title: Computing precision and recall in Named Entity Recognition
body: <p>Now I am about to report the results from Named Entity Recognition. One thing that I find a bit confusing is that my understanding of precision and recall was that one simply sums up true positives, true negatives, false positives and false negatives over all classes.</p>
  
  <p>But this seems implausible now that I think of it as each misclassification would give simultaneously rise to one false positive and one false negative (e.g. a token that should have been labelled as "A" but was labelled as "B" is a false negative for "A" and false positive for "B"). Thus the number of the false positives and the false negatives over all classes would be the same which means that precision is (always!) equal to recall. This simply can't be true so there is an error in my reasoning and I wonder where it is. It is certainly something quite obvious and straight-forward but it escapes me right now.</p>