Notation: getting one value from arg max

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Discussion Overview

The discussion revolves around the notation for obtaining the last index from an arg max operation when multiple indices yield the same maximal value. Participants explore how to express this requirement mathematically, particularly in the context of functions and their indices.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks a notation to denote the last index in an arg max operation when multiple indices yield the same maximum value.
  • Another participant expresses uncertainty about whether the desired notation refers to taking the arg max of a maximum function or the maximum of arg max values.
  • A participant clarifies that they want the index corresponding to the highest function value, specifically the last index in case of ties.
  • Another participant suggests a notation but admits to not having a standard expression for the requirement.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a standard notation for the described operation, and multiple interpretations of the notation are presented.

Contextual Notes

There is ambiguity regarding the definitions and interpretations of the arg max and max operations in this context, which may affect the clarity of the notation being sought.

Max.Planck
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I want to take the arg max over a number of functions as below, however it is possible that there are multiple i's for which the result is maximal. How do i denote that I want to take the last possible i, for example if it results in 3 and 5 I want it to return 5, is there notation available for this?

arg\,max_{i} f_{i}(\mathbf{x})
 
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I am not aware of such notation, but it's unclear to me whether you're looking to denote $$ argmax f\text{ where }f(x)=max_{\{i\}}f_i(x) $$ or $$ max_{\{i\}} argmax f_i $$
 
I want to get the index of the function with the highest value for that particular x, and if there are several, the last index should be returned.
 
OK, so ## \max(\text{argmax}_{i}f_i(x)) ##... Sorry, can't think of a standard notation for that, maybe others will.
 

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