Timeline for Combination of probability distributions with maximum relative entropy
Current License: CC BY-SA 2.5
5 events
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| Nov 6, 2010 at 20:39 | comment | added | skypemesm | @KConrad: Yes we can say that p and q are both positive and real-valued in the interval (0,1]. Additionally we can say that they are closed under convex linear combinations. How can we approach this problem? Can we apply any other constraint in order to consider only finite-valued relative entropy? | |
| Nov 6, 2010 at 18:11 | answer | added | Anand Sarwate | timeline score: 1 | |
| Nov 6, 2010 at 18:06 | comment | added | Michael Hardy | Don't you want a minus sign in front of "log" if you write it in that form? If there are no constraints on $p$, I think the value of $p$ that would maximize $D$ with $q$ fixed is just $q$ itself. | |
| Nov 6, 2010 at 17:37 | comment | added | KConrad | What are your constraints on the probability distributions you are looking at? Do you want them to be closed under convex linear combinations or something else? If you're not going to say there are any actual constraints then I don't see how the question can be answered. (If, for instance, we limit our universe to one pair of probability distributions p and q, the answer is quite different than if we imposed some kind of constraints that would be natural.) Perhaps something in section 6 of math.uconn.edu/~kconrad/blurbs/analysis/entropypost.pdf will address what you meant to ask. | |
| Nov 6, 2010 at 16:00 | history | asked | skypemesm | CC BY-SA 2.5 |