I have trouble understanding the delineation of "non-parametric" methods. It seems to me most non-parametric methods are parametric, just on a different space than the "standard ones".
Graph-based inferences are often described as non-parametric, but graphs are fully described by the set of adjacency matrix parameter values. Likewise rankings can be considered a transformation of values onto a different parameter space. Non-parametric seems to get tossed around whenever something is parametric in a high dimensional way on a space we don't typically use.
If the definition is a question of the use of a distribution, coming from a Bayesian background, I guess my intuition is often that usually when we don't put a distribution on something we're often neglecting to capture its uncertainty, rather than something intrinsic to the method.
Hence there seem to be bayesian formulations of "non-parametric" methods which involve parameter distributions, suggesting that a lack of a distribution isn't inherent to the representation or method, but more of a modeling decision.