Surely the burden is squarely on the author to show what the generalization (in this context) offers that the specific concept of sufficient statistics does not? In other words, how else can a statistician or ML expert use this foreign "monoid" concept to improve or better understand parameter estimation?
"show what the generalization (in this context) offers that the specific concept ... does not"
What does group theory tell me in the context of 1+1 that knowing the answer is 2 doesn't? Generalizations are useful because they apply to more than one context.
That said; the interesting connection between two areas of mathematics is what I took from the article, but I'd agree that his title (well, subtitle) is way overblown - his argument for "Why ML experts should care" seems to boil down to speed, but the Haskell statistics package itself contains faster algorithms that are marked unsafe, and he hasn't demonstrated safety.
