9
$\begingroup$

my main problem is that, i don't understand what argmax means in this equation (page 134., figure 4., the output part)

I want to write a code, but i don't understand this equation. Is there any simpler form of this equation ? (maybe an example)

This is how i understand it: 1. i count the sum first 2. i find the argmax

Sorry for my dummy question, but i am not realy good in this area. Thanks for your answers !

$\endgroup$
3
  • 5
    $\begingroup$ Did you do any research? $\endgroup$
    – user296602
    Aug 25 '16 at 20:47
  • 4
    $\begingroup$ You are reading an exceptionally complicated paper for someone who hasn't gotten acquainted with the term "argmax"... $\endgroup$
    – Ian
    Aug 25 '16 at 20:48
  • $\begingroup$ Note: I fully agree with the two comments above. Now, if you want an algorithm-version of this equation: "loop over all elements $y\in Y$, compute for each of them the value $\sum_{i=1}^T (\log\frac{1}{\beta_t}) h_t(x,y)$; return the $y$ for which this quantity is maximum." $\endgroup$
    – Clement C.
    Aug 25 '16 at 21:00
22
$\begingroup$

Lets say we have a funktion $f(x) = -(x-2)^2 + 3$, which has a global maximum at $x_0=2$ with $f(x_0)=3$.

This means that $\max(f) = 3$. $\arg\!\max$ answers not how high the maximum is, but where it occurs: $\arg\!\max(f) = 2$.

Note that $f(\arg\!\max(f)) = \max(f)$.

$\endgroup$
1
  • 10
    $\begingroup$ Strictly speaking, $f(\arg \max(f))=\{ \max(f) \}$, because the argmax is a set. $\endgroup$
    – Ian
    Aug 29 '16 at 20:26
2
$\begingroup$

In general $$x^*=\arg \max_x f(x) $$ means return $x$ that maximizes $f(x)$.

How to find $x^*$? 1) Find $f(x)$ for all possible values of $x$ as $\{x_n,\,f(x_n)\}$. 2) Find the maximum value of $f(x)$ in the set $\{f(x_n)\}$, let's denote it by $f(x_\max)$. 3) return $x_\max$.

You don't have to store all values. You can start by saying that $x_\max=x_1,\,f_\max=f(x_1)$. Then if $f(x_2)>f_\max$ update the values as $x_\max=x_2,\,f_\max=f(x_2)$. If not, keep the previous values. When all the possible values of $x$ are considered, your $x_\max$ at the end will be the value you are looking for.

Apply this to your situation.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.