4 ms·
All machine learning is about finding hyperplanes.
by adamnemecek 3y ago
All machine learning is about finding hyperplanes.
- nologic01 3y agoThe large dimensionality seems to be what creates the need for heuristic designs rather than a generic approach
- adamnemecek 3y agoHyperplanes are the heuristics.
- alexmolas 3y agoHyperplanes is all you need
- quickthrower2 3y agoHyperplanation is all you need
- jpfed 3y agoSomeday I'm going to write a paper that achieves SOTA results with a nigh-incomprehensible mishmash of diverse techniques and title it "All You Need Considered Harmful".
- tudorw 3y agoand multi-dimensional topological manifolds, maybe :)
- revskill 3y agoWhat is hyperplane ?
- adamnemecek 3y agoFor 2d, a line, for 3d a plane, for nd a hyperplane. https://en.wikipedia.org/wiki/Hyperplane https://en.wikipedia.org/wiki/Hyperplane
- noduerme 3y agoit's a word (a made up word)
- MattPalmer1086 3y agoAll words are made up!
- noduerme 3y agoYeah, but only a few are made up to seem like terms of art designed to obfuscate their actual meaning; and usually prepending "hyper-" to something is a signal that a more clear description of the thing doesn't yet exist. Downvote away, fellas.
- adamnemecek 3y agohttps://en.wikipedia.org/wiki/Hyperplane https://en.wikipedia.org/wiki/Hyperplane
- shakow 3y agoA subspace of dimension n-1 of a n-dimensional vector space. It is an extension of the well-known concept of a 2d-plane in a 3d-space to nd-spaces.
- eru 3y agoYou could also describe a hyperplane as the set of solutions of a system of linear equations.
- shakow 3y agoOr as the subspace of all the vectors are orthogonal to a given single vector, or as the subspace generated by any orthogonal basis with one base vector removed, or as the kernel of a linear form, ... – but a more visual explanation is probably better as a first foray in the question.
- loehnsberg 3y agoA hyperplane is a multi-dimensional linear function that splits space into two distinct regions. In the context of a classifier, it splits feature space into disjunct sub-spaces (one for each class). SVMs effectively place a hyperplane with maximum margin, thereby separating classes in an optimal way.
- im3w1l 3y agoWorth keeping in mind that though it may be optimal according to some mathematical criterion, that is no guarantee that it's the best for the purposes you have in mind.
- blt 3y agoa partition of Euclidean space into two convex sets ;)
- mafribe 3y agoThis is wrong! The term hyperplane already assumes that the hypothesis space that your learning algorithm searches has some kind of dimension and is some variant of an Euclidean / vector space (and its generalisations). This is not the case for many forms of ML, for example grammar induction (where the hypothesis space is Chomsky-style grammars) or inductive logic programming (hypothesis space are Prolog (or similar) programs), or, more generally, program synthesis (where programs form the hypothesis space).
- adamnemecek 3y agoIt can also just be some sort of partitioning. I would be really surprised if there was no partitioning of some space.
- mafribe 3y agoNote that "some sort of partitioning" isn't a hyperplane. A partition is a set-theoretic concept. A hyperplane is (a generalisation of) a geometric concept, so has much more structure.
- adamnemecek 3y agoAlright how about coalgebra.