Locally Smoothed Gaussian Process Regression

Function estimation is a fundamental problem in Machine Learning. In supervised learning tasks applied to a data set composed of observed input data and labels, the goal of function estimation is to establish a mapping between these two groups of observed quantities. Function estimation can be approached in various ways, and we can broadly divide algorithms in two categories, as global and local. Examples of global algorithms are Neural Networks [1] and kernel machines [2], which impose a functional form yielding a global representation of the function. The functional form is parameterized by a set of parameters which are optimized or inferred based on all the available data.