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2d
comment What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
Thanks for the reply! I am thinking of stuff like what is the analogue of Bourgain's theorem here.
Aug
27
comment What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
(1) Could you kindly elaborate on the proof that $\mathbb{H}_n$ is a $\delta$-Gromov hyperbolic? (2) Is there some known embedding of a $\delta$-Gromov hyperbolic metric space into some $\mathbb{H}_n$?
Aug
26
asked What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
Jul
7
accepted Is this a misuse of the term “probability space”?
Jul
7
comment What modification is this of the notion of Renyi divergence?
I am not understanding your definiton. I think X and Y are events and then one should think of P and Q as being random variables mapping the outcomes to real numbers and then define it as, D( P(Y|X) || Q(Y|X) | P_X) := \sum(x in X) P( x) \sum (y in Y) P( y )P( x) log[ ( P( y )P( x) ) / ( Q( y )Q(x) )]
Jul
7
comment What modification is this of the notion of Renyi divergence?
So P and Q are to be thought of as maps assigning a probability to each of these outcomes? P : X x Y -> [0,1] and Q : X x Y -> [0,1] ? So what are the maps $P_X,P_Y, Q_X, Q_Y$ ?
Jul
7
comment What modification is this of the notion of Renyi divergence?
So are X and Y events from a common sigma-algebra on which these two probability distributions P and Q are defined?
Jul
5
comment What modification is this of the notion of Renyi divergence?
And what is the meaning of anything like $D(P \vert \vert Q \vert R)$ ?
Jul
5
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?
Jul
5
revised What modification is this of the notion of Renyi divergence?
added 17 characters in body
Jul
5
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...
Jul
5
revised What modification is this of the notion of Renyi divergence?
added 3 characters in body
Jul
5
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 $Y$)
Jul
5
comment Positivity of Renyi Mutual Information
@Avitus What are the properties that you would want a $I_\alpha (X,Y)$ to satisfy?
Jul
5
asked What modification is this of the notion of Renyi divergence?
Jul
4
comment Is this a misuse of the term “probability space”?
Sure. I am thinking of $\Omega$ as finite to keep things simple.
Jul
4
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.
Jul
4
comment Is this a misuse of the term “probability space”?
isn't the wiki definition the same as mine with E = [0,1] ?
Jul
4
comment Is this a misuse of the term “probability space”?
Can you kindly correct it?
Jul
4
asked Is this a misuse of the term “probability space”?