Kernel Density Estimation
Overview
Kernel density estimators are a non parametric way to interpolate a value
from a sample set.
Starting with a set of data points
{% D = \{ (\vec{x}_1,y_1), ..., (\vec{x}_n, y_n) \} %}
the kernel density estimator takes a
kernel
and creates the following function
as an approximation for y given x.
{% y(x) = \frac{\sum_{i=1}^N k(x,x_i)y_i}{\sum_{j=1}^N k(x,x_j)} %}
Points with a higher similarity score as produced by the kernel function have a higher weight in the interpolation.
Examples
