Core Concepts
Permutation invariance simplifies complex ML problems.
Stats
"Our test statistics take the form T := supt∈[0,1]d √n eFn(t) − Fn(t), where Fn(t) is the empirical CDF at t, eFn(t) = Fn(sort t), and n is the size of the random sample."
"We propose a kernel density estimator (KDE) that averages over a carefully constructed subset of permutations."
"The logarithm of the covering number for the permutation invariant H¨older class with a boundary condition is reduced by a factor of d!."
Quotes
"Permutation invariance simplifies the exploitation of complex problems in machine learning."
"Our methods for testing permutation invariance and kernel ridge regression are based on sorting and averaging tricks."