I'm getting my understanding of kernel density estimation from pages 6-7 of this PDF.

If there are conceptual relationships between the "kernels" in each of these topics, I'd like to understand them.


Kernel density estimation and Kernel methods(referring to interpolation or regression by using kernels) employ the same use of kernel. The kernel of a matrix is unrelated.

In the first two problems the kernel acts a basis function centered at a data points $k(x, x_i)$. The idea is that if we take linear combinations of these basis functions we can describe other functions $f(x) = \sum_i w_ik(x,x_i)$

In kernel density estimation we approximate a pdf as the average of a bunch of these basis functions. Typically people use radial basis functions $k(x,x_i) = \exp(-||x-x_i||^2/h)$

To get a good fit we need to tune the length scale parameters $h$. For general curve fitting with basis functions we do basically the same process but typically do a weighted average.


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