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In the above paper, the authors mentioned "asymptotic error". Can anyone explain a bit about this?

For example, the abstract of the paper includes:

Discriminative learning has lower asymptotic error, a generative classifier may also approach its higher asymptotic error much faster.

What is the exact definition of "Asymptotic Error"?

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    $\begingroup$ Please add whatever context is necessary to understand & answer your question into the text of the question itself. Eg, provide a full citation for the paper, & quote the context in which the term is used. People aren't going to want to download & read a paper so that they can answer your question for you, & we want this thread to be informative in the future even if the link goes dead. $\endgroup$ Nov 20, 2015 at 0:30
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    $\begingroup$ I have added some lines from the paper. Is it understandable ? $\endgroup$
    – lighthouse
    Nov 20, 2015 at 2:37

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It means the error of a method when you run entire population through it. It's a useful measure of the method as it tells you what's the best you could get from a method. Also, you want to know how quickly the method converges to the asymptotic error, because you can't really run the population in most cases.

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What it means is just the error to which the algorithm is asymptotic. Suppose we have an error that is the limiting error that an algorithm can achieve after a number of iterations, no matter how many. The error for the $i^{th}$ iteration is then (typically) larger than the error associated with a limiting number of iterations. The text is comparing a larger terminal error that is quickly achieved for fewer iterations with a smaller terminal error that takes more iterations to achieve.

A problem with this is that the terminal error may be only relatively constant, such that the language used is inexact. In the quote, "lower" means smaller absolute error, and "higher" means larger absolute error.

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