UC Davis

This dissertation makes significant contributions to important statistical machine learning problems, including uncertainty quantification and structural break detection in dynamic systems. It focuses on these two challenges in several specific settings and develops tailored solutions. Firstly, it addresses the problem of uncertainty quantification for line spectral estimation. By leveraging the generalized fiducial inference framework, a novel method is developed to quantify the uncertainty of spectral line estimators. This method is theoretically proven to possess desirable properties and demonstrates promising empirical performance. Additionally, the proposed method has been successfully applied to exoplanet detection applications, shedding light on a crucial topic in astronomy. Secondly, the dissertation tackles the challenge of breakpoint detection in non-stationary network vector autoregression models. Thirdly, it considers breakpoint detection in pairwise ranking problems. For the latter two problems, the minimum description length principle is invoked to derive a model selection criterion, which is shown to produce statistically consistent estimates for the number and locations of change points, as well as other model parameters. Furthermore, two practical algorithms are developed to optimize the criterion for these respective problems.