Pour l’apprentissage de modèles prédictifs, la qualité des données disponibles joue un rôle important quant à la fiabilité des prédictions obtenues. Ces données d’apprentissage ont, en pratique, l’inconvénient d’être très souvent imparfaites ou incertaines (imprécises, bruitées, etc). Ce travail de doctorat s’inscrit dans ce cadre où la théorie des fonctions de croyance est utilisée de manière à adapter des outils statistiques classiques aux données incertaines.Le modèle prédictif choisi est l’arbre de décision qui est un classifieur basique de l’intelligence artificielle mais qui est habituellement construit à partir de données précises. Le but de la méthodologie principale développée dans cette thèse est de généraliser les arbres de décision aux données incertaines (floues, probabilistes,manquantes, etc) en entrée et en sortie. L’outil central d’extension des arbres de décision aux données incertaines est une vraisemblance adaptée aux fonctions de croyance récemment proposée dans la littérature dont certaines propriétés sont ici étudiées de manière approfondie. De manière à estimer les différents paramètres d’un arbre de décision, cette vraisemblance est maximisée via l’algorithme E2M qui étend l’algorithme EM aux fonctions de croyance. La nouvelle méthodologie ainsi présentée, les arbres de décision E2M, est ensuite appliquée à un cas réel : la prédiction de la qualité du caoutchouc naturel. Les données d’apprentissage, essentiellement culturales et climatiques, présentent de nombreuses incertitudes qui sont modélisées par des fonctions de croyance adaptées à ces imperfections. Après une étude statistique standard de ces données, des arbres de décision E2M sont construits et évalués en comparaison d’arbres de décision classiques. Cette prise en compte des incertitudes des données permet ainsi d’améliorer très légèrement la qualité de prédiction mais apporte surtout des informations concernant certaines variables peu prises en compte jusqu’ici par les experts du caoutchouc. / During the learning of predictive models, the quality of available data is essential for the reliability of obtained predictions. These learning data are, in practice very often imperfect or uncertain (imprecise, noised, etc). This PhD thesis is focused on this context where the theory of belief functions is used in order to adapt standard statistical tools to uncertain data.The chosen predictive model is decision trees which are basic classifiers in Artificial Intelligence initially conceived to be built from precise data. The aim of the main methodology developed in this thesis is to generalise decision trees to uncertain data (fuzzy, probabilistic, missing, etc) in input and in output. To realise this extension to uncertain data, the main tool is a likelihood adapted to belief functions,recently presented in the literature, whose behaviour is here studied. The maximisation of this likelihood provide estimators of the trees’ parameters. This maximisation is obtained via the E2M algorithm which is an extension of the EM algorithm to belief functions.The presented methodology, the E2M decision trees, is applied to a real case : the natural rubber quality prediction. The learning data, mainly cultural and climatic,contains many uncertainties which are modelled by belief functions adapted to those imperfections. After a simple descriptiv statistic study of the data, E2M decision trees are built, evaluated and compared to standard decision trees. The taken into account of the data uncertainty slightly improves the predictive accuracy but moreover, the importance of some variables, sparsely studied until now, is highlighted.

Orientador: Víctor Hugo Lachos Dávila / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:55:07Z (GMT). No. of bitstreams: 1 Massuia_MoniqueBettio_M.pdf: 2926597 bytes, checksum: 2a1154c0a61b13f369e8390159fc4c3e (MD5) Previous issue date: 2015 / Resumo: Este trabalho tem como objetivo principal apresentar os modelos de regressão lineares com respostas censuradas sob a classe de distribuições de mistura de escala skew-normal (SMSN), visando generalizar o clássico modelo Tobit ao oferecer alternativas mais robustas à distribuição Normal. Um estudo de inferência clássico é desenvolvido para os modelos em questão sob dois casos especiais desta família de distribuições, a Normal e a t de Student, utilizando o algoritmo EM para obter as estimativas de máxima verossimilhança dos parâmetros dos modelos e desenvolvendo métodos de diagnóstico de influência global e local com base na metodologia proposta por Cook (1986) e Poom & Poon (1999). Sob o enfoque Bayesiano, o modelo de regressão para respostas censuradas é estudado sob alguns casos especiais da classe SMSN, como a Normal, a t de Student, a skew-Normal, a skew-t e a skew-Slash. Neste caso, o amostrador de Gibbs é a principal ferramenta utilizada para a inferência sobre os parâmetros do modelo. Apresentamos também alguns estudos de simulação para avaliar a metodologia desenvolvida que, por fim, é aplicada em dois conjuntos de dados reais. Os pacotes SMNCensReg, CensRegMod e BayesCR para o software R dão suporte computacional aos desenvolvimentos deste trabalho / Abstract: This work aims to present the linear regression model with censored response variable under the class of scale mixture of skew-normal distributions (SMSN), generalizing the well known Tobit model as providing a more robust alternative to the normal distribution. A study based on classic inference is developed to investigate these censored models under two special cases of this family of distributions, Normal and t-Student, using the EM algorithm for obtaining maximum likelihood estimates and developing methods of diagnostic based on global and local influence as suggested by Cook (1986) and Poom & Poon (1999). Under a Bayesian approach, the censored regression model was studied under some special cases of SMSN class, such as Normal, t-Student, skew-Normal, skew-t and skew-Slash. In these cases, the Gibbs sampler was the main tool used to make inference about the model parameters. We also present some simulation studies for evaluating the developed methodologies that, finally, are applied on two real data sets. The packages SMNCensReg, CensRegMod and BayesCR implemented for the software R give computational support to this work / Mestrado / Estatistica / Mestra em Estatística

The valuation of weather derivatives is greatly dependent on accurate modeling and forecasting of the underlying temperature indices. The complexity and uncertainty in such modeling has led to several temperature processes being developed for the Monte Carlo simulation of daily average temperatures. In this report, we aim to compare the results of two recently developed models by Gyamerah et al. (2018) and Evarest, Berntsson, Singull, and Yang (2018). The paper gives a thorough introduction to option theory, Lévy and Wiener processes, and generalized hyperbolic distributions frequently used in temperature modeling. Implementations of maximum likelihood estimation and the expectation-maximization algorithm with Kim's smoothed transition probabilities are used to fit the Lévy process distributions and both models' parameters, respectively. Later, the use of both models is considered for the pricing of European HDD and CDD options by Monte Carlo simulation. The evaluation shows a tendency toward the shifted temperature regime over the base regime, in contrast to the two articles, when evaluated for three data sets. Simulation is successfully demonstrated for the model of Evarest, however Gyamerah's model was unable to be replicated. This is concluded to be due to the two articles containing several incorrect derivations, why the thesis is left unanswered and the articles' conclusions are questioned. We end by proposing further validation of the two models and summarize the alterations required for a correct implementation.

Probabilistic graphical modeling is a framework which can be used to succinctly<br>represent multivariate probability distributions of time series in terms of each time<br>series’s dependence on others. In general, it is computationally prohibitive to sta-<br>tistically infer an arbitrary model from data. However, if we constrain the model to<br>have a tree topology, the corresponding learning algorithms become tractable. The<br>expressive power of tree-structured distributions are low, since only n − 1 dependen-<br>cies are explicitly encoded for an n node tree. One way to improve the expressive<br>power of tree models is to combine many of them in a mixture model. This work<br>presents and uses simulations to validate extensions of the standard mixtures of trees<br>model for i.i.d data to the setting of time series data. We also consider the setting<br>where the tree mixture itself forms a hidden Markov chain, which could be better<br>suited for approximating time-varying seasonal data in the real world. Both of these<br>are evaluated on artificial data sets.<br><br>

Hidden Markov Models (HMMs) have seen widespread use in a variety of applications ranging from speech recognition to gene prediction. While developed over forty years ago, they remain a standard tool for sequential data analysis. More recently, Latent Dirichlet Allocation (LDA) was developed and soon gained widespread popularity as a powerful topic analysis tool for text corpora. We thoroughly develop LDA and a generalization of HMMs and demonstrate the conjunctive use of both methods in predictive data analysis for health care problems. While these two tools (LDA and HMM) have been used in conjunction previously, we use LDA in a new way to reduce the dimensionality involved in the training of HMMs. With both LDA and our extension of HMM, we train classifiers to predict development of Chronic Kidney Disease (CKD) in the near future.

Pharmacogivilance consists in carefully monitoring drugs in order to re-evaluate their risk for people’s health. The sooner the Adverse Drug Reactions are detected, the sooner one can act consequently. This thesis aims at discovering such reactions in electronical health records under the constraint of lacking annotated data, in order to replicate the scenario of the Regional Center for Pharmacovigilance of Nice. We investigate how in a semi-supervised learning design the unlabeled data can contribute to improve classification scores. Results suggest an excellent recall in discovering adverse reactions and possible classification improvements under specific data distribution. / Läkemedelsövervakningen består i kolla försiktigt läkemedlen så att utvärdera dem för samhällets hälsa. Ju tidigare de läkemedelsrelaterade biverkningarna upptäcks, desto tidigare man får handla dem. Detta exjobb söker att upptäcka de där läkemedelsrelaterade biverkningarnna inom elektroniska hälsopost med få datamärkningar, för att återskapa Nice regionalt läkemedelelsöveraknings-centrumets situationen. Vi undersöker hur en halvväglett lärande lösning kan hjälpa att förbättra klassificeringsresultat. Resultaten visar en god återställning med biverknings-upptäckning och möjliga förbättringar.

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Semiparametric modeling is a hybrid of the parametric and nonparametric modelings where some function forms are known and others are unknown. In this dissertation, we have made several contributions to semiparametric modeling based on the single index model related to the following three topics: the first is to propose a model for detecting change points simultaneously with estimating the unknown function; the second is to develop two models for spatially correlated data; and the third is to further develop two models for spatially-temporally correlated data. To address the first topic, we propose a unified approach in its ability to simultaneously estimate the nonlinear relationship and change points. We propose a single index change point model as our unified approach by adjusting for several other covariates. We nonparametrically estimate the unknown function using kernel smoothing and also provide a permutation based testing procedure to detect multiple change points. We show the asymptotic properties of the permutation testing based procedure. The advantage of our approach is demonstrated using the mortality data of Seoul, Korea from January, 2000 to December, 2007. On the second topic, we propose two semiparametric single index models for spatially correlated data. One additively separates the nonparametric function and spatially correlated random effects, while the other does not separate the nonparametric function and spatially correlated random effects. We estimate these two models using two algorithms based on Markov Chain Expectation Maximization algorithm. Our approaches are compared using simulations, suggesting that the semiparametric single index nonadditive model provides more accurate estimates of spatial correlation. The advantage of our approach is demonstrated using the mortality data of six cities, Korea from January, 2000 to December, 2007. The third topic involves proposing two semiparametric single index models for spatially and temporally correlated data. Our first model has the nonparametric function which can separate from spatially and temporally correlated random effects. We refer it to "semiparametric spatio-temporal separable single index model (SSTS-SIM)", while the second model does not separate the nonparametric function from spatially correlated random effects but separates the time random effects. We refer our second model to "semiparametric nonseparable single index model (SSTN-SIM)". Two algorithms based on Markov Chain Expectation Maximization algorithm are introduced to simultaneously estimate parameters, spatial effects, and times effects. The proposed models are then applied to the mortality data of six major cities in Korea. Our results suggest that SSTN-SIM is more flexible than SSTS-SIM because it can estimate various nonparametric functions while SSTS-SIM enforces the similar nonparametric curves. SSTN-SIM also provides better estimation and prediction. / Ph. D.

The advances in data-collecting technologies provides great opportunities to access large sample-size data sets with high dimensionality. Variable selection is an important procedure to extract useful knowledge from such complex data. While in many real-data applications, appropriate selection of variables should facilitate the model interpretation and computation efficiency. It is thus important to incorporate domain knowledge of underlying data generation mechanism to select key variables for improving the model performance. However, general variable selection techniques, such as the best subset selection and the Lasso, often do not take the underlying data generation mechanism into considerations. This thesis proposal aims to develop statistical modeling methodologies with a focus on the structured variable selection towards better model interpretation and computation efficiency. Specifically, this thesis proposal consists of three parts: an additive heredity model with coefficients incorporating the multi-level data, a regularized dynamic generalized linear model with piecewise constant functional coefficients, and a structured variable selection method within the best subset selection framework. In Chapter 2, an additive heredity model is proposed for analyzing mixture-of-mixtures (MoM) experiments. The MoM experiment is different from the classical mixture experiment in that the mixture component in MoM experiments, known as the major component, is made up of sub-components, known as the minor components. The proposed model considers an additive structure to inherently connect the major components with the minor components. To enable a meaningful interpretation for the estimated model, we apply the hierarchical and heredity principles by using the nonnegative garrote technique for model selection. The performance of the additive heredity model was compared to several conventional methods in both unconstrained and constrained MoM experiments. The additive heredity model was then successfully applied in a real problem of optimizing the Pringlestextsuperscript{textregistered} potato crisp studied previously in the literature. In Chapter 3, we consider the dynamic effects of variables in the generalized linear model such as logistic regression. This work is motivated from the engineering problem with varying effects of process variables to product quality caused by equipment degradation. To address such challenge, we propose a penalized dynamic regression model which is flexible to estimate the dynamic coefficient structure. The proposed method considers modeling the functional coefficient parameter as piecewise constant functions. Specifically, under the penalized regression framework, the fused lasso penalty is adopted for detecting the changes in the dynamic coefficients. The group lasso penalty is applied to enable a sparse selection of variables. Moreover, an efficient parameter estimation algorithm is also developed based on alternating direction method of multipliers. The performance of the dynamic coefficient model is evaluated in numerical studies and three real-data examples. In Chapter 4, we develop a structured variable selection method within the best subset selection framework. In the literature, many techniques within the LASSO framework have been developed to address structured variable selection issues. However, less attention has been spent on structured best subset selection problems. In this work, we propose a sparse Ridge regression method to address structured variable selection issues. The key idea of the proposed method is to re-construct the regression matrix in the angle of experimental designs. We employ the estimation-maximization algorithm to formulate the best subset selection problem as an iterative linear integer optimization (LIO) problem. the mixed integer optimization algorithm as the selection step. We demonstrate the power of the proposed method in various structured variable selection problems. Moverover, the proposed method can be extended to the ridge penalized best subset selection problems. The performance of the proposed method is evaluated in numerical studies. / Doctor of Philosophy / The advances in data-collecting technologies provides great opportunities to access large sample-size data sets with high dimensionality. Variable selection is an important procedure to extract useful knowledge from such complex data. While in many real-data applications, appropriate selection of variables should facilitate the model interpretation and computation efficiency. It is thus important to incorporate domain knowledge of underlying data generation mechanism to select key variables for improving the model performance. However, general variable selection techniques often do not take the underlying data generation mechanism into considerations. This thesis proposal aims to develop statistical modeling methodologies with a focus on the structured variable selection towards better model interpretation and computation efficiency. The proposed approaches have been applied to real-world problems to demonstrate their model performance.

Les dispositifs de protection de sites sensibles doivent permettre de détecter des menaces potentielles suffisamment à l’avance pour pouvoir mettre en place une stratégie de défense. Dans cette optique, les méthodes de détection et de reconnaissance d’aéronefs se basant sur des images infrarouge multispectrales doivent être adaptées à des images faiblement résolues et être robustes à la variabilité spectrale et spatiale des cibles. Nous mettons au point dans cette thèse, des méthodes statistiques de détection et de reconnaissance d’aéronefs satisfaisant ces contraintes. Tout d’abord, nous spécifions une méthode de détection d’anomalies pour des images multispectrales, combinant un calcul de vraisemblance spectrale avec une étude sur les ensembles de niveaux de la transformée de Mahalanobis de l’image. Cette méthode ne nécessite aucune information a priori sur les aéronefs et nous permet d’identifier les images contenant des cibles. Ces images sont ensuite considérées comme des réalisations d’un modèle statistique d’observations fluctuant spectralement et spatialement autour de formes caractéristiques inconnues. L’estimation des paramètres de ce modèle est réalisée par une nouvelle méthodologie d’apprentissage séquentiel non supervisé pour des modèles à données manquantes que nous avons développée. La mise au point de ce modèle nous permet in fine de proposer une méthode de reconnaissance de cibles basée sur l’estimateur du maximum de vraisemblance a posteriori. Les résultats encourageants, tant en détection qu’en classification, justifient l’intérêt du développement de dispositifs permettant l’acquisition d’images multispectrales. Ces méthodes nous ont également permis d’identifier les regroupements de bandes spectrales optimales pour la détection et la reconnaissance d’aéronefs faiblement résolus en infrarouge / Surveillance systems should be able to detect potential threats far ahead in order to put forward a defence strategy. In this context, detection and recognition methods making use of multispectral infrared images should cope with low resolution signals and handle both spectral and spatial variability of the targets. We introduce in this PhD thesis a novel statistical methodology to perform aircraft detection and classification which take into account these constraints. We first propose an anomaly detection method designed for multispectral images, which combines a spectral likelihood measure and a level set study of the image Mahalanobis transform. This technique allows to identify images which feature an anomaly without any prior knowledge on the target. In a second time, these images are used as realizations of a statistical model in which the observations are described as random spectral and spatial deformation of prototype shapes. The model inference, and in particular the prototype shape estimation, is achieved through a novel unsupervised sequential learning algorithm designed for missing data models. This model allows to propose a classification algorithm based on maximum a posteriori probability Promising results in detection as well as in classification, justify the growing interest surrounding the development of multispectral imaging devices. These methods have also allowed us to identify the optimal infrared spectral band regroupments regarding the low resolution aircraft IRS detection and classification