UC Davis

This dissertation makes contributions to the broad area of high-dimensional statistical machine learning. When the number of features $p$ is much larger than the number of observations $n$, often written as $p\gg n$, the problems are known as high-dimensional problems. With the rapid growth of the dimensionality and complexity of the data, such problems have become increasingly common and important, for example, in genomics and computational biology. This dissertation focuses on two such high-dimensional problems and develops solutions for them. The first problem concerns uncertainty quantification for the multi-task learning problem. Using the generalized fiducial inference framework, a novel method termed GMTask is developed. This method is shown to enjoy desirable theoretical and empirical properties. The second problem studies variable selection, robust estimation, and nonparametric additive model fitting in the high-dimensional scenario. The minimum description length principle is employed as one unified approach to simultaneous solve these issues.