Gaussian process provides a principled and flexible approach for modeling the response surface or the latent function in many areas, including machine learning, statistics and computer experiment. In literature, Gaussian process models have already demonstrated their effectiveness and usefulness in a variety of applications. In this dissertation, we mainly focus on three challenges associated with the Gaussian process models. The first chapter concentrates on including a nugget effect in the lifted Brownian covariance Gaussian process model, which enables the model to deal with both the deterministic and stochastic data. We also derive a number of important theoretical results, including the invariance property and the Bayesian connections. The second chapter introduces a new variable selection approach for the Gaussian process regression model via variational dropout random variables. The new approach offers superior predictive performance than the widely-accepted automatic relevance determination method in high-dimensional noisy cases, and is much faster than the golden-standard MCMC algorithms. The third chapter provides two new scalable algorithms for latent Gaussian process models dealing with non-Gaussian response variables. The new methods avoid the cumbersome numerical integration required by the popular variational inference algorithm and have fewer parameters to optimize. Our empirical results convincingly demonstrate that the new algorithms are efficient and effective.

Creator

• Yu, Yang

DOI

• https://doi.org/10.21985/n2-n5jn-fj90

Subject

• Statistics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15098
• etdadmin_upload_742660

Keyword

• variable selection
• variational inference
• Gaussian process
• lifted Brownian random field

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright