I'm gonna talk about math for a sec, cuz I'm working late and being nerdy.
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This basic fact is the achilles heel of a lot of modern data science. Eigenvalue methods are everywhere, and all rely on costly iteration.
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The proof of this, believe it or not, is an *immediate* corollary of the Abel-Ruffini theorem, from 1824 (and more elegantly by Galois).
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That's right. In 18-friggin-24 we came up with a proof that has major consequences on how we do data science in 2017.
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Most modern improvement has been continuous, incremental improvement on these traditional methods. But new math is needed.
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The explosion in data science hasn't been due to technical reasons so much as it has been due to cost and availability.
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We finally have the ability to gather, transmit, and store data at reasonable costs. The algorithms? Most are older than their practitioners
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Most machine learning algorithms are unexplainable, but controlling them is easy: we can simply turn them off.
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Is there some more fundamental reason why it stops at 4, or is that just the way it is?
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Yes, there is! but it is very complicated to explain.
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The short version is that eigenvalues are the roots k of the determinant of the matrix pencil A-kI, which is a polynomial.
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Abel-Ruffini explains that there is no general solution solvable by radicals for a polynomial of degree 5 or higher.
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Okay, so looks like I guessed right! I can imagine that might need Analysis to prove.
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The elegant proof resides in Galois theory, which is generally considered part of abstract algebra
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Well I'm already looking forward to algebra next semester! Thanks for the explanation.
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Didn't know this! We use this in a statistical model but I don't know much about it
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if u throw enough qubits at phase estimation u can get close enough tho
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