公式 t0=arg max g(t) 的 arg 是什么意思啊？

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公式 t0=arg max g(t) 的 arg 是什么意思啊？

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关键词：是什么意思 max 意思 公式 arg max

是指使得函数g(t)最大时，t的取值

jinnson 发表于 2010-3-17 11:20 公式 t0=arg max g(t) 的 arg 是什么意思啊？

更严格一些，argmax g(t)，表达的是定义域的一个子集，该子集中任一元素都可使函数g(·)取最大值。

t0=arg max g(t) 的 arg :
t0 belongs to the set of ARGUMENTS that MAXIMIZE the function value g(t)
就是说，t0是一个能使得g（t）这个函数取最大值的一个值 （当然，这个函数有可能有N个最大值点）

类似于反函数一样，不过是一个定的数字或者集合

精彩！非常感谢各位！

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1# jinnson

n mathematics, arg max (or argmax) stands for the argument of the maximum, that is to say, the set of points of the given argument for which the value of the given expression attains its maximum value:[note 1]
In other words,
is the set of values of x for which f(x) has the largest value M. For example, if f(x) is 1?|x|, then it attains its maximum value of 1 at x = 0 and only there, so .

Equivalently, if M is the maximum of f, then the arg max is the level set of the maximum:
If the maximum is reached at a single value, then one refers to the point as the arg max, meaning we define the arg max as a point, not a set of points. So, for example,
(rather than the singleton set {5}), since the maximum value of x(10 ? x) is 25, which happens when x = 5.[note 2]
However, in case the maximum is reached at many values, arg max is a set of points.
Then, we have for example
since the maximum value of cos(x) is 1, which happens on this interval when x = 0, 2π or 4π. On the whole real line, the arg max is
arg min (or argmin) is defined analogously.
Note also that functions do not in general attain a maximum value, and hence will in general not have an arg max: is undefined, as x isunbounded on the real line. However, by the extreme value theorem (or the classical compactness argument), a continuous function on a compact intervalhas a maximum, and thus an arg max.




from :    http://en.wikipedia.org/wiki/Arg_max

学习了，多谢。

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