With the advent of the internet and advances in computing power, the collection of very large high-dimensional datasets has become feasible { understanding and modelling high-dimensional data has thus become a crucial activity, especially in the field of pattern recognition. Since non-parametric density estimators are data-driven and do not require or impose a pre-defined probability density function on data, they are very powerful tools for probabilistic data modelling and analysis. Conventional non-parametric density estimation methods, however, originated from the field of statistics and were not originally intended to perform density estimation in high-dimensional features spaces { as is often encountered in real-world pattern recognition tasks. Therefore we address the fundamental problem of non-parametric density estimation in high-dimensional feature spaces in this study. Recent advances in maximum-likelihood (ML) kernel density estimation have shown that kernel density estimators hold much promise for estimating nonparametric probability density functions in high-dimensional feature spaces. We therefore derive two new iterative kernel bandwidth estimators from the maximum-likelihood (ML) leave one-out objective function and also introduce a new non-iterative kernel bandwidth estimator (based on the theoretical bounds of the ML bandwidths) for the purpose of bandwidth initialisation. We name the iterative kernel bandwidth estimators the minimum leave-one-out entropy (MLE) and global MLE estimators, and name the non-iterative kernel bandwidth estimator the MLE rule-of-thumb estimator. We compare the performance of the MLE rule-of-thumb estimator and conventional kernel density estimators on artificial data with data properties that are varied in a controlled fashion and on a number of representative real-world pattern recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces and to determine whether these estimators are suitable for initialising the bandwidths of iterative ML bandwidth estimators in high dimensions. We find that there are several regularities in the relative performance of conventional kernel density estimators across different tasks and dimensionalities and that the Silverman rule-of-thumb bandwidth estimator performs reliably across most tasks and dimensionalities of the pattern recognition datasets considered, even in high-dimensional feature spaces. Based on this empirical evidence and the intuitive theoretical motivation that the Silverman estimator optimises the asymptotic mean integrated squared error (assuming a Gaussian reference distribution), we select this estimator to initialise the bandwidths of the iterative ML kernel bandwidth estimators compared in our simulation studies. We then perform a comparative simulation study of the newly introduced iterative MLE estimators and other state-of-the-art iterative ML estimators on a number of artificial and real-world high-dimensional pattern recognition tasks. We illustrate with artificial data (guided by theoretical motivations) under what conditions certain estimators should be preferred and we empirically confirm on real-world data that no estimator performs optimally on all tasks and that the optimal estimator depends on the properties of the underlying density function being estimated. We also observe an interesting case of the bias-variance trade-off where ML estimators with fewer parameters than the MLE estimator perform exceptionally well on a wide variety of tasks; however, for the cases where these estimators do not perform well, the MLE estimator generally performs well. The newly introduced MLE kernel bandwidth estimators prove to be a useful contribution to the field of pattern recognition, since they perform optimally on a number of real-world pattern recognition tasks investigated and provide researchers and practitioners with two alternative estimators to employ for the task of kernel density estimation. / PhD (Information Technology), North-West University, Vaal Triangle Campus, 2014

Increases in alcohol availability have caused crime rates to escalate across multiple regions around the world. As individuals consume alcohol they experience impaired judgment and a dose-response escalation in aggression that, for some, leads to criminal behaviour. By limiting alcohol availability it is possible to reduce crime; however, the literature remains mixed on the best practices for alcohol access restrictions. Variances in data quality and statistical methods have created an inconsistency in the reported effects of price, hour of sales, and alcohol outlet restrictions on crime. Most notably, the research findings are influenced by the different effects of alcohol establishments on crime. The objective of this PhD research was to develop novel quantitative approaches to establish the extent alcohol access (outlets) influences the frequency of crime (liquor, disorder, violent) at a fine level of spatial detail (x,y locations and block groups). Analyses were focused on British Columbia’s largest cities where policies are changing to allow greater alcohol access, but little is known about the crime-alcohol access relationship. Two reviews were conducted to summarize and contrast the effects of alcohol access restrictions (price, hours of sales, alcohol outlet density) on crime, and evaluate the state-of-the-art in statistical methods used to associate crime with alcohol availability. Results highlight key methodological limitations and fragmentation in alcohol policy effects on crime across multiple disciplines. Using a spatial data science approach, recommendations were made to increase spatial detail in modelling to limit the scale effects on crime-alcohol association. Providing guidelines for alcohol-associated crime reduction, kernel density space-time change detection methods were also applied to provide the first evaluation of active policing on alcohol-associated crime in the Granville St. entertainment district of Vancouver, British Columbia. Foot patrols were able to reduce the spatial density of crime, but hot spots of liquor and violent assaults remained within 60m proximity to bars (nightclubs). To estimate the association between alcohol establishment size, and type on disorder and violent crime reports in block groups across Victoria, British Columbia a Poisson Generalized Linear Model with spatial lag effects was applied. Estimates provided the factor increase (1.0009) expected in crime for every additional patron seat added to an establishment capacity, and indicated that establishments should be spaced greater than 300m a part to significantly reduce alcohol-associated crime. These results offer the first evaluation of seating capacity and establishment spacing on alcohol-associated crime for alcohol license decision making, and are pertinent at a time when alcohol policy reform is being prioritized by the British Columbia government. In summary, this dissertation contributes 1) cross-disciplinary policy and methodological reviews, 2) expands the application of spatial statistics to alcohol-attributable crime research, 3) advances knowledge on local scale of effects of different alcohol establishment types on crime, 4) and develops transferable models to estimate the effects of alcohol establishment seating capacity and proximity between establishments on the frequency of crime. / Graduate / 2018-02-27

The financial situations of households are among the key factors influencing the market in the country. This thesis focuses on analyzing and evaluating the potential and financial position of Czech and Slovak households. It deals mainly with the analysis of data from the years 2004 to 2008, which is the period of the entrance of Slovakia and the Czech Republic into the European Union. The theoretical section describes events in particular, the economic and financial situation of households in those two countries during the observed years. The practical process uses different types of statistical methods and analysis to identify the financial situation in the Czech Republic and Slovakia, as well as identify the differences between them. The conclusion summarizes the findings and observations of the research findings, which are implemented in the practical section.

A destruição de florestas tropicais é intensa e pode levar à extinção de espécies sensíveis à fragmentação. Na Mata Atlântica, mamíferos com importantes funções no equilíbrio do ecossistema, como Panthera onca (onça-pintada), já estão ausentes em grande parte do bioma. Logo, é de extrema urgência compreender os processos que influenciam na permanência dessas espécies em uma área, para evitar futuras extinções locais. Assim, o objetivo geral deste estudo foi analisar as influências das características ambientais sobre a riqueza e ocorrência de mamíferos terrestres de médio e grande porte e as relações espaço-temporais entre o predador de topo, mesopredadores e presas em uma área de Mata Atlântica contíngua ao Parque Estadual da Serra do Mar com recente histórico de perturbação (Parque das Neblinas, Bertioga, SP). A coleta de dados foi realizada por armadilhamento fotográfico, durante 90 dias em 2013 e 2014, em 27 pontos amostrais, distantes 1 km entre si. As características ambientais avaliadas foram altitude, densidade de drenagem, precipitação média, temperatura média, número de palmitos (Euterpe edulis) e presença de trilhas naturais. Para analisar as influências do ambiente sobre a riqueza e ocorrência de espécies (com mais de três registros por ano) foram utilizados Modelos Lineares Generalizados. Para as demais análises, as espécies foram agrupadas em predador, mesopredadores, presas de grande, médio e pequeno porte. O período e sobreposição de atividade destes grupos foram estimados por meio da densidade de Kernel. A abundância foi estimada para mesopredadores e presas, através de modelos N-mixture. Para analisar a probabilidade de ocupação e detecção do predador de topo foram usados modelos de ocupação single-season. Foram amostrados 18 mamíferos terrestres de médio e grande porte, dos quais nove estão ameaçados de extinção ((Cabassous unicinctus (tatu-de-rabo-mole), Cuniculus paca (paca), Leopardus guttulus (gato-do-mato-pequeno), Leopardus pardalis (jaguatirica), Leopardus wiedii (gato-maracajá), Pecari tajacu (cateto), Puma concolor (onça-parda), Puma yagouaroundi (gato-mourisco) e Tapirus terrestris (anta)). A riqueza de espécies foi positivamente influenciada pelo maior volume de chuvas e a ocorrência da maioria das espécies (C. unicinctus, Dasypus novemcinctus (tatu-galinha), P. concolor, Sylvilagus brasiliensis (tapiti) e T. terrestris) foi influenciada pela densidade de drenagem em 2013. Em 2014, a riqueza não foi explicada por nenhuma característica e apenas quatro espécies sofreram influência de alguma característica ambiental. O predador de topo registrado foi catemeral, os mesopredadores e presas de grande porte mostraram-se mais noturnos e presas de médio e pequeno porte foram mais diurnas. Presas menores apresentaram a maior sobreposição total com o predador (Δ1=0,72). A influência sobre a probabilidade de ocupação da área pelo predador variou entre os anos, tendo sido pela abundância de presas de grande e pequeno porte, em 2013, e pela abundância de presas de médio porte, em 2014. A detecção foi influenciada apenas em 2014, de forma negativa pelas ocasiões. A partir destes resultados foi possível identificar as características ambientais que devem ser mantidas na área, como a disponibilidade de recursos hídricos e abundância de presas, a fim de conservar das espécies resilientes. / The destruction of tropical forests is alarming and may lead to the extinction of species susceptible to fragmentation. In the Atlantic Forest, mammals with important functions in the ecosystem balance, such as Panthera onca (jaguar), are already absent in part of the biome. Therefore, it is urgent to understand the processes that influence the permanence of these species in an area, in order to prevent future local extinctions. Thus, this study aimed to analyze the influence of environmental characteristics on the richness and occurrence of terrestrial mammals of medium and large size; as well as the spatio-temporal relationship between the top predator, mesopredator and preys, in the Atlantic foreste area continuos continuous with Serra do Mar State Park, with recent degradation history (Neblinas Park, Bertioga, State of São Paulo). Sample data was collected by camera trapping for 90 days in 2013 and 2014, 27 sampling points 1km distant from each other. The environmental characteristics were altitude, drainage density, average rainfall, average temperature, number of palm hearts (Euterpe edulis) and the presence of nature trails. Generalized Linear Models were used to analyze the environmental influences on the richness and occurrence of species (with more than 3 records per year). For the other analyses, species were grouped into predator, mesopredators, preys of large, medium and small size. The period and overlap activity of these groups were estimated by the Kernel density. Abundance was estimated for mesopredators and prey through N-mixture models. Single-season occupancy models were used to analyze the probability of occupancy and detection of top predators. A total of 18 terrestrial mammals of medium and large size were sampled, with nine of them being threatened with extinction: Cabassous unicinctus (naked-tailed armadillo), Cuniculus paca (paca), Leopardus guttulus (oncilla), Leopardus pardalis (ocelot), Leopardus wiedii (margay), Pecari tajacu (collared peccary), Puma concolor (cougar), Puma yagouaroundi (jaguarundi) and Tapirus terrestris (tapir). In the 2013, the species richness was positively influenced by the largest volume of precipitation and the species occurrence (C. unicinctus, Dasypus novemcinctus (tatu-galinha), P. concolor, Sylvilagus brasiliensis (tapiti) e T. terrestris) was interfered by the drainage density. In 2014, richness was not explained by any of the environmental characteristics mentioned and only four species have suffered influence of them. The top predator recorded was catemeral, the mesopredator and large prey were mainly nocturnal and prey of medium and small size were mainly daylight. Smaller prey had the highest total overlap with the predator (Δ1=0.72). The influence on the probability of occupancy of the area by the predator varied between the years: in 2013 it was the abundance of large and small preys, and in 2014, the influence was the abundance of medium preys. The detection was negatively influenced by the occasion only in 2014. Our findings showed the environmental characteristics that should be maintained in the area, such as water resources and abundance of prey, for conservation of Atlantic Forest and its fauna community.

Cette thèse explore l’utilisation des modèles de contours déformables pour la segmentation basée sur la forme des images médicales. Nous apportons des contributions sur deux fronts: dans le problème de l’apprentissage statistique, où le modèle est formé à partir d’un ensemble d’images annotées, et le problème de l’inférence, dont le but est de segmenter une image étant donnée un modèle. Nous démontrons le mérite de nos techniques sur une grande base d’images à rayons X, où nous obtenons des améliorations systématiques et des accélérations par rapport à la méthode de l’état de l’art. Concernant l’apprentissage, nous formulons la formation de la fonction de score des modèles de contours déformables en un problème de prédiction structurée à grande marge et construisons une fonction d’apprentissage qui vise à donner le plus haut score à la configuration vérité-terrain. Nous intégrons une fonction de perte adaptée à la prédiction structurée pour les modèles de contours déformables. En particulier, nous considérons l’apprentissage avec la mesure de performance consistant en la distance moyenne entre contours, comme une fonction de perte. L’utilisation de cette fonction de perte au cours de l’apprentissage revient à classer chaque contour candidat selon sa distance moyenne du contour vérité-terrain. Notre apprentissage des modèles de contours déformables en utilisant la prédiction structurée avec la fonction zéro-un de perte surpasse la méthode [Seghers et al. 2007] de référence sur la base d’images médicales considérée [Shiraishi et al. 2000, van Ginneken et al. 2006]. Nous démontrons que l’apprentissage avec la fonction de perte de distance moyenne entre contours améliore encore plus les résultats produits avec l’apprentissage utilisant la fonction zéro-un de perte et ce d’une quantité statistiquement significative.Concernant l’inférence, nous proposons des solveurs efficaces et adaptés aux problèmes combinatoires à variables spatiales discrétisées. Nos contributions sont triples: d’abord, nous considérons le problème d’inférence pour des modèles graphiques qui contiennent des boucles, ne faisant aucune hypothèse sur la topologie du graphe sous-jacent. Nous utilisons un algorithme de décomposition-coordination efficace pour résoudre le problème d’optimisation résultant: nous décomposons le graphe du modèle en un ensemble de sous-graphes en forme de chaines ouvertes. Nous employons la Méthode de direction alternée des multiplicateurs (ADMM) pour réparer les incohérences des solutions individuelles. Même si ADMM est une méthode d’inférence approximative, nous montrons empiriquement que notre implémentation fournit une solution exacte pour les exemples considérés. Deuxièmement, nous accélérons l’optimisation des modèles graphiques en forme de chaîne en utilisant l’algorithme de recherche hiérarchique A* [Felzenszwalb & Mcallester 2007] couplé avec les techniques d’élagage développés dans [Kokkinos 2011a]. Nous réalisons une accélération de 10 fois en moyenne par rapport à l’état de l’art qui est basé sur la programmation dynamique (DP) couplé avec les transformées de distances généralisées [Felzenszwalb & Huttenlocher 2004]. Troisièmement, nous intégrons A* dans le schéma d’ADMM pour garantir une optimisation efficace des sous-problèmes en forme de chaine. En outre, l’algorithme résultant est adapté pour résoudre les problèmes d’inférence augmentée par une fonction de perte qui se pose lors de l’apprentissage de prédiction des structure, et est donc utilisé lors de l’apprentissage et de l’inférence. [...] / This thesis explores the use of discriminatively trained deformable contour models (DCMs) for shape-based segmentation in medical images. We make contributions in two fronts: in the learning problem, where the model is trained from a set of annotated images, and in the inference problem, whose aim is to segment an image given a model. We demonstrate the merit of our techniques in a large X-Ray image segmentation benchmark, where we obtain systematic improvements in accuracy and speedups over the current state-of-the-art. For learning, we formulate training the DCM scoring function as large-margin structured prediction and construct a training objective that aims at giving the highest score to the ground-truth contour configuration. We incorporate a loss function adapted to DCM-based structured prediction. In particular, we consider training with the Mean Contour Distance (MCD) performance measure. Using this loss function during training amounts to scoring each candidate contour according to its Mean Contour Distance to the ground truth configuration. Training DCMs using structured prediction with the standard zero-one loss already outperforms the current state-of-the-art method [Seghers et al. 2007] on the considered medical benchmark [Shiraishi et al. 2000, van Ginneken et al. 2006]. We demonstrate that training with the MCD structured loss further improves over the generic zero-one loss results by a statistically significant amount. For inference, we propose efficient solvers adapted to combinatorial problems with discretized spatial variables. Our contributions are three-fold:first, we consider inference for loopy graphical models, making no assumption about the underlying graph topology. We use an efficient decomposition-coordination algorithm to solve the resulting optimization problem: we decompose the model’s graph into a set of open, chain-structured graphs. We employ the Alternating Direction Method of Multipliers (ADMM) to fix the potential inconsistencies of the individual solutions. Even-though ADMMis an approximate inference scheme, we show empirically that our implementation delivers the exact solution for the considered examples. Second,we accelerate optimization of chain-structured graphical models by using the Hierarchical A∗ search algorithm of [Felzenszwalb & Mcallester 2007] couple dwith the pruning techniques developed in [Kokkinos 2011a]. We achieve a one order of magnitude speedup in average over the state-of-the-art technique based on Dynamic Programming (DP) coupled with Generalized DistanceTransforms (GDTs) [Felzenszwalb & Huttenlocher 2004]. Third, we incorporate the Hierarchical A∗ algorithm in the ADMM scheme to guarantee an efficient optimization of the underlying chain structured subproblems. The resulting algorithm is naturally adapted to solve the loss-augmented inference problem in structured prediction learning, and hence is used during training and inference. In Appendix A, we consider the case of 3D data and we develop an efficientmethod to find the mode of a 3D kernel density distribution. Our algorithm has guaranteed convergence to the global optimum, and scales logarithmically in the volume size by virtue of recursively subdividing the search space. We use this method to rapidly initialize 3D brain tumor segmentation where we demonstrate substantial acceleration with respect to a standard mean-shift implementation. In Appendix B, we describe in more details our extension of the Hierarchical A∗ search algorithm of [Felzenszwalb & Mcallester 2007] to inference on chain-structured graphs.

Ce travail s’inscrit dans une tentative de liaison entre la communauté classique de la Vision par ordinateur et la communauté du traitement d’images de documents, analyse être connaissance (DAR). Plus particulièrement, nous abordons la question des détecteurs de points d’intérêts et des descripteurs locaux dans une image. Ceux-ci ayant été conçus pour des images issues du monde réel, ils ne sont pas adaptés aux problématiques issues du document dont les images présentent des caractéristiques visuelles différentes.Notre approche se base sur la résolution du problème de la confusion entre les descripteurs,ceux-ci perdant leur pouvoir discriminant. Notre principale contribution est un algorithme de réduction de la confusion potentiellement présente dans un ensemble de vecteurs caractéristiques d’une même image, ceci par une approche probabiliste en filtrant les vecteurs fortement confusifs. Une telle conception nous permet d’appliquer des algorithmes d’extractions de descripteurs sans avoir à les modifier ce qui constitue une passerelle entre ces deux mondes. / This work tries to establish a bridge between the field of classical computer vision and document analysis and recognition. Specificaly, we tackle the issue of keypoints detection and associated local features computation in the image. These are not suitable for document images since they were designed for real-world images which have different visual characteristic. Our approach is based on resolving the issue of reducing the confusion between feature vectors since they usually lose their discriminant power with document images. Our main contribution is an algorithm reducing the confusion between local features by filtering the ones which present a high confusing risk. We are tackling this by using tools from probability theory. Such a method allows us to apply features extraction algorithms without having to modify them, thus establishing a bridge between these two worlds.

We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Like coral reefs worldwide, the Florida Reef Tract has dramatically declined within the past two decades. Monitoring of 40 sites throughout the Florida Keys National Marine Sanctuary has undertaken a multiple-parameter approach to assess spatial and temporal changes in the status of the ecosystem. The objectives of the present study consist of the following: In chapter one, we review past coral reef studies; emphasis is placed on recent studies on the stony corals of reefs in the lower Florida Keys. We also review the economic impact of coral reefs on the state of Florida. In chapter two, we identify the underlying probability distribution function of the stony coral cover proportions and we obtain better estimates of the statistical properties of stony coral cover proportions. Furthermore, we improve present procedures in constructing confidence intervals of the true median and mean for the underlying probability distribution. In chapter three, we investigate the applicability of the normal probability distribution assumption made on the pseudovalues obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies. We investigate a new and more effective approach to estimating the Shannon-Wiener and Simpson's diversity index. In chapter four, we develop the best possible estimate of the probability distribution function of the jackknifing pseudovalues, obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies, using the xi nonparametric kernel density estimate method. This nonparametric procedure gives very effective estimates of the statistical measures for the jackknifing pseudovalues. Lastly, the present study develops a predictive statistical model for stony coral cover. In addition to identifying the attributable variables that influence the stony coral cover data of the lower Florida Keys, we investigate the possible interactions present. The final form of the developed statistical model gives good estimates of the stony coral cover given some information of the attributable variables. Our nonparametric and parametric approach to analyzing coral reef data provides a sound basis for developing efficient ecosystem models that estimate future trends in coral reef diversity. This will give the scientists and managers another tool to help monitor and maintain a healthy ecosystem.

對樣本資料之機率密度函數f(x)的無母數估計方法，一直是統計推論領域的研究重點之一，而且在通訊理論與圖形辨別上有非常重要的地位。傳統的文獻對密度函數的估計方法大部分著重於獨立樣本的情形。對於時間數列的相關樣本（例如：經濟指標或加權股票指數資料）比較少提到。本文針對具有弱相關性的穩定時間數列樣本，嘗試提出一個核密度估計的方法並探討其性質。 / For a sample data, the nonparametric estimation of a probability density f(x) is always one point of research problem in statistical inference and plays an important role in communication theory and pattern recognition. Traditionally, the literature dealing with density estimation when the observations are independent is extensive. Time series sample with weak dependence, (for example, an economic indicator or a stock market index data), less in this aspect of discussion. Our main purpose is concerned with the estimation of the probability density function f(x) of a stationary time series sample and discusses some properties of this kernel density.

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.