Online Regression Using Reproducing Kernel Hilbert Spaces

Abstract

Suppose we have $X \subset \mathbb{R}^2$ and there exists an unknown function $F: X \to \mathbb{R}$. We will consider the Unnikrishnan -Vetterli problem in which a vehicle moves on $X$ making observations (input-output pairs) $(x_1,y_1), (x_2,y_2), (x_3,y_3), \dots$ (where $y_i$ is a noisy version of $F(x_i)$. The task is to maintain a running estimate for $F$ using the observations. In learning literature, such a task is referred to as regression. In this thesis, we have surveyed regression methods suitable for this scenario when data arrive sequentially. The methods that have been included in this thesis consider the Reproducing Kernel Hilbert Spaces (RKHS) as their hypothesis space. Towards the end, we propose improvement and present some results without any mathematical proofs.