It is -- there's a whole area called Information Geometry which treats the parameter spaces of statistical models as Riemannian manifolds under the Fisher infor

It is -- there's a whole area called Information Geometry which treats the parameter spaces of statistical models as Riemannian manifolds under the Fisher information metric. As an example application, when sampling from the posterior of a Bayesian model it can help to take this natural geometry of the parameter space into account, e.g. via Riemannian Manifold Hamiltonian Monte Carlo [1] Then again, from what I've seen most Manifold Learning only uses the word manifold in a loose handwavey sense to motivate what they're doing -- the added abstraction level of differential geometry doesn't always add very much you're just interested in learning smooth functions from R^m -> R^n. [1] http://www.dcs.gla.ac.uk/publications/PAPERS/9149/RMHMC_MG_BC_SC_07_09.pdf http://www.dcs.gla.ac.uk/publications/PAPERS/9149/RMHMC_MG_B...