Recent comments

Pas7alavista t1_jegu8de wrote

The span describes the entire space. It's a set of vectors that you can combine using addition and multiplication in order to obtain any other vector in the space. For example a spanning set over the real number plane would be {(1,0), (0,1)}. This particular set is also an orthonormal basis and you can think of each vector as representing two orthogonal dimensions. This is because their dot product is 0.

However, any set of two vectors that are not on the same line will span the real number plane. For example, {(1,1), (0,1)} spans the real number plane, but they are not orthogonal.

Overall though it is always important to be aware of your input space, and the features/dimensions that you use to represent it. You can easily introduce bias or just noise in a number of ways if you aren't thorough. One example would be not normalizing your data.

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Fluffy-Station-8803 t1_jegu7yg wrote

LSC has redone their second floor now (not sure how long it’s been since you went) and it is very cute and fun. I’d say a lot of LSC appeal for younger kids, (I took my nanny kid starting from age 14 months), Is fun in the way everything is fun for them: everything is brand new, interesting, exciting. Not necessarily because they care about how trains work or how honey is made but cuz hey… it’s fun to look at a glass pane full of bees

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turnip_burrito t1_jegu7uk wrote

Yeah I made the simplification of random vectors myself just to approximate what uncorrelated "features" in an embedding space could be like.

One thing that's relevant for embedding space size Takens theorem: https://en.wikipedia.org/wiki/Takens%27s_theorem?wprov=sfla1

If you have an originally D dimensional system (measured using correlation or information dimension for example), and you time delay embed data from the system, you at most (can be lower) need 2*D+1 embedding dimensions to ensure no false nearest neighbors.

This sets an upper bound if you use time delays. Now, for a *non-*time delayed embedding, I don't know the answer. I asked GPT4 and it said no analytical method for determining embedding dimension M presently exists ahead of time. An experimental method does exist that you can perform before training a model: You need to grow the number of embedding dimensions M and calculate FNN every time M grows. Once FNN drops to near zero, then you've finally found a suitable M.

One neat part about all this is that if you have some complex D-dimensional manifold or distribution with features that "poke out" into different directions in the embedding space (imagine a wheel hub with spokes), then increasing the embedding space size M will also increase the distance between the spokes. If M gets large enough, all the spokes should be nearly equal in distance from each other, but points along a singular spoke are also far from each other in most directions except for just a small subset.

I don't think that making it super large would actually make learning on the data any easier though. Best to stick with close to the minimum embedding dimension M. If you get larger, then measurement noise in your data becomes more represented in the embedded distribution. These dynamics also unfold when you increase M, which means if you're trying to only predict the D-dimensional system, you'll have harder time because now you're predicting a (D+large#) dimensional system and the obviousness of the D-dimensional system distribution gets lost in the larger distribution.

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AntiqueCelebration69 t1_jegu7aw wrote

> Any movie that is weird, outside of the norm, or an indie film gets barely any comments or traction, and you have users in comments going: “looks boring”, “who cares”

Pretty much any non-capeshit. Shit I’ve seen people call classics like Lawrence of Arabia and Casablanca “boring”

This sub is allergic to art in films

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