'Metrizing Weak Convergence with Maximum Mean Discrepancies', by Carl-Johann Simon-Gabriel, Alessandro Barp, Bernhard Schölkopf, Lester Mackey.

http://jmlr.org/papers/v24/21-0599.html

#measures #kernels #rkhs

Following on from this, I rewrote the 30-line Python script into Java, using the excellent XChart library.

This script illustrates how different functions can be created from providing different indices: each index is used to create a single-argument function from a two-argument kernel:

f_y(x) = K(y, x)

So the indices give a set of y's, and the overall evaluation is:

f(x) = sum_{y in ys} K(y, x)

https://notabug.org/peterlane/rkhs

#machinelearning #rkhs

New term, new courses to write. Starts me thinking again about Support Vector Machines and underlying theory.

Found an interesting 'primer' article, describing the basics of Reproducing Kernel Hilbert Spaces, and how adding together kernel functions can approximate new functions. Especially useful in statistical applications, as collections of individual data points can be efficiently converted into a continuous function.

https://hpccsystems.com/resources/reproducing-kernel-hilbert-space-rkhs-a-primer-for-non-mathematicians/

#machinelearning #rkhs