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Does using tensors for storage yield some benefit over the 'panels' metaphor that Python Pandas affords? It seems like the real power of tensors is in the calcu
by clebio 11y ago
Does using tensors for storage yield some benefit over the 'panels' metaphor that Python Pandas affords? It seems like the real power of tensors is in the calculus that can be run over them, rather than just them by themselves.
If I want to store lists of numbers, arrays and (linked) lists are basically equivalent. It's when I want to calculate cross- and dot-products that vectors prove especially useful.
The discussions I've seen recently in data science about tensors seems to only be about the storage aspect. And, I suppose, if your libraries _don't_ provide such a storage mechanism, then yes, you'll benefit from adding that capability. But I keep waiting for more from the ML community about leveraging differential geometry full-on. I assume it's out there somewhere, in some shops, but I've not found a lot of discussion about it.
- tel 11y agoThere's actually quite a lot of this under the phrase "information geometry". Offhand, I feel like a lot of this work is coming out of Japan. http://www.amazon.com/Information-Translations-Mathematical-Monographs-Tanslations/dp/0821843028/ref=pd_sim_b_2?ie=UTF8&refRID=0E92317F4Y8R9KQWT7JM http://www.amazon.com/Information-Translations-Mathematical-... http://www.amazon.com/Algebraic-Statistical-Monographs-Computational-Mathematics/dp/0521864674 http://www.amazon.com/Algebraic-Statistical-Monographs-Compu...
- clebio 11y agoOh, awesome, thanks for those links!
- tel 11y agoNo problem! There's also one more book I was trying to find which basically recasts normal linear regression in the geometric projection terms that most people know but that are never emphasized when learning it. The nice part of that method is that then you can extend the geometric interpretation to manifolds and get, I believe, GLM very naturally.
- clebio 11y agoThanks again. I'd found this text[1], but it's a bit pricey! [1]: http://www.amazon.com/gp/product/0412398605/ http://www.amazon.com/gp/product/0412398605/