3 ms·
Treating data as a distribution in high-dimensional space is at the core of machine learning, and differentiating across those dimensions is typically how learn
by cowpig 12y ago
Treating data as a distribution in high-dimensional space is at the core of machine learning, and differentiating across those dimensions is typically how learning is done.
I don't know if this is true, but at a glance it looks to me like differential geometry could be useful to people in machine learning. Am I right about that? I am probably going to look closer tonight...
- crasshopper 12y agoYes, you're right about that.
- kevdevnull 12y agotake a look at manifold learning, this should point you in the right direction: http://web.mit.edu/6.454/www/www_fall_2003/ihler/slides.pdf http://web.mit.edu/6.454/www/www_fall_2003/ihler/slides.pdf
- deleted 12y ago[deleted]
- deleted 12y ago[deleted]
- mjw 12y agoIt 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...