Gaussian Processes for Supervised Learning and Kernel Based Two-Sample Test

Srivastava, Umang (2022) Gaussian Processes for Supervised Learning and Kernel Based Two-Sample Test. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Umang Srivastava (17MS180)) 17MS180_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (984kB)

Abstract

Kernel machines is an extremely powerful class of models for machine learning. The most common techniques in this class of methods are the “Support Vector Machines” and “Gaussian process models”. The aim of this report is to conduct and present a review of Gaussian Processes Models used for Unsupervised learning and an application of Kernels to design a Statistical Two-Sample Test. Gaussian processes is a probabilistic approach to learning with the use of kernel machines and have recently been used in a large spectrum of fields for practical supervised learning applications. The second part of the report focuses on presenting a kernel based setup for comparing distributions, and ultimately constructing a statistical test based on asymptotic distribution to determine if two samples are drawn from different distributions. The test statistic being considered is called the Maximum Mean Discrepancy (MMD) which is defined as the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS).

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