Theil-Sen Robust Linear Regression

This function executes a fast version of the non-parametric Theil-Sen robust linear regression algorithm by finding the median slope between all pairwise combinations of points in a given data set.
For my application I needed to run a robust regression on large data sets (many thousands of points), but the implementations I found on the File Exchange were far too slow (see figure). This code is substantially faster, and for large data sets can be two orders of magnitude faster than those currently available.