The study seeks to determine the robustness and power of parametric analysis of covariance and analysis of covariance using rank transformation to violation of the assumption of normality. The study employs a Monte Carlo simulation procedure with varying conditions of population distribution, group size, equality of group size, scale length, regression slope, and Y-intercept. The procedure was performed on raw data and ranked data with untied ranks and tied ranks.

Cette thèse est organisée en deux parties indépendantes. La première partie s'intéresse à l'estimation convexe de matrice en prenant en compte à la fois la parcimonie et le rang. Dans le contexte de graphes avec une structure de communautés, on suppose souvent que la matrice d'adjacence sous-jacente est diagonale par blocs dans une base appropriée. Cependant, de tels graphes possèdent généralement une matrice d'adjacente qui est aussi parcimonieuse, ce qui suggère que combiner parcimonie et range puisse permettre de modéliser ce type d'objet de manière plus fine. Nous proposons et étudions ainsi une pénalité convexe pour promouvoir parcimonie et rang faible simultanément. Même si l'hypothèse de rang faible permet de diminuer le sur-apprentissage en diminuant la capacité d'un modèle matriciel, il peut être souhaitable lorsque suffisamment de données sont disponible de ne pas introduire une telle hypothèse. Nous étudions un exemple dans le contexte multiple kernel learning localisé, où nous proposons une famille de méthodes a vaste-marge convexes et accompagnées d'une analyse théorique. La deuxième partie de cette thèse s'intéresse à des problèmes de détection d'objets ou de signaux structurés. Dans un premier temps, nous considérons un problème de test statistique, pour des modèles où l'alternative correspond à des capteurs émettant des signaux corrélés. Contrairement à la littérature traditionnelle, nous considérons des procédures de test séquentielles, et nous établissons que de telles procédures permettent de détecter des corrélations significativement plus faible que les méthodes traditionnelles. Dans un second temps, nous considérons le problème de localiser des objets dans des images. En s'appuyant sur de récents résultats en apprentissage de représentation pour des problèmes similaires, nous intégrons des features de grande dimension issues de réseaux de neurones convolutionnels dans les modèles déformables traditionnellement utilisés pour ce type de problème. Nous démontrons expérimentalement que ce type d'approche permet de diminuer significativement le taux d'erreur de ces modèles. / This thesis is organized in two independent parts. The first part focused on convex matrix estimation problems, where both rank and sparsity are taken into account simultaneously. In the context of graphs with community structures, a common assumption is that the underlying adjacency matrices are block-diagonal in an appropriate basis. However, these types of graphs are usually far from complete, and their adjacency representations are thus also inherently sparse. This suggests that combining the sparse hypothesis and the low rank hypothesis may allow to more accurately model such objects. To this end, we propose and analyze a convex penalty to promote both low rank and high sparsity at the same time. Although the low rank hypothesis allows to reduce over-fitting by decreasing the modeling capacity of a matrix model, the opposite may be desirable when enough data is available. We study such an example in the context of localized multiple kernel learning, which extends multiple kernel learning by allowing each of the kernels to select different support vectors. In this framework, multiple kernel learning corresponds to a rank one estimator, while higher-rank estimators have been observed to increase generalization performance. We propose a novel family of large-margin methods for this problem that, unlike previous methods, are both convex and theoretically grounded. The second part of the thesis is about detection of objects or signals which exhibit combinatorial structures, and we present two such problems. First, we consider detection in the statistical hypothesis testing sense, in models where anomalous signals correspond to correlated values at different sensors. In most existing work, detection procedures are provided with a full sample of all the sensors. However, the experimenter may have the capacity to make targeted measurements in an on-line and adaptive manner, and we investigate such adaptive sensing procedures. Finally, we consider the task of identifying and localizing objects in images. This is an important problem in computer vision, where hand-crafted features are usually used. Following recent successes in learning ad-hoc representations for similar problems, we integrate the method of deformable part models with high-dimensional features from convolutional neural networks, and shows that this significantly decreases the error rates of existing part-based models.

Um dos principais problemas em testes de hipóteses para a homogeneidade de curvas de sobrevivência ocorre quando as taxas de falha (ou funções de intensidade) não são proporcionais. Apesar do teste de Log-rank ser o teste não paramétrico mais utilizado para se comparar duas ou mais populações sujeitas a dados censurados, este teste apresentada duas restrições. Primeiro, toda a teoria assintótica envolvida com o teste de Log-rank, tem como hipótese o fato das populações envolvidas terem distribuições contínuas ou no máximo mistas. Segundo, o teste de Log-rank não apresenta bom comportamento quando as funções intensidade cruzam. O ponto inicial para análise consiste em assumir que os dados são contínuos e neste caso processos Gaussianos apropriados podem ser utilizados para testar a hipótese de homogeneidade. Aqui, citamos o teste de Renyi e Cramér-von Mises para dados contínuos (CCVM), ver Klein e Moeschberger (1997) [15]. Apesar destes testes não paramétricos apresentar bons resultados para dados contínuos, esses podem ter problemas para dados discretos ou arredondados. Neste trabalho, fazemos um estudo simulação da estatística de Cramér von-Mises (CVM) proposto por Leão e Ohashi [16], que nos permite detectar taxas de falha não proporcionais (cruzamento das taxas de falha) sujeitas a censuras arbitrárias para dados discretos ou arredondados. Propomos também, uma modificação no teste de Log-rank clássico para dados dispostos em uma tabela de contingência. Ao aplicarmos as estatísticas propostas neste trabalho para dados discretos ou arredondados, o teste desenvolvido apresenta uma função poder melhor do que os testes usuais / One of the main problems in hypothesis testing for homogeneity of survival curves occurs when the failure rate (or intensity functions) are nonproportional. Although the Log-rank test is a nonparametric test most commonly used to compare two or more populations subject to censored data, this test presented two constraints. First, all the asymptotic theory involved with the Log-rank test, is the hypothesis that individuals and populations involved have continuous distributions or at best mixed. Second, the log-rank test does not show well when the intensity functions intersect. The starting point for the analysis is to assume that the data is continuous and in this case suitable Gaussian processes may be used to test the assumption of homogeneity. Here, we cite the Renyi test and Cramér-von Mises for continuous data (CCVM), and Moeschberger see Klein (1997) [15]. Despite these non-parametric tests show good results for continuous data, these may have trouble discrete data or rounded. In this work, we perform a simulation study of statistic Cramér-von Mises (CVM) proposed by Leão and Ohashi [16], which allows us to detect failure rates are nonproportional (crossing of failure rates) subject to censure for arbitrary data discrete or rounded. We also propose a modification of the test log-rank classic data arranged in a contingency table. By applying the statistics proposed in this paper for discrete or rounded data, developed the test shows a power function better than the usual testing

Learning to rank is utilized in many scenarios, such as disease-gene association, information retrieval and recommender system. Improving the prediction accuracy of the ranking model is the main target of existing works. Contextual information has a significant influence in the ranking problem, and has been proved effective to increase the prediction performance of ranking models. Then we construct similarities for different types of entities that could utilize contextual information uniformly in an extensible way. Once we have the similarities constructed by contextual information, how to uti- lize them for different types of ranking models will be the task we should tackle. In this thesis, we propose four algorithms for learning to rank with contextual informa- tion. To refine the framework of matrix factorization, we propose an area under the ROC curve (AUC) loss to conquer the sparsity problem. Clustering and sampling methods are used to utilize the contextual information in the global perspective, and an objective function with the optimal solution is proposed to exploit the contex- tual information in the local perspective. Then, for the deep learning framework, we apply the graph convolutional network (GCN) on the ranking problem with the combination of matrix factorization. Contextual information is utilized to generate the input embeddings and graph kernels for the GCN. The third method in this thesis is proposed to directly exploit the contextual information for ranking. Laplacian loss is utilized to solve the ranking problem, which could optimize the ranking matrix directly. With this loss, entities with similar contextual information will have similar ranking results. Finally, we propose a two-step method to solve the ranking problem of the sequential data. The first step in this two-step method is to generate the em- beddings for all entities with a new sampling strategy. Graph neural network (GNN) and long short-term memory (LSTM) are combined to generate the representation of sequential data. Once we have the representation of the sequential data, we could solve the ranking problem of them with pair-wise loss and sampling strategy.

Living in the booming age of information, we have to rely on powerful information retrieval tools to seek the unique piece of desired knowledge from such a big data world, like using personalized search engine and recommendation systems. As one of the core components, ranking model can appear in almost everywhere as long as we need a relative order of desired/relevant entities. Based on the most general and intuitive assumption that entities without user actions (e.g., clicks, purchase, comments) are of less interest than those with user actions, the objective function of pairwise ranking models is formulated by measuring the contrast between positive (with actions) and negative (without actions) entities. This contrastive relationship is the core of pairwise ranking models. The construction of these positive-negative pairs has great influence on the model inference accuracy. Especially, it is challenging to explore the entity relationships in heterogeneous information network. In this thesis, we aim at advancing the development of the methodologies and principles of mining heterogeneous information network through learning entity relations from a pairwise learning to rank optimization perspective. More specifically we first show the connections of different relation learning objectives modified from different ranking metrics including both pairwise and list-wise objectives. We prove that most of popular ranking metrics can be optimized in the same lower bound. Secondly, we propose the class-imbalance problem imposed by entity relation comparison in ranking objectives, and prove that class-imbalance problem can lead to frequency 5 clustering and gradient vanishment problems. As a response, we indicate out that developing a fast adaptive sampling method is very essential to boost the pairwise ranking model. To model the entity dynamic dependency, we propose to unify the individual-level interaction and union-level interactions, and result in a multi-order attentive ranking model to improve the preference inference from multiple views.

This paper discusses results of a computer simulation to investigate the effect of jittering to simulate measurement error. In addition, the classical F ratio, the bootstrap F and the F for ranked data are compared. Empirical powers and p-values suggest the bootstrap is a good and robust procedure and the rank procedure seems to be too liberal when compared to the classical F ratio.

This study aims to find a relationship between the distribution of locals inside of Sweden and the municipalities’ relative concentration of foreigners. With the usage of data found in the website Statistics Sweden, we aim to investigate the existence of any relationship between the local population size of a municipality against the number of foreigners present in said municipalities, and see whether foreigners and immigrants are more concentrated in more populated municipalities rather than less populated ones. We aim to do this by utilizing multiple regression and dummy variables to identify whether there is a significant extra negative or positive effect on foreigners. The answer seems to be that foreigners are in fact more concentrated in more locally populated municipalities, rather than less populated ones

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第21622号 / 医博第4428号 / 新制||医||1033(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 妻木 範行, 教授 松田 秀一, 教授 渡邊 直樹 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

Nowadays, many real-world problems must deal with collections of high-dimensional data. High dimensional data usually have intrinsic low-dimensional representations, which are suited for subsequent analysis or processing. Therefore, finding low-dimensional representations is an essential step in many machine learning and data mining tasks. Low-rank and sparse modeling are emerging mathematical tools dealing with uncertainties of real-world data. Leveraging on the underlying structure of data, low-rank and sparse modeling approaches have achieved impressive performance in many data analysis tasks. Since the general rank minimization problem is computationally NP-hard, the convex relaxation of original problem is often solved. One popular heuristic method is to use the nuclear norm to approximate the rank of a matrix. Despite the success of nuclear norm minimization in capturing the low intrinsic-dimensionality of data, the nuclear norm minimizes not only the rank, but also the variance of matrix and may not be a good approximation to the rank function in practical problems. To mitigate above issue, this thesis proposes several nonconvex functions to approximate the rank function. However, It is often difficult to solve nonconvex problem. In this thesis, an optimization framework for nonconvex problem is further developed. The effectiveness of this approach is examined on several important applications, including matrix completion, robust principle component analysis, clustering, and recommender systems. Another issue associated with current clustering methods is that they work in two separate steps including similarity matrix computation and subsequent spectral clustering. The learned similarity matrix may not be optimal for subsequent clustering. Therefore, a unified algorithm framework is developed in this thesis. To capture the nonlinear relations among data points, we formulate this method in kernel space. Furthermore, the obtained continuous spectral solutions could severely deviate from the true discrete cluster labels, a discrete transformation is further incorporated in our model. Finally, our framework can simultaneously learn similarity matrix, kernel, and discrete cluster labels. The performance of the proposed algorithms is established through extensive experiments. This framework can be easily extended to semi-supervised classification.

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