Gaussian processes for pattern recognition applications - Yan, Gao (2009)
Gaussian process (GP) is a stochastic process that has been studied for a long time and gained wide interests in the machine learning community in recent years. In this thesis, several interesting pattern analysis problems are solved using Gaussian process. Gaussian process models can be interpreted in two views, the weight space view and the function space view. Their different interpretations can be helpful in applying GPs to solve real problems. Its capability as functional prior inspired the original work on learning nonparametric similarity measure in this thesis. The similarity between pairwise inputs is considered a smooth function described by a GP prior. Given known similarity constraints, the model can be tuned by maximum likelihood and similarity on new inputs can be inferred. The advantage is that the learned similarity measure does not assume any parametric form. It is flexible to model various data with arbitrary distributions, and handles noise and outliers in the data. Gaussian process latent variable model (GPLVM) is a data modeling tool that is derived based on Gaussian processes from the weight space view. It was originally proposed for visualization of high dimensional data.