Transforming Region-Detection, a One-Dimensional (1D) Problem to Point Detection, a Zero-Dimensional (0D) Problem

摘要

Kernel regression is a nonparametric method in which the underlying signal can be estimated at any given point using the local noisy observations. In this method, the signal Y (dependent variable) is defined as a random variable and the goal is to estimate the conditional expectation value of Y given the independent variable X. A bandwidth controls the degree of smoothness by defining the maximum distance of the observations form the center of the kernel (located at x) to be considered local. Thus, observations which are contained inside the kernel (local observations) will be used for estimating the conditional expectation E (Y|X).