The ever growing desire for accurate estimation and efficient learning necessitates the efforts to quantitatively characterize uncertainties for models. In this thesis, four problems pertaining to uncertainty quantification are discussed: A sequential stopping framework of constructing fixed-precision confidence regions is proposed for a class of multivariate simulation problems where variance estimation is difficult. An algorithm is developed to construct asymptotically valid confidence regions for model parameters for Stochastic Gradient Descent using the batch means method. Statistical inference for reinforcement learning is studied and the statistical property can be applied to develop efficient exploration policies. Uncertainty of decision making is discussed under three asymptotic regimes for ranking and selection (best arm identification) problems with general sample distributions.

Creator

• Zhu, Yi

DOI

• https://doi.org/10.21985/n2-ecc7-3c29

Subject

• Applied mathematics
• Statistics
• Computer science

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15080
• etdadmin_upload_741745

Keyword

• Ranking and Selection
• Reinforcement Learning
• Statistical Learning
• Stochastic Gradient Descent
• Uncertainty Quantification

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright