Body: <p>The divergence between two probability distributions is used in calculating the difference between the true distribution and generated distribution. These divergence metrics are used in loss functions.</p>
  <p>Some divergence metrics that are generally used in literature are:</p>
  <ol>
  <li><a href="https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence" rel="nofollow noreferrer">Kullback-Leibler Divergence</a></li>
  <li><a href="https://en.wikipedia.org/wiki/Jensen%E2%80%93Shannon_divergence" rel="nofollow noreferrer">Jensen–Shannon divergence</a></li>
  <li><a href="https://en.wikipedia.org/wiki/F-divergence" rel="nofollow noreferrer">f-divergence</a></li>
  <li><a href="https://en.wikipedia.org/wiki/Wasserstein_metric" rel="nofollow noreferrer">Wasserstein distance</a></li>
  </ol>
  <p>Some other divergence measures <a href="https://en.wikipedia.org/wiki/Divergence_(statistics)" rel="nofollow noreferrer">include</a>:</p>
  <ol start="5">
  <li>Squared Hellinger distance</li>
  <li>Jeffreys divergence</li>
  <li>Chernoff's <span class="math-container">$\alpha-$</span>divergence</li>
  <li>Exponential divergence</li>
  <li>Kagan's divergence</li>
  <li><span class="math-container">$(\alpha, \beta)-$</span>product divergence</li>
  <li>Bregman divergence</li>
  </ol>
  <p>I think some naive divergence measures include</p>
  <ol start="12">
  <li>Least-squares divergence</li>
  <li>Absolute deviation</li>
  </ol>
  <p>Along with these, are there any other divergence measures available to compute the distance between the true probability distribution and estimated probability distribution in artificial intelligence?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-08T12:29:59.297Z
Comments.Text: You're already listing many measures. Probably all the major ones used in the literature that I know too. Anyway, keep in mind that our site is not appropriate for asking questions that require very long answers that require a lot of effort and time to write. So, it may be a good idea to reformulate your question that you provide more details about **why** you're interested in more measures and maybe ask for a reference that covers them (rather than asking for us to enumerate them), if you're interested in an extensive list. In that case, you may want to use the tag [tag:reference-request].
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-08T12:30:28.213Z
Comments.Text: Having said that, in [this answer](https://ai.stackexchange.com/a/25167/2444), I provide a link to a paper that talks about the topic, but I don't remember which measures are listed there (maybe you already list all the ones mentioned there too).
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-08T13:44:54.700Z
Comments.Text: @nbro Thanks... I rephrased, I think now even any single metric is eligible as an answer.
Comments.UserDisplayName: hanugm
Tags: <probability-distribution><metric>
Title: Are there any other metrics available for calculating the distance between two probability distributions other than those mentioned?
UserDisplayName: hanugm
ThreadText: # Are there any other metrics available for calculating the distance between two probability distributions other than those mentioned?
  
  (Asked by: username_0 on 2021-08-08)
  
  The divergence between two probability distributions is used in calculating the difference between the true distribution and generated distribution. These divergence metrics are used in loss functions.
  
  Some divergence metrics that are generally used in literature are:
  
  1. [Kullback-Leibler Divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence)
  2. [Jensen–Shannon divergence](https://en.wikipedia.org/wiki/Jensen%E2%80%93Shannon_divergence)
  3. [f-divergence](https://en.wikipedia.org/wiki/F-divergence)
  4. [Wasserstein distance](https://en.wikipedia.org/wiki/Wasserstein_metric)
  
  Some other divergence measures [include](https://en.wikipedia.org/wiki/Divergence_(statistics)):
  
  5. Squared Hellinger distance
  6. Jeffreys divergence
  7. Chernoff's $\alpha-$divergence
  8. Exponential divergence
  9. Kagan's divergence
  10. $(\alpha, \beta)-$product divergence
  11. Bregman divergence
  
  I think some naive divergence measures include
  
  12. Least-squares divergence
  13. Absolute deviation
  
  Along with these, are there any other divergence measures available to compute the distance between the true probability distribution and estimated probability distribution in artificial intelligence?
  
  **Tags:** probability-distribution, metric
  
  > **Comments:**
  > **username_1**: You're already listing many measures. Probably all the major ones used in the literature that I know too. Anyway, keep in mind that our site is not appropriate for asking questions that require very long answers that require a lot of effort and time to write. So, it may be a good idea to reformulate your question that you provide more details about **why** you're interested in more measures and maybe ask for a reference that covers them (rather than asking for us to enumerate them), if you're interested in an extensive list. In that case, you may want to use the tag [tag:reference-request].  
  > **username_1**: Having said that, in [this answer](https://ai.stackexchange.com/a/25167/2444), I provide a link to a paper that talks about the topic, but I don't remember which measures are listed there (maybe you already list all the ones mentioned there too).  
  > **username_0**: @username_1 Thanks... I rephrased, I think now even any single metric is eligible as an answer.  
  
  ---
  
  ## 0 answers
  
  