@srean -- I agree with you. To make the GP statement true, you have to adopt sweepingly wide definitions of the terms "parametric" and "density estimation", an

@srean -- I agree with you. To make the GP statement true, you have to adopt sweepingly wide definitions of the terms "parametric" and "density estimation", and a very narrow concept of ML to boot. You have given some good background and I feel a need to add more examples. The idea of boosting comes to mind. A quintessential ML concept, widely applicable, but really nothing to do with density estimation. All the PAC learning results are another example. They show very strong results over very wide problem classes, but don't have to do with density estimation. They apply, for example, to problems where no density exists (just a probability measure), much less a smooth-enough density to estimate. Another example of ML research that comes to mind is time and space efficient learning. There is a whole body of work on probabilistic analysis of data structures used for ML (I'm thinking partly about Alex Gray's work, http://www.cc.gatech.edu/~agray/ http://www.cc.gatech.edu/~agray/). The work fits solidly into ML, but it's not about density estimation, it's about making provably fast algorithms for large problems.