Graduate student in physics at UIUC

2h
comment What modification is this of the notion of Renyi divergence?
And what is the meaning of anything like $D(P \vert \vert Q \vert R)$ ?
2h
comment What modification is this of the notion of Renyi divergence?
This isn't clear. $Q$ is a probability distribution on its own. So basically it is a random variable which is assigning a probability to every outcome in some space. (though $Q$ is not a probability measure because on its own it doesn't know what the "events" are) So what is $Q_{Y \vert X}$? What do $Y$ and $X$ have to be for this to make sense?
3h
revised What modification is this of the notion of Renyi divergence?
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3h
comment What modification is this of the notion of Renyi divergence?
@b yen Can you kindly define this quantity "$Q_{Y\vert X}$" and ``$P_{Y \vert X }$" ? I am unable to see why even your first-line is true. Is that a definition? I can't see it to be following from the definition of Renyi divergence...
19h
revised What modification is this of the notion of Renyi divergence?
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19h
comment Positivity of Renyi Mutual Information
@Avitus Can you give a definition of $P_{(X,Y)}$ and $P_X \times P_Y$ ? I guess both are defined on the space of outcomes $\Omega \times \Omega$ and events $F \times F$ (while $\Omega$ is the outcome space and $F$ is the event space of both $X$ and $Y$)
19h
comment Positivity of Renyi Mutual Information
@Avitus What are the properties that you would want a $I_\alpha (X,Y)$ to satisfy?
19h
asked What modification is this of the notion of Renyi divergence?
1d
comment Is this a misuse of the term "probability space"?
Sure. I am thinking of $\Omega$ as finite to keep things simple.
1d
comment Is this a misuse of the term "probability space"?
Sure! That is true. But I hope inside my post it is self-contained. This is obviously a special case of the most general possible definition.
1d
comment Is this a misuse of the term "probability space"?
isn't the wiki definition the same as mine with E = [0,1] ?
1d
comment Is this a misuse of the term "probability space"?
Can you kindly correct it?
1d
asked Is this a misuse of the term "probability space"?
1d
comment Is there a definition of relative Renyi entropy?
Is there any relationship between $H(X \vert Y)$ and $D_1 (X \vert \vert Y)$ ?
Jun
29
revised About properties of polynomials with common interlacing
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Jun
29
comment About properties of polynomials with common interlacing
Edited the question to add in the definition. Hope you can help!
Jun
29
revised About properties of polynomials with common interlacing
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Jun
24
revised Is there a definition of relative Renyi entropy?
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Jun
24
comment What is known about Renyi entropy of a probability density function?
Thanks for the reference. Any reason why this definition is not popular in physics?
Jun
24
asked Is there a definition of relative Renyi entropy?
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