I was wondering (about a more semantic question), is there a difference between data-driven methods and machine learning? Or is it more correct to state that machine learning is a category of data-driven methods (and what then are other categories)?
Based on the quotation you have added in your comments, data-driven approaches are approaches where you use data that describes past states ("historical data") to get a (not defined) system to give a desired output.
To understand whether this definition includes machine learning or not we will have to define "machine learning", and while there could be plenty of ways to define it I expect that it will be quite difficult to come up with a definition that does not include within it "Using a system that, based on given states will give a desired output".
Note that in this last definition I use "given states" and not "past states" as to include approaches such as online learning.
Bottom line is that unless you really want to hold to a narrow definition of "past states" it seems that machine learning approaches are a subset of data-driven approaches.
In my view, Empirical Likelihood method is a very data-driven method but it has nothing to do with machine learning. Here is a link talking about the Empirical Likelihood method: