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I'm trying to calculate PMI using probabilities estimated using binary occurrence counts from a set of documents. In short:

$P(x)$ = # documents x appears in / # documents
$P(y)$ = # documents y appears in / # documents
$P(x,y)$ = # documents x and y appear in / # documents

$PMI(x,y) = log\left(\frac{P(x, y)}{P(x)P(y)}\right)$

My question is: how do I handle the case where $P(x,y)=0$ , where $x$ and $y$ appear in no documents together?

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    $\begingroup$ What is PMI? I found many acronyms online. $\endgroup$
    – ERT
    Commented Aug 9, 2018 at 17:21
  • $\begingroup$ What will you be using these results for? That will help determine what to do when $P(x,y)=0.$ $\endgroup$
    – whuber ♦
    Commented Aug 9, 2018 at 17:58
  • $\begingroup$ I'm using it to calculate Semantic Orientation, for the purpose of Sentiment Analysis. $\endgroup$
    – infinitely_improbable
    Commented Aug 9, 2018 at 18:56

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