All Questions
12 questions
48
votes
2
answers
14k
views
Research situation in the field of Information Geometry
I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field.
I have read (4) and parts of (3). ...
- 8,071
14
votes
1
answer
3k
views
How is the "conformal prediction" conformal?
The question is clarified by Prof.V.Vovk. See his answer below for discussion.
Recently, early works of Gammerman, Vanpnik and Vovk[4] are rediscovered by Wasserman et.al[1] and proposed it as a ...
- 8,071
5
votes
1
answer
237
views
Rate-Distortion theory: What is the distribution of distortion on an optimal Gaussian encoder?
If we wish to encode a gaussian source, $X\sim\mathcal{N}(0,\sigma^2)$ at rate $R$, then decode it to create an estimate $\hat{X}$, rate-distortion theory tells us that the lowest mean-squared-error ...
4
votes
1
answer
361
views
Information monotonicity of divergence => function of $f$-divergence
It is well-known that $f$-divergences defined on $\mathcal P(\mathcal X)$ where $\mathcal X$ is a measure space with $\sigma$-algebra $\mathcal B$ satisfy the property of information monotonicity:
...
- 203
3
votes
1
answer
737
views
Exponential deconvolution using the first derivative
There is an interesting observation using the first derivative to deconvolve an exponentially modified Gaussian:
The animation is here at terpconnect.umd.edu.
The main idea is that if we have an ...
- 879
3
votes
1
answer
306
views
Mutual information decrease with coarse-graining
Let $X,A,Y,B,C,D$ be random binary variables. $D$ is independent from $X,A,C$ and $C$ is independent from $Y,B,D$.
Is it true that:
If $I(Y:B|D=0)\leq \epsilon$ then $I(X\oplus Y:A\oplus B|C=0,D=0)\...
- 585
2
votes
1
answer
539
views
What is the sum capacity of a scalar gaussian broadcast channel?
"On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel" by Giuseppe Carie and Shlomo Shamai talks, in part, about the following type of link (paraphrasing):
A transmitter with $...
2
votes
1
answer
199
views
Do enough permutations of an initial set probably cover most permutations?
Fix $\alpha, \epsilon \in(0,1)$. Take $(S_n)_n$ to be any sequence of sets with each $S_n$ containing $ \lceil (n!)^\alpha\rceil$ permutations of $n$ elements. Also build another sequence of sets $(...
1
vote
0
answers
438
views
Chain rule for maximal correlation
Let a pair of random variables $(X,Y)$ be defined over finite alphabet $\mathcal{X}\times \mathcal{Y}$ with joint distribution $P_{XY}$. The maximal correlation $\rho(X;Y)$ between $X$ and $Y$ is ...
- 1,109
0
votes
0
answers
85
views
When is a family of distributions "closed" with respect to minimal sufficient statistics?
As in the title, I am interested in understanding how to express the idea that a parametric family of distribution is "closed" with respect to minimal sufficient statistics. Before giving ...
0
votes
0
answers
52
views
Classifier-specific lower bounds on the misclassification rate in binary classification
Consider a binary classification problem for $(X,Y)$, and let $\hat{f}$ be a proposed classifier. We wish to bound the misclassification rate $P(\hat{f}(X)\ne Y)$. There are many known lower bounds on ...
- 13
0
votes
0
answers
171
views
A basic property of maximal correlation
Let $𝑋$ and $𝑌$ be random variables. Then the maximal correlation $\rho_{m}(X;Y)$ is defined as:
$$\rho_{m}(X;Y):=\max_{f,g}\mathbb{E}[f(X)g(Y)],$$
where the maximization is taken over real-valued ...
- 11