Direkt viktoptimering (Direct Weight Optimization, DWO) är en ickeparamterisk systemidentifieringsmetod. DWO bygger på att man skattar ett funktionsvärde i en viss punkt genom en viktad summa av mätvärden, där vikterna optimeras fram. Det faktum att DWO har en inparameter som man måste veta i förväg leder till att man på något sätt vill skatta denna inparameter. Det finns många sätt man kan göra denna skattning på men det centrala i denna uppsats är att skatta inparametern lokalt. Fördelen med detta är att metoden anpassar sig om till exempel systemet ändrar beteende från att variera långsamt till att variera snabbare. Denna typ av metoder brukar kallas adaptiva metoder.Det finns flera metoder för att skatta en inparameter lokalt och anpassningen till DWO är redan klar för ett fåtal som lämpar sig bra. Det är dock inte undersökt vilken av dessa metoder som ger det bästa resultatet för just DWO. Syftet med denna uppsats är alltså att ta reda på hur man lokalt kan skatta en inparameter till DWO på bästa sätt och om DWO är en bra grund att basera en adaptiv metod på.Det har visat sig att DWO kanske är för känslig för en lokalt vald inparameter för att vara en bra grund att basera en adaptiv metod på. Däremot utmärker sig en av metoderna för att skatta inparametern genom att vara mycket bättre än de andra metoderna när den kanske inte borde vara det. Varför den är så bra kan vara ett bra ämne för vidare forskning. / Direct Weight Optimization (DWO) is a nonparametric system identification meth\-od. In DWO the value of a function in a certain point is estimated by a weighted sum of measured values. The weights are obtained as a solution to a convex optimization problem. DWO has a design parameter which has to be chosen or estimated a priori. There are many ways to estimate this parameter. The main focus of this thesis is to estimate this parameter locally. The advantage of estimating the parameter locally is that the estimate will adapt if the system changes behavior from slowly varying to rapidly varying. Estimation methods of this type are usually called adaptive estimation methods.There are a number of adaptive estimation methods and the adaptation of some of these methods to DWO has already been done. There are however no evaluation studies done. The goal with this thesis is therefore to find out how to estimate the parameter in DWO in the best way and to find out whether DWO is a good base for an adaptive method.It turned out that DWO might be too sensitive to local changes in the design parameter to be a good base for an adaptive method. However, one of the adaptive estimation methods stands out from the rest because it is much better than the other methods when it, perhaps, should not. Why this method is good might be a good subject for further research.

<p>As a growing number of agents are deployed in complex environments for scientific research and human well-being, there are increasing demands for designing efficient learning algorithms for these agents to improve their control polices. Such policies must account for uncertainties, including those caused by environmental stochasticity, sensor noise and communication restrictions. These challenges exist in missions such as planetary navigation, forest firefighting, and underwater exploration. Ideally, good control policies should allow the agents to deal with all the situations in an environment and enable them to accomplish their mission within the budgeted time and resources. However, a correct model of the environment is not typically available in advance, requiring the policy to be learned from data. Model-free reinforcement learning (RL) is a promising candidate for agents to learn control policies while engaged in complex tasks, because it allows the control policies to be learned directly from a subset of experiences and with time efficiency. Moreover, to ensure persistent performance improvement for RL, it is important that the control policies be concisely represented based on existing knowledge, and have the flexibility to accommodate new experience. Bayesian nonparametric methods (BNPMs) both allow the complexity of models to be adaptive to data, and provide a principled way for discovering and representing new knowledge.</p><p>In this thesis, we investigate approaches for RL in centralized and decentralized sequential decision-making problems using BNPMs. We show how the control policies can be learned efficiently under model-free RL schemes with BNPMs. Specifically, for centralized sequential decision-making, we study Q learning with Gaussian processes to solve Markov decision processes, and we also employ hierarchical Dirichlet processes as the prior for the control policy parameters to solve partially observable Markov decision processes. For decentralized partially observable Markov decision processes, we use stick-breaking processes as the prior for the controller of each agent. We develop efficient inference algorithms for learning the corresponding control policies. We demonstrate that by combining model-free RL and BNPMs with efficient algorithm design, we are able to scale up RL methods for complex problems that cannot be solved due to the lack of model knowledge. We adaptively learn control policies with concise structure and high value, from a relatively small amount of data.</p> / Dissertation

<p>The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher&rsquo / s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available.</p>

No description available.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Computer Science, 2009. / Includes bibliographical references.

Nous nous intéressons dans cette thèse aux méthodes d’estimation non paramétriques par noyaux récursifs ainsi qu’à leurs applications à la prévision. Nous introduisons dans un premier chapitre une famille d’estimateurs récursifs de la densité indexée par un paramètre ℓ ∈ [0, 1]. Leur comportement asymptotique en fonction de ℓ va nous amener à introduire des critères de comparaison basés sur les biais, variance et erreur quadratique asymptotiques. Pour ces critères, nous comparons les estimateurs entre eux et aussi comparons notre famille à l’estimateur non récursif de la densité de Parzen-Rosenblatt. Ensuite, nous définissons à partir de notre famille d’estimateurs de la densité, une famille d’estimateurs récursifs à noyau de la fonction de régression. Nous étudions ses propriétés asymptotiques en fonction du paramètre ℓ. Nous utilisons enfin les résultats obtenus sur l’estimation de la régression pour construire un prédicteur non paramétrique par noyau. Nous obtenons ainsi une famille de prédicteurs non paramétriques qui permettent de réduire considérablement le temps de calcul. Des exemples d’application sont donnés pour valider la performance de nos estimateurs / The aim of this thesis is to study methods of nonparametric estimation based on recursive kernel and their applications to forecasting. We introduce in the first chapter a family of recursive density estimators indexed by a parameter ℓ ∈ [0, 1]. We study their asymptotic behavior according to ℓ, and then we introduce criteria of comparison based on bias, variance and asymptotic quadratic error. For these criteria, we compare our estimators in terms of ℓ, and also compare our family to the non-recursive density estimator of Parzen-Rosenblatt. As for density, we define a family of recursive kernel estimators of regression function. We study its asymptotic properties according to the parameter ℓ. Finally, results of regression estimation are applied to define a family of nonparametric predictors that reduce considerably the computing time and examples of application are given to validate the performance of our methods

La première partie de ce travail présente un état de l'art des principaux critères non supervisés, non paramétriques, d'évaluation d'une partition, des méthodes d'estimation préliminaires du nombre de classes, et enfin des méthodes de classification supervisées, semi-supervisées et non supervisées. Une analyse des avantages et des inconvénients de ces critères et méthodes est menée. L'analyse des performances des méthodes de classification et des critères d'évaluation a été également conduite via l'application visée dans cette thèse. Une approche de partitionnement non supervisée, non paramétrique et hiérarchique s'avère la plus adaptée au problème posé. En effet, ce type d'approche et plus particulièrement la classification descendante donne un partitionnement à plusieurs niveaux et met en évidence des informations plus détaillées d'un niveau à l'autre, ce qui permet une meilleure interprétation de la richesse d'information apportée par l'imagerie hyperspectrale et ainsi conduire à une meilleure décision. Dans ce sens, la deuxième partie de cette thèse présente, tout d'abord l'approche de classification descendante hiérarchique non supervisée (CDHNS) développée. Cette approche non paramétrique, permet l'obtention de résultats stables et objectifs indépendamment des utilisateurs finaux. Le second développement conduit, porte sur la sélection de bandes spectrales parmi celles qui composent l'image hyperspectrale originale afin de réduire la quantité d'information à traiter avant le processus de classification. Cette méthode est également non supervisée et non paramétrique. L'approche de classification et la méthode de réduction ont été expérimentées et validées sur une image hyperspectrale synthétique construite à partir des images réelles puis sur des images réelles dont l'application porte sur l'identification des différentes classes algales. Les résultats de partitionnement obtenus sans réduction montrent d'une part, la stabilité des résultats et, d'autre part, la discrimination des classes principales (végétation, substrat et eau) dès les premiers niveaux. Les résultats de la sélection des bandes spectrales font apparaître leur bonne répartition sur toute la gamme spectrale du capteur (visible et proche-infrarouge). Les résultats montrent aussi que le partitionnement avec et sans réduction sont globalement similaires. De plus, le temps de calcul est fortement réduit. / The upstream location of the different algal species causing clogging in the EDF nuclear power plants cooling systems along the Channel coastline, by analyzing hyperspectral aerial image is today the most appropriate means. Indeed, hyperspectral imaging allows, through its spatial resolution and its broad spectral range covering the areas of visible and near infrared, the objective discrimination of plant species on the foreshore, necessarily yielding accurate maps on large coastal areas. To provide a solution to this problem and achieve the objectives, the work conducted within the framework of this thesis lies in the development of unsupervised partitioning approaches to data with large spectral and spatial dimensions. The first part of this work presents a state of the art of main unsupervised criteria, and nonparametric, for partitioning evaluation, the preliminary methods for estimating the number of classes, and finally, supervised, semi-supervised and unsupervised classification methods. An analysis of the advantages and drawbacks of these methods and criteria is conducted. The analysis of the performances of these classification methods and evaluation criteria was also conducted through the application targeted in this thesis. An unsupervised, nonparametric, hierarchical partitioning approach appears best suited to the problem. Indeed, this type of approach, and particularly the descending classification, gives a partitioning at several levels and highlights more detailed information from one level to another, allowing a better interpretation of the wealth of information provided by hyperspectral imaging and therefore leading to a better decision. In this sense, the second part of this thesis presents, firstly the unsupervised hierarchical descending classification (UHDC) approach developed. This nonparametric approach allows obtaining stable and objective results regardless of end users. The second development proposed concerns the selection of spectral bands from those that make up the original hyperspectral image, in order to reduce the amount of information to be processed before the classification process. This method is also unsupervised and nonparametric. The classification approach and the reduction method have been tested and validated on a synthetic hyperspectral image constructed from real images, and then on real images, with application to the identification of different algal classes. The partitioning results obtained without reduction show firstly, the stability of the results and, secondly, the discrimination of the main classes (vegetation, substrate and water) from the first levels. The results of the spectral bands selection method show that the retained bands are well distributed over the entire spectral range of the sensor (visible and near-infrared). The results also show that partitioning results with and without reduction are broadly similar. Moreover, the computation time is greatly reduced.

Plusieurs auteurs ont proposé récemment des modèles et des algorithmes pour l'estimation nonparamétrique de mélanges multivariés finis dont l'identifiabilité n'est pas toujours assurée. Entre les modèles considérés, l'hypothèse des coordonnées indépendantes conditionnelles à la sous-population de provenance des individus fait l'objet d'une attention croissante, en raison des développements théoriques et pratiques envisageables, particulièrement avec la multiplicité des variables qui entrent en jeu dans le framework statistique moderne. Dans ce travail, nous considérons d'abord un modèle plus général supposant l'indépendance, conditionnellement à la composante, de blocs multivariés de coordonnées au lieu de coordonnées univariées, permettant toute structure de dépendance à l'intérieur de ces blocs. Par conséquent, les fonctions de densité des blocs sont complètement multivariées et non paramétriques. Nous présentons des arguments d'identifiabilité et introduisons pour l'estimation dans ce modèle deux algorithmes méthodologiques dont les procédures de calcul ressemblent à un véritable algorithme EM mais incluent une étape additionnelle d'estimation de densité: un algorithme rapide montrant l'efficacité empirique sans justification théorique, et un algorithme lissé possédant une propriété de monotonie comme certain algorithme EM, mais plus exigeant en terme de calcul. Nous discutons également les méthodes efficaces en temps de calcul pour l'estimation et proposons quelques stratégies. Ensuite, nous considérons une extension multivariée des modèles de mélange utilisés dans le cadre de tests d'hypothèses multiples, permettant une nouvelle version multivariée de contrôle du False Discovery Rate. Nous proposons une version contrainte de notre algorithme précédent, adaptée spécialement à ce modèle. Le comportement des algorithmes de type EM que nous proposons est étudié numériquement dans plusieurs expérimentations de Monte Carlo et sur des données réelles de grande dimension et comparé avec les méthodes existantes dans la littérature. En n, les codes de nos nouveaux algorithmes sont progressivement ajoutés sous forme de nouvelles fonctions dans le package en libre accès mixtools pour le logiciel de statistique R. / Recently several authors have proposed models and estimation algorithms for finite nonparametric multivariate mixtures, whose identifiability is typically not obvious. Among the considered models, the assumption of independent coordinates conditional on the subpopulation from which each observation is drawn is subject of an increasing attention, in view of the theoretical and practical developments it allows, particularly with multiplicity of variables coming into play in the modern statistical framework. In this work we first consider a more general model assuming independence, conditional on the component, of multivariate blocks of coordinates instead of univariate coordinates, allowing for any dependence structure within these blocks. Consequently, the density functions of these blocks are completely multivariate and nonparametric. We present identifiability arguments and introduce for estimation in this model two methodological algorithms whose computational procedures resemble a true EM algorithm but include an additional density estimation step: a fast algorithm showing empirical efficiency without theoretical justification, and a smoothed algorithm possessing a monotony property as any EM algorithm does, but more computationally demanding. We also discuss computationally efficient methods for estimation and derive some strategies. Next, we consider a multivariate extension of the mixture models used in the framework of multiple hypothesis testings, allowing for a new multivariate version of the False Discovery Rate control. We propose a constrained version of our previous algorithm, specifically designed for this model. The behavior of the EM-type algorithms we propose is studied numerically through several Monte Carlo experiments and high dimensional real data, and compared with existing methods in the literature. Finally, the codes of our new algorithms are progressively implemented as new functions in the publicly-available package mixtools for the R statistical software.

Orientadores: Nancy Lopes Garcia, Ronaldo Dias / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T04:43:13Z (GMT). No. of bitstreams: 1 Ludwig_GuilhermeVieiraNunes_M.pdf: 4540322 bytes, checksum: c767b4a6c7cd883a70e9ebbc33fe04ec (MD5) Previous issue date: 2011 / Resumo: O objetivo desta dissertação é desenvolver estimadores não paramétricos para a função de covariância de dados funcionais agregados, que consistem em combinações lineares de dados funcionais que não podem ser observados separadamente. Estes métodos devem ser capazes de produzir estimativas que separem a covariância típica de cada uma das subpopulações que geram os dados, e que sejam funções não negativas definidas. Sob estas restrições, foi definida uma classe de funções de covariância não estacionarias, à qual resultados da teoria de estimação de covariância de processos estacionários podem ser estendidos. Os métodos desenvolvidos foram ilustrados com a aplicação em dois problemas reais: a estimação do perfil de consumidores de energia elétrica, em função do tempo, e a estimação da transmitância de substâncias puras em espectroscopia de infravermelho, através da inspeção de misturas, em função do espectro da luz / Abstract: The goal of this dissertation is to develop nonparametric estimators for the covariance function of aggregated functional data, which consists into linear combinations of functional data that cannot be sampled separately. Such methods must be able to produce estimates that not only separate the typical covariance of the subpopulations composing the data, but also be nonnegative definite functions. Under these restrictions, a class of nonstationary covariance functions was proposed, to which stationary processes' covariance function estimation results can be readily extended. The developed methods were illustrated with an application to two real problems: the estimation of electric energy consumers' profiles, as a function of the time of the day, and the estimation of the transmittance of pure substances in infrared spectroscopy, while inspecting mixtures of them, as a function of light spectrum / Mestrado / Estatistica Não Parametrica / Mestre em Estatística

Orientadores: Ronaldo Dias, Nancy Lopes Garcia / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T03:32:13Z (GMT). No. of bitstreams: 1 Nascimento_FernandoFerrazdo_M.pdf: 973412 bytes, checksum: 97b1cf4137bd59eb99ae987305700439 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho, comparamos diversas técnicas de previsão de IBNR (Incurred But Not Reported) para dados de um triângulo Run-OjJ, desde as mais simples, como por exemplo as técnicas Chain- Ladder e a técnica da Separação, até as técnicas mais sofisticadas, considerando modelos Log-Normais ou pela distribuição Poisson Composta. Além disso, nosso trabalho enfatiza a necessidade do uso de técnicas não-paramétricas, considerando um modelo de truncamento das variáveis. Foi possível mostrar que, mesmo não tendo nenhuma informação sobre a distribuição dos dados, é possível estimar o IBNR com menor erro e variabilidade do que as técnicas usuais conhecidas. Para fazer as comparações, foram realizadas simulações de sinistros ocorrendo através de um Processo de Poisson não homogêneo, e com dependência no tempo de relato e valor do sinistro. A medida de comparação utilizada foi o Erro Quadrático Médio (EQM) entre os valores simulados e os valores previstos por cada técnica. A abordagem paramétrica, quando os dados provém de uma distribuição Poisson Composta, apresentou o menor EQM dentre todas as técnicas. Entretanto, se não há informação sobre a distribuição dos dados, a técnica de Mista de truncamento foi a melhor entre as não-paramétricas / Abstract: We compare several forecast techniques for IBNR(Incurred But Not Reported) from a Run-Off triangle data, since the most simple techniques like Chain-Ladder and Separation Technique, to the more complex using Log-Normal models and Compound Poisson distribution. Therefore, exist the necessity of the use of Nonparametric techniques, using a model that consider variable Truncation. It was possible shown that, when we don't have any information about the data, it's possible estimate de IBNR forecasting with less mistake and variability than the usual techniques. For make the forecasting, we used claims simulations occurring by a nonhomogeneous Poisson process and with dependence entry the time to report and value paid for one claim. The measure of comparison used was the Mean Square Error (MSE) of simulated values and forecasting values for each technique. The parametric boarding when the data come from a Compound Poisson distribution, was the best MSE entry all techniques. However, when we don't have any information about the data, the Truncation Technique was the best of the nonparametric techniques / Mestrado / Mestre em Estatística