[pt] Motivado pelos desafios de processar a grande quantidade de dados disponíveis, pesquisas recentes em estatística tem sugerido novas técnicas de modelagem e inferência. Paralelamente, outros campos como processamento de sinais e otimização também estão produzindo métodos para lidar problemas em larga escala. Em particular, este trabalho é focado nas teorias e métodos baseados na regularização l1. Após uma revisão compreensiva da norma l1 como uma ferramenta para definir soluções esparsas, estudaremos mais a fundo o método LASSO. Para exemplificar como o LASSO possui uma ampla gama de aplicações, exibimos um estudo de caso em processamento de sinal esparso. Baseado nesta idea, apresentamos o l1 level-slope filter. Resultados experimentais são apresentados para uma aplicação em transmissão de dados via fibra óptica. Para a parte final da dissertação, um novo método de estimação é proposto para modelos em alta dimensão com variância periódica. A principal ideia desta nova metodologia é combinar esparsidade, induzida pela regularização l1, com o método de máxima verossimilhança. Adicionalmente, esta metodologia é utilizada para estimar os parâmetros de um modelo mensal estocástico de geração de energia eólica e hídrica. Simulações e resultados de previsão são apresentados para um estudo real envolvendo cinquenta geradores de energia renovável do sistema Brasileiro. / [en] Motivated by the challenges of processing the vast amount of available data, recent research on the ourishing field of high-dimensional statistics is bringing new techniques for modeling and drawing inferences over large amounts of data. Simultaneously, other fields like signal processing and optimization are also producing new methods to deal with large scale problems. More particularly, this work is focused on the theories and methods based on l1-regularization. After a comprehensive review of the l1-norm as tool for finding sparse solutions, we study more deeply the LASSO shrinkage method. In order to show how the LASSO can be used for a wide range of applications, we exhibit a case study on sparse signal processing. Based on this idea, we present the l1 level-slope filter. Experimental results are given for an application on the field of fiber optics communication. For the final part of the thesis, a new estimation method is proposed for high-dimensional models with periodic variance. The main idea of this novel methodology is to combine sparsity, induced by the l1-regularization, with the maximum likelihood criteria. Additionally, this novel methodology is used for building a monthly stochastic model for wind and hydro inow. Simulations and forecasting results for a real case study involving fifty Brazilian renewable power plants are presented.

Orlando di Lasso is regarded as one of the great polyphonic masters of the Renaissance. An international composer of both sacred and secular music, his sacred works have always held an important place in the choral repertory. Especially significant are Lasso's Parody Masses, which comprise the majority of settings in this genre. The "Missa Ad Imitatiomem Moduli Doulce Memoire" and its model, the chanson "Doulce Memoire" by Sandrin, have been selected as the subject of this lecture recital. In the course of this study, the two works have been compared and analyzed, focusing on the exact material which has been borrowed from the chanson. In addition to the borrowed material, the longer movements, especially the Gloria and the Credo, exhibit considerable free material. This will be considered in light of its relation to the parody sections. Chapter One gives an introduction to the subject of musical parody with definitions of parody by several contemporary authors. In addition, several writers of the sixteenth century, including Vicentino, Zarlino, Ponzio, and Cerone are mentioned. Chapter Two relates biographical information on Lasso and gives a brief summary of his compositions. Attention is given to the number and type of Parody Masses by Lasso. Chapter Three discusses Sandrin and the chanson model, "Doulce Memoire." The original French text, an English translation, and form of the chanson are given. Chapter Four gives a detailed analysis of the "Missa Doulce Memoire" illustrating the use of borrowed material on specific sections of the Mass. The free sections of the Mass are discussed and compared with the parody sections. Other compositional devices, such as text painting, varied textures, and coloration are also mentioned. In Chapter Five, the "Missa Doulce Memoire" is compared to Lasso's other parody works and conclusions will be drawn concerning the composer's choice of material and treatment of the text, especially with regard to the free sections, the place of the Parody Mass in Lasso's ouevre. and their place in the modern choral repertory.

Market prices in the liberalized European electricity system play a crucial role in promoting competition, ensuring grid stability, and maximizing profits for market participants. Accurate electricity price forecasting algorithms have, therefore, become increasingly important in this competitive market. However, existing evaluations of forecasting models primarily focus on overall accuracy, overlooking the underlying causality of the predictions. The thesis explores two state-of-the-art forecasters, the deep neural network (DNN) and the Lasso Estimated AutoRegressive (LEAR) models, in the EPEX-BE and Nord Pool markets. The aim is to understand if their predictions can be trusted in more general settings than the limited context they are trained in. If the models produce poor predictions in extreme conditions or if their predictions are inconsistent with reality, they cannot be relied upon in the real world where these forecasts are used in downstream decision-making activities. The results show that for the EPEX-BE market, the DNN model outperforms the LEAR model in terms of overall accuracy. However, the LEAR model performs better in predicting negative prices, while the DNN model performs better in predicting price spikes. For the Nord Pool market, a simpler DNN model is more accurate for price forecasting. In both markets, the models exhibit behaviours inconsistent with reality, making it challenging to trust the models’ predictions. Overall, the study highlights the importance of understanding the underlying causality of forecasting models and the limitations of relying solely on overall accuracy metrics. / Priserna på den liberaliserade europeiska elmarknaden spelar en avgörande roll för att främja konkurrens, säkerställa stabilitet i elnätet och maximera aktörernas vinster. Exakta prisprognoalgoritmer har därför blivit allt viktigare på denna konkurrensutsatta marknad. Existerande utvärderingar av prognosverktyg fokuserar emellertid på den övergripande noggrannheten och förbiser de underliggande orsakssambanden i prognoserna. Denna rapport utforskar två moderna prognosverktyg, DNN (Deep Neural Network) och LEAR (Lasso Estimated AutoRegressive) på elmarknaderna i Belgien respektive Norden. Målsättningen är att förstå om deras prognoser är pålitliga i mer allmänna sammanhang än det begränsade sammahang som de är tränade i. Om modellerna producerar dåliga prognoser under extrema förhållanden eller om deras prognoser inte överensstämmer med verkligheten så kan man inte förlita sig på dem i den verkliga världen, där prognoserna ligger till grund för beslutsfattande aktiviteter. Resultaten för Belgien visar att DNN-modellen överträffar LEAR-modellen när det gäller övergripande noggrannhet. LEAR-modellen presterar dock bättre när det gäller att förutse negativa priser, medan DNN-modellen presterar bättre när det gäller prisspikar. På den nordiska elmarknaden är en enklare DNN-modell mer noggrann för prisprognoser. På båda marknaden visar modellerna beteenden som inte överensstämmer med verkligheten, vilket gör det utmanande att lita på modellernas prognoser. Sammantaget belyser studien vikten av att förstå de underliggande orsakssambanden i prognosmodellerna och begränsningarna med att enbart förlita sig på övergripande mått på noggrannhet.

[pt] A dissertação é composta por três ensaios empíricos que usam dados históricos de ações americanas. O primeiro avalia o desempenho de uma abordagem de otimização de carteiras baseada na otimização de Markowitz. Os resultados mostram valor econômico positivo do portfólio resultante, mesmo na presença de custos de transação. O segundo artigo visa comparar e combinar a técnica desenvolvida no artigo anterior à abordagem paramétrica e avalia o desempenho da combinação das técnicas. Os resultados mostram que o desempenho da técnica paramétrica é inferior à técnica de Markowitz modificada e pouco melhor do que o mercado agregado. Isto sugere que o valor econômico de explorar a estrutura de covariância entre as ações é superior a aumentar pesos em ações cujas características oferecem relações risco-retorno maiores até o período. O terceiro ensaio avalia modelos de previsão da variação de retornos entre ações. As estatísticas utilizadas apontam que os modelos padrão não possuem poder preditivo superior a modelos que supõem que não há variação ou que usam a média histórica. Por meio do uso tanto de combinações de modelos lineares quanto estimação restrita de modelos com muitos fatores, mostro que é possível obter resultados ligeiramente superiores. / [en] The dissertation consists of three empirical essays which use historical data of stocks listed in NYSE. The first essay evaluates a portfolio selection approach based on the Markowitz optimization. Results show the portfolios have positive economic value, even after including transaction costs. The second essay compares the technique proposed in the first essay to the parametric approach. Results show the parametric approach performs worse than the modified Markowitz approach and shlightly better than the aggregated market. This suggests that exploring the covariance structure of stocks provides better results than overweighting stocks with characteristics associated to better riskreturn ratios in the past. The third essay evaluates models that forecast the cross-sectional variation in stock returns. Given the statistics used, benchmark models do not show greater forecasting power than skeptical or naive models. By using linear model combination or lasso technique on a model with several factors, I show it is possible to obtain slightly better results.

變數選取方法已經成為各領域在處理多維度資料的工具。Zhou與Hwang在2005年，為了改善James-Stein positive part估計量(JS+)只能在完全模型(full model)與原始模型(origin model)兩者去做挑選，建立了具有Minimax性質同時加上門檻值的估計量，即James-Stein with Threshoding positive part估計量(JSWT+)。由於JSWT+估計量具有門檻值，使得此估計量可以在完全模型與其線性子集下做變數選取。我們想進一步了解如果將JSWT+估計量應用於線性迴歸分析時，藉由JSWT+估計具有門檻值的性質去做變數選取的效果如何？本文目的即是利用JSWT+估計量具有門檻值的性質，建立JSWT+估計量應用於線性迴歸模型變數挑選的流程。建立模擬資料分析，以可同時做係數壓縮及變數選取的LASSO方法與我們所提出JSWT+變數選取的流程去比較係數路徑及變數選取時差異比較，最後將我們提出JSWT+變數選取的流程對實際資料攝護腺癌資料(Tibshirani，1996)做變數挑選。則當考慮解釋變數個數小於樣本個數情況下，JSWT+與LASSO在變數選取的比較結果顯示，JSWT+表現的比較好，且可直接得到估計量的理想參數。

Esta tese trata de investigar as configurações das práticas equestres no estado do Rio Grande do Sul, no século XX. A proposição da pesquisa parte da noção de que as práticas tiveram um papel relevante para a história do Rio Grande do Sul, em particular nos campos da sociabilidade, lazer e preservação das culturas. No cenário sul-rio-grandense, a pesquisa dedica atenção ao desenvolvimento das carreiras de cancha reta, do turfe, do hipismo, do tiro de laço, do freio de ouro e da equoterapia. Tais práticas equestres foram conjecturadas por uma perspectiva socio-histórica, cuja análise foi guiada pela categoria ―configuração‖. Esta foi operacionalizada a partir da obra de Norbert Elias, conduzindo o estudo no sentido de compreender o processo de emergência, distinção e as relações de interdependência estabelecidas entre as práticas equestres no estado. A investigação assentou-se na análise de documentos escritos e impressos, os quais foram concebidos enquanto materiais e textos históricos, portadores de mensagens, sentidos e intuitos reservados à sua conjuntura. As fontes revelaram que o processo de desenvolvimento de configurações no cenário equestre sul-rio-grandense sublinhou uma reconstrução da variada e heterogênea rede de interdependências entre os domínios socializadores representados pelas corridas de cavalos, pelo hipismo, pela equoterapia e pelo tiro de laço. De igual forma, as transformações ocorridas no contexto destes domínios socializadores, ao longo do tempo, derivam das relações de interdependência entre os mesmos, nas esferas do trabalho, da cultura, do lazer, do esporte e da reabilitação. Por conseguinte, a noção de configuração entre práticas equestres pode auxiliar a compreender um campo mais amplo de interações e intercâmbios entre os esportes em geral enquanto domínios socializadores. / This thesis is to investigate the configurations of equestrian practices in the state of Rio Grande do Sul, in the twentieth century. The proposition of the research builds on the notion that the practices had a significant role in the history of Rio Grande do Sul, in particular in the fields of sociability, leisure and preservation of cultures. In the scenario of Rio Grande do Sul, the research devoted attention to the development of straight line horse races, horse racing, equestrianism, shot of lasso with horse and equine-assisted therapy. Such equestrian practices were conjectured by a sociohistorical perspective, whose analysis was guided by the category "configuration". This was operationalized from Norbert Elias work, leading the study in order to understand the process of emergence, distinction and interdependence of relations between the equestrian sports practices in the state. The research was based on the analysis of written and printed documents, which are designed as historical materials and texts, carrying messages, meanings and intentions reserved to their conjuncture. The sources revealed that a configuration development process in Rio Grande do Sul‘s equestrian scene emphasized a reconstruction of the varied and heterogeneous network of independencies between socializing areas represented by the horse racing, equestrian sports, equine-assisted therapy and shot of lasso with horse. Similarly, the changes occurred in the context of these socializing areas, over time, derived from the interrelationship between them, in the spheres of work, culture, leisure, sport and rehabilitation. Therefore, the notion of a configuration between equestrian practices can help understanding a new broader field of interactions and exchanges between the sports in general as socializing areas.

Combining embedded systems and machine learning models is an exciting prospect. However, to fully target any embedded system, with the most stringent resource requirements, the models have to be designed with care not to overwhelm it. Decision tree ensembles are targeted in this thesis. A benchmark model is created with LightGBM, a popular framework for gradient boosted decision trees. This model is first transformed and regularized with RuleFit, a LASSO regression framework. Then it is further optimized with quantization and weight sharing, techniques used when compressing neural networks. The entire process is combined into a novel framework, called ESRule. The data used comes from the domain of frequency measurements in cellular networks. There is a clear use-case where embedded systems can use the produced resource optimized models. Compared with LightGBM, ESRule uses 72ˆ less internal memory on average, simultaneously increasing predictive performance. The models use 4 kilobytes on average. The serialized variant of ESRule uses 104ˆ less hard disk space than LightGBM. ESRule is also clearly faster at predicting a single sample.

When scientists know in advance that some features (variables) are important in modeling a data, then these important features should be kept in the model. How can we utilize this prior information to effectively find other important features? This dissertation is to provide a solution, using such prior information. We propose the Conditional Adaptive Lasso (CAL) estimates to exploit this knowledge. By choosing a meaningful conditioning set, namely the prior information, CAL shows better performance in both variable selection and model estimation. We also propose Sufficient Conditional Adaptive Lasso Variable Screening (SCAL-VS) and Conditioning Set Sufficient Conditional Adaptive Lasso Variable Screening (CS-SCAL-VS) algorithms based on CAL. The asymptotic and oracle properties are proved. Simulations, especially for the large p small n problems, are performed with comparisons with other existing methods. We further extend to the linear model setup to the generalized linear models (GLM). Instead of least squares, we consider the likelihood function with L1 penalty, that is the penalized likelihood methods. We proposed for Generalized Conditional Adaptive Lasso (GCAL) for the generalized linear models. We then further extend the method for any penalty terms that satisfy certain regularity conditions, namely Conditionally Penalized Estimate (CPE). Asymptotic and oracle properties are showed. Four corresponding sufficient variable screening algorithms are proposed. Simulation examples are evaluated for our method with comparisons with existing methods. GCAL is also evaluated with a read data set on leukemia.

Dans cette thèse nous traitons deux sujets. Le premier sujet concerne l'apprentissage statistique en grande dimension, i.e. les problèmes où le nombre de paramètres potentiels est beaucoup plus grand que le nombre de données à disposition. Dans ce contexte, l'hypothèse généralement adoptée est que le nombre de paramètres intervenant effectivement dans le modèle est petit par rapport au nombre total de paramètres potentiels et aussi par rapport au nombre de données. Cette hypothèse est appelée ``\emph{sparsity assumption}''. Nous étudions les propriétés statistiques de deux types de procédures : les procédures basées sur la minimisation du risque empirique muni d'une pénalité $l_{1}$ sur l'ensemble des paramètres potentiels et les procédures à poids exponentiels. Le second sujet que nous abordons concerne l'étude de procédures d'agrégation dans un modèle de densité. Nous établissons des inégalités oracles pour la norme $L^{\pi}$, $1\leqslant \pi \leqslant \infty$. Nous proposons ensuite une application à l'estimation minimax et adaptative en la régularité de la densité.

Dans cette thèse nous étudions certains designs déterministes pour la régression parcimonieuse. Notre problématique est largement inspirée du " Compressed Sensing " où l'on cherche à acquérir et compresser simultanément un signal de grande taille à partir d'un petit nombre de mesures linéaires. Plus précisément, nous faisons le lien entre l'erreur d'estimation et l'erreur de prédiction des estimateurs classiques (lasso, sélecteur Dantzig et basis pursuit) et la distorsion (qui mesure l'" écart " entre la norme 1 et la norme Euclidienne) du noyau du design considéré. Notre étude montre que toute construction de sous-espaces de faibles distorsions (appelés sous-espaces " presque "- Euclidiens) conduit à de " bons " designs. Dans un second temps, nous nous intéressons aux designs construits à partir de graphes expanseurs déséquilibrés. Nous en établissons de manière précise les performances en termes d'erreur d'estimation et d'erreur de prédiction. Enfin, nous traitons la reconstruction exacte de mesures signées sur la droite réelle. Nous démontrons que tout système de Vandermonde généralisé permet la reconstruction fidèle de n'importe quel vecteur parcimonieux à partir d'un très faible nombre d'observations. Dans une partie indépendante, nous étudions la stabilité de l'inégalité isopérimétrique sur la droite réelle pour des mesures log-concaves.