Tagged Questions
1
vote
1answer
36 views
how to calculate E[vech(x x')vech(x x')']?
Supposing a vector x follows normal distribution. I want to calculate the expectation of the "fourth moment" in a vector form, meaning $\text{E}[\text{vech}(x x')\text{vech}(x x')']$, given that we ...
0
votes
0answers
25 views
Different kind of scaling matrices
I was reading through a publication and it suggested there are different kinds of scaling matrices. They suggest the use of the fisher information matrix and I never heard it referred to as a scaling ...
4
votes
0answers
54 views
Orthogonal intersection in a Riemannian manifold
Let $S$ be the set of all probability distributions on $\mathbb{R}$ and $S_n=\{p_\theta\}$ be an $n$ dimensional submanifold of parameterized family of probability distributions on $\mathbb{R}$ where ...
3
votes
1answer
86 views
Orthogonal intersection of linear family and exponential family
I asked the following question in MSE for which I couldn't get any answer yet. I thought this would be a better place for that question.
In statistical maniolds ...
3
votes
1answer
131 views
ID3 and C4.5: how does “gain ratio” normalize “gain”?
The ID3 algorithm uses "Information Gain" measure.
The C4.5 uses "Gain Ratio" measure which is Information Gain divided by SplitInfo, whereas SplitInfo is high for a split where records split evenly ...
5
votes
3answers
215 views
Information theoretic central limit theorem
The simplest form of the information theoretic CLT is the following:
Let $X_1, X_2,\dots$ be iid with mean $0$ and variance $1$. Let $f_n$ be the density of the normalized sum $\frac{\sum_{i=1}^n ...
1
vote
1answer
76 views
How does one express the decrease in minimal type II error bound for each observation added?
Problem: I have a "classifier" that uses some arbitrary hypothesis test on observations from one of two known probability distributions:
$P_0$ (null hypothesis $H_0$) is a zero-mean Gaussian ...
5
votes
2answers
932 views
Hypothesis testing and total variation distance vs. Kullback-Leibler divergence
In my research I have run into the following general problem: I have two distributions $P$ and $Q$ over the same domain, and a large (but finite) number of samples from those distributions. Samples ...
