Seasonal allergic rhinitis (SAR) is a disease caused by allergens from both environmental and genetic factors. Some researchers have studied the SAR based on traditional genetic methodologies. As technology develops, a new technique called single-cell RNA sequencing (scRNA-seq) is developed, which can generate high-dimension data. We apply two machine learning (ML) algorithms, random forest (RF) and partial least squares discriminant analysis (PLS-DA), for cell source classification and gene selection based on the SAR scRNA-seq time-series data from three allergic patients and four healthy controls denoised by single-cell variational inference (scVI). We additionally propose a new fitting method consisting of bootstrap and cubic smoothing splines to fit the averaged gene expressions per cell from different populations. To sum up, we find that both RF and PLS-DA could provide high classification accuracy, and RF is more preferable, considering its stable performance and strong gene-selection ability. Based on our analysis, there are 10 genes having discriminatory power to classify cells of allergic patients and healthy controls at any timepoints. Although there is no literature founded to show the direct connections between such 10 genes and SAR, the potential associations are indirectly confirmed by some studies. It shows a possibility that we can alarm allergic patients before a disease outbreak based on their genetic information. Meanwhile, our experiment results indicate that ML algorithms may discover something between genes and SAR compared with traditional techniques, which needs to be analyzed in genetics in the future.

Cette thèse s'inscrit dans le cadre des modèles de contours actifs. Il s'agit de méthodes dynamiquesappliquées à la segmentation d'image, en image fixe et vidéo. L'image est représentée par desdescripteurs régions et/ou contours. La segmentation est traitée comme un problème deminimisationd'une fonctionnelle. La recherche du minimum se fait via la propagation d'un contour actif dit basérégions. L'efficacité de ces méthodes réside surtout dans leur robustesse et leur rapidité. L'objectifde cette thèse est triple : le développement (i) d'une représentation paramétrique de courbes respectantcertaines contraintes de régularités, (ii) les conditions nécessaires à une évolution stable de cescourbes et (iii) la réduction des coûts calcul afin de proposer une méthode adaptée aux applicationsnécessitant une réponse en temps réel.Nous nous intéressons principalement aux contraintes de rigidité autorisant une plus granderobustesse vis-à-vis du bruit. Concernant l'évolution des contours actifs, nous étudions les problèmesd'application de la force de propagation, de la gestion de la topologie et des conditionsde convergence. Nous avons fait le choix des courbes splines cubiques. Cette famille de courbesoffre d'intéressantes propriétés de régularité, autorise le calcul exact des grandeurs différentiellesqui interviennent dans la fonctionnelle et réduit considérablement le volume de données à traiter.En outre, nous avons étendu le modèle classique des splines d'interpolation à un modèle de splinesd'approximation, dites smoothing splines. Ce dernier met en balance la contrainte de régularité etl'erreur d'interpolation sur les points d'échantillonnage du contour. Cette flexibilité permet ainsi deprivilégier la précision ou la robustesse.L'implémentation de ces modèles de splines a prouvé son efficacité dans diverses applicationsde segmentation.

本文採用可加性模型分析法建立台灣地區小型商用車市場之需求模型，並 引進Box-Jenkins時間序列模型處理具自我相關之誤差項，以利進行拔靴 推論設計時，能拔靴白干擾(bootstrapping white noise)，即重抽樣白 干擾的經驗分配。在此次研究過程中，除配適Box-Jenkins時間序列模型 外，所有分析步驟都是完全自動的，不須作假設和檢驗的工作，所以可降 低傳統上因統計人員主觀判斷錯誤所造成的估計偏誤。可加性模型改進傳 統迴歸模型須先假設模型形式的限制，可從商用車實證分析中，直接由資 料配適平滑函數，顯見其合理性。拔靴法免除傳統推論程序須強使隨機干 擾項分配為常態分配或漸近常態分配之束縛，改由殘差經驗分配模擬隨機 干擾項分配行為，在推論商用車市場上，也獲得不錯的結果。

Diffusion-weighted magnetic resonance imaging (MRI) has allowed unprecedented non-invasive mapping of brain neural connectivity in vivo by means of fiber tractography applications. Fiber tractography has emerged as a useful tool for mapping brain white matter connectivity prior to surgery or in an intraoperative setting. The advent of high angular resolution diffusion-weighted imaging (HARDI) techniques in MRI for fiber tractography has allowed mapping of fiber tracts in areas of complex white matter fiber crossings. Raw HARDI images, as a result of elevated diffusion-weighting, suffer from depressed signal-to-noise ratio (SNR) levels. The accuracy of fiber tractography is dependent on the performance of the various methods extracting dominant fiber orientations from the HARDI-measured noisy diffusivity profiles. These methods will be sensitive to and directly affected by the noise. In the first part of the thesis this issue is addressed by applying an objective and adaptive smoothing to the noisy HARDI data via generalized cross-validation (GCV) by means of the smoothing splines on the sphere method for estimating the smooth diffusivity profiles in three dimensional diffusion space. Subsequently, fiber orientation distribution functions (ODFs) that reveal dominant fiber orientations in fiber crossings are then reconstructed from the smoothed diffusivity profiles using the Funk-Radon transform. Previous ODF smoothing techniques have been subjective and non-adaptive to data SNR. The GCV-smoothed ODFs from our method are accurate and are smoothed without external intervention facilitating more precise fiber tractography. Diffusion-weighted MRI studies in amyotrophic lateral sclerosis (ALS) have revealed significant changes in diffusion parameters in ALS patient brains. With the need for early detection of possibly discrete upper motor neuron (UMN) degeneration signs in patients with early ALS, a HARDI study is applied in order to investigate diffusion-sensitive changes reflected in the diffusion tensor imaging (DTI) measures axial and radial diffusivity as well as the more commonly used measures fractional anisotropy (FA) and mean diffusivity (MD). The hypothesis is that there would be added utility in considering axial and radial diffusivities which directly reflect changes in the diffusion tensors in addition to FA and MD to aid in revealing neurodegenerative changes in ALS. In addition, applying adaptive smoothing via GCV to the HARDI data further facilitates the application of fiber tractography by automatically eliminating spurious noisy peaks in reconstructed ODFs that would mislead fiber tracking.

Model and variable selection have attracted considerable attention in areas of application where datasets usually contain thousands of variables. Variable selection is a critical step to reduce the dimension of high dimensional data by eliminating irrelevant variables. The general objective of variable selection is not only to obtain a set of cost-effective predictors selected but also to improve prediction and prediction variance. We have made several contributions to this issue through a range of advanced topics: providing a graphical view of Bayesian Variable Selection (BVS), recovering sparsity in multivariate nonparametric models and proposing a testing procedure for evaluating nonlinear interaction effect in a semiparametric model. To address the first topic, we propose a new Bayesian variable selection approach via the graphical model and the Ising model, which we refer to the ``Bayesian Ising Graphical Model'' (BIGM). There are several advantages of our BIGM: it is easy to (1) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (2) extend this approach to nonparametric regression models, and (3) incorporate graphical prior information. In the second topic, we propose a Nonnegative Garrote on a Kernel machine (NGK) to recover sparsity of input variables in smoothing functions. We model the smoothing function by a least squares kernel machine and construct a nonnegative garrote on the kernel model as the function of the similarity matrix. An efficient coordinate descent/backfitting algorithm is developed. The third topic involves a specific genetic pathway dataset in which the pathways interact with the environmental variables. We propose a semiparametric method to model the pathway-environment interaction. We then employ a restricted likelihood ratio test and a score test to evaluate the main pathway effect and the pathway-environment interaction. / Ph. D.