Talk:Conditional mutual information

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I think the section "Multivariate mutual information" should be renamed. "Multivariate mutual information" is a term that simply does not exist in the literature and is defined and used solely within Wikipedia. I think it is inappropriate for wikipedia to be a primary source for the definition of terms. Other terms for the same (or oppositely signed quantity) include co-information (Bell 2003), multiple mutual information (Han 1980), interaction information (opposite sign) (McGill 1954) or separately as redundancy or synergy (Gawne and Richmond 1993; Schneidman et al. 2003). Without a reference to a published source which defines and uses the term "multivariate mutual information" I think it is confusing and misleading to have it on wikipedia. It is anyway a very ambiguous term as mutual information between two multidimensional variables might very well be (and frequency is) referred to as multivariate mutual information. 130.209.89.69 (talk) 14:06, 7 April 2016 (UTC)[reply]

References for formulas

I am looking for a reference for the formula:

I(X;Y|Z)=H(Z|X)+H(X)+H(Z|Y)+H(Y)-H(Z|X,Y)-H(X,Y)-H(Z)=I(X;Y)+H(Z|X)+H(Z|Y)-H(Z|X,Y)-H(Z)

I checked ^[1] but couldn't find it in it. Magomahot (talk) 06:07, 19 July 2016 (UTC)[reply]

_{There is now a link to StackExchange^[2] answering this question. I also replaced the ref ^[3] which seemed mis-cited there by a ref to ^[4] which is more appropriate. Magomahot (talk) 00:43, 20 July 2016 (UTC)}[reply]

References

^ K. Makarychev et al. A new class of non-Shannon-type inequalities for entropies. Communications in Information and Systems, Vol. 2, No. 2, pp. 147–166, December 2002 PDF
^ Decomposition on Math.StackExchange
^ K. Makarychev et al. A new class of non-Shannon-type inequalities for entropies. Communications in Information and Systems, Vol. 2, No. 2, pp. 147–166, December 2002 PDF
^ Cover, Thomas; Thomas, Joy A. (2006). Elements of information theory (2nd ed.). New York: Wiley-Interscience. ISBN 0-471-24195-4.

Slight Notation Confusion

Maybe this is just my unfamiliarity with the topic, but what is meant by the notation in this section: $I(X;Y,Z)$ ? Is this the same thing as Interaction Information, which is notated $I(X;Y;Z)$ ? Zjwilliams20 (talk) 15:26, 23 February 2024 (UTC)[reply]

[1] K. Makarychev et al. A new class of non-Shannon-type inequalities for entropies. Communications in Information and Systems, Vol. 2, No. 2, pp. 147–166, December 2002 PDF

[2] Decomposition on Math.StackExchange

[3] K. Makarychev et al. A new class of non-Shannon-type inequalities for entropies. Communications in Information and Systems, Vol. 2, No. 2, pp. 147–166, December 2002 PDF

[4] Cover, Thomas; Thomas, Joy A. (2006). Elements of information theory (2nd ed.). New York: Wiley-Interscience. ISBN 0-471-24195-4.

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