Holmes said that law should be seen as induction, not deduction. Induction involves pattern matching, analogizing, and so on. I think that at least the first 4 of the 5 types of argument described in the article can be thought of as types of induction.
Holmes also said that the law consists of nothing more than prediction of what courts will do. And he described the development of the law in language that would make any Machine Learning person think of nearest neighbour classification: "The growth of the law is very apt to take place in this way: two widely different cases suggest a general distinction, which is a clear one when stated broadly. But as new cases cluster around the opposite poles, and begin to approach each other [...] at last a mathematical line is arrived at by the contact of contrary decisions."
It seems to me that the legal theory of Holmes, and the modern practice of machine learning, are remarkably similar. They're both about prediction based on experience / datasets. Shameless plug: I've written a (free!) book about it, "On the path to AI: Law’s prophecies and the conceptual foundations of the machine learning age".