Imaging genetics is an emerging and promising technique that investigates how genetic variations affect brain development, structure, and function. By exploiting disorder-related neuroimaging phenotypes, this class of studies provides a novel direction to reveal and understand the complex genetic mechanisms. Oftentimes, imaging genetics studies are challenging due to the relatively small number of subjects but extremely high-dimensionality of both imaging data and genomic data. In this dissertation, I carry on my research on imaging genetics with particular focuses on two tasks---building predictive models between neuroimaging data and genomic data, and identifying disorder-related genetic risk factors through image-based biomarkers. To this end, I consider a suite of structured sparse methods---that can produce interpretable models and are robust to overfitting---for imaging genetics. With carefully-designed sparse-inducing regularizers, different biological priors are incorporated into learning models. More specifically, in the Allen brain image--gene expression study, I adopt an advanced sparse coding approach for image feature extraction and employ a multi-task learning approach for multi-class annotation. Moreover, I propose a label structured-based two-stage learning framework, which utilizes the hierarchical structure among labels, for multi-label annotation. In the Alzheimer's disease neuroimaging initiative (ADNI) imaging genetics study, I employ Lasso together with EDPP (enhanced dual polytope projections) screening rules to fast identify Alzheimer's disease risk SNPs. I also adopt the tree-structured group Lasso with MLFre (multi-layer feature reduction) screening rules to incorporate linkage disequilibrium information into modeling. Moreover, I propose a novel absolute fused Lasso model for ADNI imaging genetics. This method utilizes SNP spatial structure and is robust to the choice of reference alleles of genotype coding. In addition, I propose a two-level structured sparse model that incorporates gene-level networks through a graph penalty into SNP-level model construction. Lastly, I explore a convolutional neural network approach for accurate predicting Alzheimer's disease related imaging phenotypes. Experimental results on real-world imaging genetics applications demonstrate the efficiency and effectiveness of the proposed structured sparse methods.

Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed.

Learning from high dimensional biomedical data attracts lots of attention recently. High dimensional biomedical data often suffer from the curse of dimensionality and have imbalanced class distributions. Both of these features of biomedical data, high dimensionality and imbalanced class distributions, are challenging for traditional machine learning methods and may affect the model performance. In this thesis, I focus on developing learning methods for the high-dimensional imbalanced biomedical data. In the first part, a sparse canonical correlation analysis (CCA) method is presented. The penalty terms is used to control the sparsity of the projection matrices of CCA. The sparse CCA method is then applied to find patterns among biomedical data sets and labels, or to find patterns among different data sources. In the second part, I discuss several learning problems for imbalanced biomedical data. Note that traditional learning systems are often biased when the biomedical data are imbalanced. Therefore, traditional evaluations such as accuracy may be inappropriate for such cases. I then discuss several alternative evaluation criteria to evaluate the learning performance. For imbalanced binary classification problems, I use the undersampling based classifiers ensemble (UEM) strategy to obtain accurate models for both classes of samples. A small sphere and large margin (SSLM) approach is also presented to detect rare abnormal samples from a large number of subjects. In addition, I apply multiple feature selection and clustering methods to deal with high-dimensional data and data with highly correlated features. Experiments on high-dimensional imbalanced biomedical data are presented which illustrate the effectiveness and efficiency of my methods.