Timeline for Is the square root of the Kullback-Leibler divergence a convex map?
Current License: CC BY-SA 4.0
23 events
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| Feb 22, 2022 at 21:04 | comment | added | Michael Hardy | @LSpice : You're right: I was inattentive to the distinction between "operation" and "relation", although much of what I said applies to both. | |
| Feb 22, 2022 at 0:27 | comment | added | LSpice |
@MichaelHardy, if semantic spacing is the main goal (a good one!), then one can distinguish a binary operation \mathbin from a binary relation \mathrel. \parallel is a binary relation. (I wonder if you may just have got the words switched, since you referred to $+$ as a binary relation?) One can get an operation as \mathbin\Vert if desired, like $\mu \mathbin\Vert \nu$, and then save it as a macro if desired. (It seems like there is some question about whether binary-operator spacing is the right thing here, but I just wanted to point out that these are distinct options.)
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| Feb 21, 2022 at 23:59 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Fixed misspelling of "Leibler"
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| Feb 21, 2022 at 23:54 | comment | added | Timothy Chow | @MichaelHardy You can view the PDF of their original paper on Project Euclid. It was not typeset in monospace. By comparing with, say, equals signs in the same article, you can readily confirm that the typesetter did not insert extra space around the colons. Iosef Pinelis's compromise looks pretty close to me. By the way, it's "Leibler" not "Liebler." That mistake is far more important than the spacing issue we're talking about. | |
| Feb 21, 2022 at 22:42 | comment | added | Iosif Pinelis | @MichaelHardy : Thank you for your further comments. | |
| Feb 21, 2022 at 21:53 | comment | added | Michael Hardy | @IosifPinelis : $\qquad\uparrow\qquad$ | |
| Feb 21, 2022 at 21:49 | comment | added | Michael Hardy | @TimothyChow : And I wonder whether Kullback and Liebler used a typewriter with the monospaced Courier font. That would put more space around the colon then the thing in text mode above does. | |
| Feb 21, 2022 at 21:45 | comment | added | Michael Hardy |
@TimothyChow : Let's try it: $\mu:\nu$ is coded as \mu:\nu and $\mu{:}\nu$ is coded as \mu{:}\nu. The former clearly has space to the left and right of the colon that does not appear to the left and right of the colon when no objects appear there. And the space surrounding a colon that has objects to its left and right is clearly more than the space that would be there in text mode rather than in math mode: $\text{a:b}$ is coded as \text{a:b} and $\text{a}:\text{b}$ as \text{a}:\text{b}. $\qquad$
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| Feb 21, 2022 at 15:23 | comment | added | Iosif Pinelis |
@MichaelHardy : After all this discussion, since (i) $\mu$ and $\nu$ are, not operands, but the arguments of the explicitly given function $\text{KL}$ and (ii) the spaces in $\mu\parallel\nu$ look excessive to me, I have now replaced the instances of $\mu\parallel\nu$ by $\mu\,\|\,\nu$ (an intermediate version between $\mu\parallel\nu$ and $\mu\|\nu$), now using the code \,\|\,. Thank you and Timothy Chow for the editing and discussion.
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| Feb 21, 2022 at 14:52 | comment | added | Timothy Chow | @MichaelHardy In general I am fastidious about $\rm\TeX$ but I agree with Iosif Pinelis that in this case, the parallel lines aren't really functioning as a binary relation. Kullback and Leibler originally used a colon rather than parallel lines. This was long before do-it-yourself typesetting, and extra space was not inserted around the colons. So for this particular case, I don't think there's clear right or wrong about how much space to insert. | |
| Feb 20, 2022 at 21:27 | history | became hot network question | |||
| Feb 20, 2022 at 20:57 | comment | added | Michael Hardy |
Notice that the amount of space to the left and right of $\text{“}{+}\text{”}$ are different in different contexts, thus: $$ \begin{array}{c} 5+3 \\ \\ 5+ \\ \\ +3 \end{array} $$ That's part of how binary relation symbols work. That's one reason for coding a quotient structure $X/{\sim}$ as X/{\sim} rather than as X/\sim. With the latter you see $X/\sim$ instead of $X/{\sim},$ so that's wrong.
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| Feb 20, 2022 at 20:44 | comment | added | Iosif Pinelis |
@MichaelHardy : Thank you for your response. Let me try this code: \mu\|\nu. As for $\mu$ and $\nu$, they are arguments of a scalar-valued function $\text{KL}$, rather than operands of a binary operation (from $P(X)\times P(X)$ to $P(X)$). So, I think the best would be to use $\text{KL}(\mu,\nu)$, except that for historical reasons people use something like $\text{KL}(\mu\|\nu)$.
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| Feb 20, 2022 at 20:28 | comment | added | Michael Hardy | @IosifPinelis : The short answer to your first question is that this is similar to a binary operation symbol or a binary relation symbol. To type code, you use the symbol that on the QUERTY keyboard is on the same key as the tilde. | |
| Feb 20, 2022 at 19:06 | comment | added | Iosif Pinelis | @MichaelHardy : BTW, how do you type code in comments? | |
| Feb 20, 2022 at 19:03 | comment | added | Iosif Pinelis | @MichaelHardy : Is there a reason to prefer \mu\parallel\nu to \mu\|\nu? To me, actually the latter looks better (even though I accepted your edits). | |
| Feb 20, 2022 at 18:33 | comment | added | Michael Hardy |
Note that $\mu\|\nu,$ coded as \mu\|\nu, looks different from $\mu\parallel\nu,$ coded as \mu\parallel\nu. I changed the former to the latter. Daily I see things typed by mathematicians using LaTeX that have convinced me that few among them even suspect that some sober-minded people think that things like this matter, and that there are good and substantial reasons for that. In particular, people who don't notice these differences are affected by them.
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| Feb 20, 2022 at 18:25 | comment | added | Michael Hardy | I am finally fully convinced that Civilized people need to send missionaries to that exotic tribe whose members are called Mathematicians, to acquaint them with spelling, etc. MathJax evolved from LaTeX and that evolved from TeX, and TeX was the invention of Donald Knuth. That he designed it as he did for the reasons for which he did is among the things that prove that he is a genius. And he was quite explicit in his book about this that uppermost in his mind was the purpose of making it easy to be fastidious about certain things, among them the reasons for my edits to this question. $\qquad$ | |
| Feb 20, 2022 at 18:20 | history | edited | Michael Hardy | CC BY-SA 4.0 |
proper MathJax usage
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| Feb 20, 2022 at 17:56 | vote | accept | ECL | ||
| Feb 20, 2022 at 14:46 | answer | added | Iosif Pinelis | timeline score: 10 | |
| Feb 20, 2022 at 13:49 | comment | added | kodlu | duplicate of same question asked simultaneously in math stackexchange | |
| Feb 20, 2022 at 13:24 | history | asked | ECL | CC BY-SA 4.0 |