Answers.Body: <p>Their reasoning is that mutual information is symmetric, giving equal value to 1s and 0s, as it is derived from information theory, where they are just two symbols used to encode a message, with neither being more important than the other. A message encodes a lot of information if the two symbols are roughly equal in probability.</p>
  <p>The Dice coefficient, however, centres on two events occurring at the same time, and so handles 1-1 differently from 0-0, as 1 stands for the occurrence of a (comparatively rare) event, whereas 0 represents the (much more common) absence of the event.</p>
  <p>In the formulae, the Dice coefficient adds up the individual probabilities in the denominator, whereas in mutual information they are multiplied. If you add two small numbers, you get a number that is slightly larger than the two individual ones, but if you multiply them, you get one that is much smaller. Mutual information has a well-known problem in that it emphasises extremely rare events, which is why it is not used as much any more as it was in the early 1990s.</p>
  <p>Thus the Dice coefficient looks for the mutual occurrences but is less concerned with how often each item occurs on its own (addition vs multiplication of individual probabilities).</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-11T08:48:39.840Z
Answers.LastActivityDate: 2021-08-11T08:48:39.840Z
Answers.UserDisplayName: Oliver Mason
Body: <p>I'm confused about the interpretation and assumptions of the <a href="https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient" rel="nofollow noreferrer">Dice coefficient</a> versus the more popular measure <a href="https://en.wikipedia.org/wiki/Mutual_information" rel="nofollow noreferrer">mutual information</a>. I'm specifically referencing its use in hierarchical semantic network analysis, or ranking the significance of collocation of words.</p>
  <p>I'm referencing <a href="https://aclanthology.org/J96-1001.pdf" rel="nofollow noreferrer">Translating Collocations for Bilingual
  Lexicons: A Statistical Approach </a> which talks about how the Dice coefficient is more appropriate when you don't want 0-0 matches to be significant. However, as a amateur in probability, it's not really clear to me from the respective formulas why this would be.</p>
  <p>Could someone explain?</p>
  
Tags: <comparison><information-theory><semantic-networks>
Title: Why would the Dice coefficient be more suitable than mutual information when you don't want 0-0 matches to be significant?
UserDisplayName: Arden
ThreadText: # Why would the Dice coefficient be more suitable than mutual information when you don't want 0-0 matches to be significant?
  
  (Asked by: username_0 on 2021-08-10)
  
  I'm confused about the interpretation and assumptions of the [Dice coefficient](https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient) versus the more popular measure [mutual information](https://en.wikipedia.org/wiki/Mutual_information). I'm specifically referencing its use in hierarchical semantic network analysis, or ranking the significance of collocation of words.
  
  I'm referencing [Translating Collocations for Bilingual
  Lexicons: A Statistical Approach](https://aclanthology.org/J96-1001.pdf)  which talks about how the Dice coefficient is more appropriate when you don't want 0-0 matches to be significant. However, as a amateur in probability, it's not really clear to me from the respective formulas why this would be.
  
  Could someone explain?
  
  **Tags:** comparison, information-theory, semantic-networks
  
  
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  ## 1 answers
  
  ### Answer by username_1 on 2021-08-11. Score: 1
  
  Their reasoning is that mutual information is symmetric, giving equal value to 1s and 0s, as it is derived from information theory, where they are just two symbols used to encode a message, with neither being more important than the other. A message encodes a lot of information if the two symbols are roughly equal in probability.
  
  The Dice coefficient, however, centres on two events occurring at the same time, and so handles 1-1 differently from 0-0, as 1 stands for the occurrence of a (comparatively rare) event, whereas 0 represents the (much more common) absence of the event.
  
  In the formulae, the Dice coefficient adds up the individual probabilities in the denominator, whereas in mutual information they are multiplied. If you add two small numbers, you get a number that is slightly larger than the two individual ones, but if you multiply them, you get one that is much smaller. Mutual information has a well-known problem in that it emphasises extremely rare events, which is why it is not used as much any more as it was in the early 1990s.
  
  Thus the Dice coefficient looks for the mutual occurrences but is less concerned with how often each item occurs on its own (addition vs multiplication of individual probabilities).
  
  
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