied to cosmology Hee, Sonke January 2018 (has links) This thesis presents work around 3 themes: dark energy, gravitational waves and Bayesian inference. Both dark energy and gravitational wave physics are not yet well constrained. They present interesting challenges for Bayesian inference, which attempts to quantify our knowledge of the universe given our astrophysical data. A dark energy equation of state reconstruction analysis finds that the data favours the vacuum dark energy equation of state $w {=} -1$ model. Deviations from vacuum dark energy are shown to favour the super-negative ‘phantom’ dark energy regime of $w {< } -1$, but at low statistical significance. The constraining power of various datasets is quantified, finding that data constraints peak around redshift $z = 0.2$ due to baryonic acoustic oscillation and supernovae data constraints, whilst cosmic microwave background radiation and Lyman-$\alpha$ forest constraints are less significant. Specific models with a conformal time symmetry in the Friedmann equation and with an additional dark energy component are tested and shown to be competitive to the vacuum dark energy model by Bayesian model selection analysis: that they are not ruled out is believed to be largely due to poor data quality for deciding between existing models. Recent detections of gravitational waves by the LIGO collaboration enable the first gravitational wave tests of general relativity. An existing test in the literature is used and sped up significantly by a novel method developed in this thesis. The test computes posterior odds ratios, and the new method is shown to compute these accurately and efficiently. Compared to computing evidences, the method presented provides an approximate 100 times reduction in the number of likelihood calculations required to compute evidences at a given accuracy. Further testing may identify a significant advance in Bayesian model selection using nested sampling, as the method is completely general and straightforward to implement. We note that efficiency gains are not guaranteed and may be problem specific: further research is needed.

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