Answers.Body: <p>I agree that this notation is unclear. I would interpret it as follows: </p>
  
  <p>Given that the expression is supposed to denote the <strong>average norm</strong> <span class="math-container">$|p_i|$</span> is likely the cardinality of the set <span class="math-container">$\{p_i\}$</span>. </p>
  
  <p>In that case the expression would just be the sum over all norms divided by the number of norms, resulting in the average norm. The authors likely use this notation because they didn't want to introduce the number <span class="math-container">$n$</span> of <span class="math-container">$p_{i &lt; n}$</span>. <span class="math-container">$|\{p_i\}|$</span> would be clearer, but maybe uglier to typeset. </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-01-28T04:56:17.683Z
Answers.Text: Much obliged for the response, I'm confused with the usage of mod('|x|') notation, since cardinality will either take zero or a positive number.
Answers.UserDisplayName: Stephen Philip
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-01-27T13:48:37.307Z
Answers.LastActivityDate: 2020-01-27T13:57:36.367Z
Answers.LastEditDate: 2020-01-27T13:57:36.367Z
Answers.UserDisplayName: BlindKungFuMaster
Body: <p>In the snippet below, the highlighted part is the average norm, but since <span class="math-container">$1/|p_i|$</span> is outside the summation, it is very confusing to understand.</p>
  
  <ul>
  <li><p>is <span class="math-container">$|p_i|$</span> l2-norm(as per wolfram) or l1-norm or absolute value as per wiki.</p></li>
  <li><p>Should the <span class="math-container">$i$</span> inside summation be considered for <span class="math-container">$1/|p_i|$</span>, which is outside the summation?</p></li>
  </ul>
  
  <p><a href="https://i.sstatic.net/RtTjF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RtTjF.png" alt="enter image description here"></a></p>
  
Tags: <machine-learning><math><objective-functions><notation>
Title: How to understand the average l2 loss?
UserDisplayName: Stephen Philip
ThreadText: # How to understand the average l2 loss?
  
  (Asked by: username_0 on 2020-01-27)
  
  In the snippet below, the highlighted part is the average norm, but since $1/|p\_i|$ is outside the summation, it is very confusing to understand.
  
  * is $|p\_i|$ l2-norm(as per wolfram) or l1-norm or absolute value as per wiki.
  * Should the $i$ inside summation be considered for $1/|p\_i|$, which is outside the summation?
  
  [![enter image description here](https://i.sstatic.net/RtTjF.png)](https://i.sstatic.net/RtTjF.png)
  
  **Tags:** machine-learning, math, objective-functions, notation
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-01-27. Score: 1 | Accepted answer
  
  I agree that this notation is unclear. I would interpret it as follows:
  
  Given that the expression is supposed to denote the **average norm** $|p\_i|$ is likely the cardinality of the set $\{p\_i\}$.
  
  In that case the expression would just be the sum over all norms divided by the number of norms, resulting in the average norm. The authors likely use this notation because they didn't want to introduce the number $n$ of $p\_{i < n}$. $|\{p\_i\}|$ would be clearer, but maybe uglier to typeset.
  
  > **Comments:**
  > **username_0**: Much obliged for the response, I'm confused with the usage of mod('|x|') notation, since cardinality will either take zero or a positive number.  
  
  ---
  
  