Statistical Machine Learning in Computational Genetics.
Statistical machine learning has played a key role in many areas, such as biology, health sciences, finance and genetics. Important tasks in computational genetics include disease prediction, capturing shapes within images, computation of genetic sharing between pairs of individuals, genome-wide association studies and image clustering. This thesis develops several learning methods to address these computational genetics problems. Firstly, motivated by the need for fast computation of genetic sharing among pairs of individuals, we propose the fastest algorithms for computing the kinship coefficient of a set of individuals with a known large pedigree. Moreover, we consider the possibility that the founders of the known pedigree may themselves be inbred and compute the appropriate inbreeding-adjusted kinship coefficients, which has not been addressed in literature. Secondly, motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative, we develop a Bayesian bivariate spatial group lasso model for multivariate regression analysis applicable to exam the influence of genetic variation on brain structure. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data. We develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We also incorporate Bayesian false discovery rate procedures to select SNPs. The new spatial model demonstrates superior performance over a standard model in our application. Thirdly, we propose the Random Tessellation Process (RTP) to model complex genetic data structure to predict disease status. The RTP is a multi-dimensional partitioning tree with non-axis aligned cuts. We develop a sequential Monte Carlo (SMC) algorithm for inference. Our process is self-consistent and can relax axis-aligned constraints, allowing complex inter-dimensional dependence to be captured. Fourthly, we propose the Random Tessellation with Splines (RTS) to acquire complex shapes within images. The RTS provides a framework for describing Bayesian nonparametric models based on partitioning two-dimensional Euclidean space with splines. We also develop an inference algorithm that is "embarrassingly parallel". Finally, we extend the mixtures of spatial spline regression with mixed-effects model under the Bayesian framework to accommodate streaming image data. We propose an SMC algorithm to analyze online fashion brain image.