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I want to avoid the repetition of the words "mutual information" in the following sentence:

"where I(X_i;X_j|Y) and I(X_i;X_j) denote, respectively, the conditional mutual information and the mutual information."

Is there a way to avoid repeating "mutual information" without losing the general meaning of the sentence?

Thank you.

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    Without knowing what the notation is supposed to represent, it's not easy to answer. If the two sets of data do not overlap, then you could say "the conditional mutual information and the unconditional", for example. – Andrew Leach Jan 25 '16 at 14:07
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    If conditional mutual information and mutual information are defined terms it is better to use them rather than attempt to avoid repetition; one wouldn't try to find a synonym when writing absolutely convergent and therefore convergent, for instance. – Brian Hooper Jan 25 '16 at 14:13
  • @BrianHooper , Yes, they are defined terms. But, the sentence looks awkward because of the repetition. – Hadjer Jan 25 '16 at 14:42
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It's possible to make the repetition sound less awkward by re-arranging the sentence:

"...where I(X_i;X_j|Y) denotes the conditional mutual information and I(X_i;X_j) denotes the mutual information."

or, depending on the preceding context,

"...with mutual information I(X_i; X_j) and conditional mutual information I(X_i;X_j|Y)."

The second may be appropriate if the phrase immediately follows an equation, and a complete sentence precedes the equation, but that's hard to tell without more information.

  • here is the complete sentence: "The function f is defined by: f(h_i,h_j)=I(X_i;X_j|Y)-I(X_i;X_j), where I(X_i;X_j|Y) and I(X_i;X_j) denote, respectively, the conditional mutual information and the mutual information. I think that your second suggestion solves my problem. What do you think? – Hadjer Jan 25 '16 at 14:38
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You could write:

where I(X_i;X_j|Y) and I(X_i;X_j) denote the conditional and the non-conditional mutual information, respectively

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