**0**

votes

**0**answers

18 views

### Upper bound for chi-square divergence in terms of KL divergence

In my research I need an upper bound for chi-square divergence in terms KL divergence which works for general alphabets. To make this precise, note that for two probability measures $P$ and $Q$ ...

**1**

vote

**0**answers

36 views

### How to fit a stochastic matrix to given data.?

Given a data sequence of noisy observations of a 3-state Markov chain $X$ -- $y_1$,$y_2$,...$y_n$, with two transition matrices $A_1$ and $A_2$ corresponding to different regions (**) in the (unit) ...

**0**

votes

**0**answers

31 views

### How to put together a set of modified conditional distributions to a joint distribution? [on hold]

I am abstracting my original problem to a simple scenario.Consider a bi-variate multi-modal mixture of gaussian distribution, P(x,y). When we slice through x or y we get a univariate multi-modal ...

**0**

votes

**0**answers

18 views

### Finding the bound of a mixture model percentile [on hold]

I could do with some help on the following issue. I'm trying to obtain $\alpha$ from:
$\beta = \int_{\alpha}^{\infty} \sum_{i=1}^{n} p_i f_i(x) dx$
I have that:
$0 \leq p_i \leq 1$, $\sum_{i=1}^{n} ...

**0**

votes

**1**answer

281 views

### Size of KL-divergence neighbourhoods

I am new here. I was reading another
post
here and this got me wondering what can be said about the size of the following kl divergence neighborhoods.
Consider these two kl-divergence neighbourhood ...

**-6**

votes

**0**answers

40 views

### formula for turning star reviews into upvotes [on hold]

I want to turn reviews of up to 5 stars and the number of reviews into upvotes. Whats a good algorithm for doing this?
A venue with 10 reviews total with a 5 star average rating should obviously get ...

**-1**

votes

**0**answers

11 views

### How to test the significance of covariance [closed]

I'm using the Mutual Informacion covariance in RNA sequences and I want to know if there exits a way to test if some covariance is significant, let's say, an associated p-value.
Thanks to all for ...

**-2**

votes

**0**answers

33 views

### Backpropagation KL-divergence for training “one level neural network” [closed]

Hi I hope that some one could help me.
I have a L matrix (25x1000) (I have 10000 works each work is represent by 25 bits)
I map each word to one of 5 classes {vary negative,negative, ...

**-2**

votes

**0**answers

30 views

### The computation of a maximazation [closed]

I really need a help to compute the following maximization problem.
$\max _{p(x), E(x) \leq \alpha} \int_x \int_y (\frac{p(x,y)^2}{p(x)p(y)})dx dy$.
Suppose that :
$p(y|x)=\frac{1}{\sqrt{2 \pi ...

**-1**

votes

**0**answers

18 views

### Simulate correlated random field of probabilities [closed]

Hi I am trying to simulate a spatial latent random field that are probabilities not correlated binary data as specified in other posts. The goal is to have the probabilities correlated by distance. ...

**0**

votes

**2**answers

154 views

### Third order central moment of a positive linear combination of log-normal random variables

What is the sign (+tive/-tive) of the third order central moment of a positive linear combination of log-normal random variables?
It seems to be a common notion that the skewness of random variables ...

**0**

votes

**0**answers

41 views

### Taking power of the integrand in a Riemann-Stieltjie Integral

This is a problem I am trying to solve as part of a calculation for Value-at-Risk.
Given that
$P(X<x)=F(x)=\int_{\theta}F(x|\theta)dG(\theta)=1-\alpha$,
where $F$ and $G$ are CDF's, is there a ...

**2**

votes

**0**answers

117 views

### Inequality with CDF of order statistics

here is a problem I have been struggling with for a while now. This is for a paper I am working on. Any help would be appreciated! Here we go:
Each bidder's valuation $\theta _{i},$ $i=1,...,N$, is ...

**6**

votes

**1**answer

387 views

### Table with the most seated customers in Chinese restaurant process

Suppose we have some initial configuration of people seated at some tables. We start taking new customers and seat them following Chinese restaurant process. Is there some known work on finding the ...

**0**

votes

**2**answers

38 views

### Is it possible to find an asymptotic distribution for the LRT without the ML estimators being consistent?

I'm reading a comment(last page) to a paper, and the author states that sometimes, even though the estimators (found by ML or maximum quasilikelihood) may not be consistent, the test may be ...

**5**

votes

**2**answers

312 views

### Applications of cohomology to probability and statistics

Are there interesting/useful applications of cohomology (and homological algebra in general) to probability and statistics, or information theory?
By "interesting/useful", I mean "not merely ...

**1**

vote

**0**answers

30 views

### Implementing the Bivariate survival function (Dabrowska estimator etc) [migrated]

I am trying to implement the Dabrowska estimator to apply to some data that has been collected and I am wondering if anyone can help. The original paper is Kaplan-Meier Estimate on the Plane by Dorota ...

**2**

votes

**2**answers

91 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 ...

**0**

votes

**0**answers

34 views

### Is a conditional copula invariant under strictly increasing transformations?

currently I am working on conditional copulas and I have a theoretical question. In "An Introduction to Copulas", Nelsen (2006) there is a theorem (2.4.3) which says:
Let $X$ and $Y$ be continuous ...

**4**

votes

**5**answers

2k views

### book recommendation on data analysis and statistics

I am looking for a book on data analysis and statistics.
My objective is to better analyse and understand data over time (like trends or events) and extract useful information from raw statistics. I ...

**2**

votes

**1**answer

104 views

### Maximization of specific Likelihood function

N coins have probability $p_n = e^{-t_n/s}$ of heads, $t_n$ being specific for each coin. Coins 1 to m came up heads and m+1 to N came up tails. Now I'm trying to estimate $s$ using the Maximum ...

**1**

vote

**0**answers

31 views

### Is it possible to distinguish between to edge orientation while learning a network structure?

I'm considering the case of learning bayesian network structure using a dataset $\mathcal{D}$ with scoring methods :
$$\mathcal{G}^*=\max_{\mathcal{G}}\text{Score}(\mathcal{G}, \mathcal{D})$$
I'm ...

**3**

votes

**1**answer

207 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 ...

**1**

vote

**0**answers

22 views

### assumptions on local rademacher complexities

A lot of the work on Local Rademacher complexities of Koltchinskii, and Bartlett for fast rates of convergence is based on Bousquet's version of Talagrand's inequality [1] (Theorem 2.11). However the ...

**2**

votes

**2**answers

113 views

### PDF of the product of normal and Cauchy distributions

I am having trouble in finding out the resulting PDF of the product of normal and Cauchy distributions. It turns out that we have a general formula for calculating the PDF of product of two random ...

**2**

votes

**3**answers

515 views

### When do binomial distributions occur?

A binomial distribution is the distribution of the number of successes of n independent, identical Bernoulli trials. What happens when the trials are dependent and the Bernoulli trials are not ...

**0**

votes

**1**answer

385 views

### central limit theorem for binomial random variable

I'm confused about applying central limit theorem to Bernoulli random variables. Let
$X_i=\frac{n}{\sqrt{n-1}}(Z_i - \frac{1}{n})$ where $Z_i$ is iid Bernoulli($\frac{1}{n}$). Then $E[X_i]=0$ and ...

**5**

votes

**0**answers

100 views

### What's the variance in the Six Degrees model?

Recall the six degrees of Kevin Bacon game. You can even play the game at The Oracle of Bacon, and their search works via Breadth First Search.
I interpret the punchline as saying that if I start ...

**1**

vote

**2**answers

927 views

### Derivative of a differentiable stationary Gaussian process

Thanks for your help in advance. I'm interested in understanding the properties of derivatives of a differentiable stationary Gaussian process. Specifically, is the derivative also a Gaussian ...

**4**

votes

**0**answers

219 views

### An integral with respect to the Haar measure on a unitary group

Let $A,D\in \mathbb{C}^{n \times n}$ be diagonal matrices. I need to calculate
$$\int_{U(n)}\det{(A-HDH^\dagger)}\,\mathrm{d}H$$
where $dH$ is the unit invariant Haar measure on the group of unitary ...

**0**

votes

**0**answers

55 views

### Continuous self-information

Let $I(X,Y)$ be the mutual information between two continuous random variables $X$ and $Y$.
We have $I(X,Y) = H(X)-H(X|Y)$, and setting $X=Y$ leads to $I(X,X) = H(X)-H(X|X)$. If $X$ was discrete, ...

**0**

votes

**1**answer

32 views

### distances-based dispersion measuring approach

Is there any known approach or method to measure the dispersion of a set depending on the distances between its points (i.e.: without calculating the average or the mean) ?
thanks.

**1**

vote

**0**answers

66 views

### Bound the expectation of trace norm of random Hermitian matrix

Suppose $H_i$ are traceless $d\times d$ Hermitians, $X_i$ are Standard normal distribution for $1\leq i\leq d^2$.
We would like to bound the following expectation on the trace norm
...

**1**

vote

**1**answer

91 views

### 1-wasserstein distance v.s. total variation distance

Suppose that $\mu_1$ and $\mu_2$ are two distributions defined on $\mathbb{R}^n$ and $\gamma$ is a symmetric distribution (around $0$) on $\mathbb{R}^n$ with compact support. Let $\gamma_x$ denote the ...

**2**

votes

**1**answer

136 views

### Statistical distance between discrete and continuous distributions

Are there any statistical distance functions that are capable of comparing a continuous and a discrete distribution? From reading this list
http://en.wikipedia.org/wiki/Statistical_distance
the only ...

**0**

votes

**0**answers

40 views

### Integral over conditioning variable of a Gaussian

The marginal of a multivariate Gaussian can be computed in closed form, i.e.,
$p(x) = \int_y \mathcal{N}((x,y);\mu,\Sigma)\ dy$
is simple. But what I need is
$L(x) = \int_y \mathcal{N}((x\mid y); ...

**8**

votes

**2**answers

383 views

### Inequality in information theory

I am reading the paper "chain independence and common information" (http://ttic.uchicago.edu/~yury/papers/independ.pdf). In this paper, an inequality is used several times (without proof) which looks ...

**3**

votes

**1**answer

113 views

### Does bounding moments make distributions close in total variation distance?

Let $W\sim\mathcal{N}(0,\sigma^2)$ be a "reference" Gaussian random variable.
Suppose I have a set of distributions, $\mathcal{W}$, where $W_a\in\mathcal{W}$ if it satisfies the following criteria:
...

**1**

vote

**0**answers

53 views

### Lower bound on difference between polynomials at moderate distance

Fix $r > 0$ and $k, n \in \mathbb{N}$. Also consider a function $f: \mathbb{R}^{d} \rightarrow \mathbb{R}$. Let $x_{1},\ldots, x_{n+1}$ be points chosen uniformly from $[-r,r]^{d}$. For $1 \leq i ...

**0**

votes

**1**answer

96 views

### Independence of Eigenvalues of Wishart

This question regards a previous post, but it is not immediately obvious the two are related, so I ask it anyways: are the eigenvalues of a Wishart matrix $\mathbf{S}$ $=$ ...

**0**

votes

**2**answers

112 views

### What are some examples of isotrophic sets?

What are some examples of isotrophic sets? and is there a "good" way to describe them?
Isotrophic meaning that a random vector X uniformly distributed in the set has the isotrophic property for all ...

**2**

votes

**1**answer

922 views

### Choice of Lipschitz constant for proximal gradient optimization

I'm trying to use proximal gradient methods (Forward-Backwards Splitting and FISTA) to minimize a function
$f(B) = \frac{1}{2}|| XB - Y||_F^2 + \frac{\gamma}{2}||B C^T||_F^2$, where $X \in ...

**8**

votes

**4**answers

705 views

### What does it mean when we say we have computed a number to a certain accuracy using a probabilistic algorithm?

My intention is to ask a general question about probabilistic (Monte Carlo) algorithms. But to keep things simple, I will focus on a few specific examples.
Let me start the discussion with ...

**1**

vote

**0**answers

57 views

### limit distribution of multinomial distribution with increasing categories

If $\bf{X} \sim \text{multi}(n,p)$ with $k$ categories, we know
$$ \sqrt{n}\left( \frac{\bf{X}}{n} - \bf{p} \right) \rightarrow^D N(0,\Sigma),$$
where $\bf{X}=(X_1,\ldots,X_k)^T$ and ...

**1**

vote

**0**answers

29 views

### Inverse of the covariance of the estimate of a covariance

I have a covariance matrix, $V_{ij}$, which (for reasons that aren't important) I'm going to call the visibilities. I have an estimator for the visibilities $\hat V_{ij}$, and I've derived that the ...

**1**

vote

**0**answers

39 views

### Kaplan-Meier estimator for mixtures

Let $\mathbf F=(F_1,\ldots ,F_m)^\top$ be a vector of continuous CDFs and $W$ is a matrix of weight coefficients, such that:
$W\in \operatorname{Mat}_{n\times m}([0,1])$
$\forall i\in [n]:\sum ...

**0**

votes

**0**answers

25 views

### Coordinates Poisson Cluster parent point

Is there any method to know the position of parent point in 'Poisson Cluster Process'?
For information I use data with poisson distribution. data consist of (longitude, latitude, date).
I want ...

**2**

votes

**0**answers

70 views

### Sum of the entries of the inverse covariance matrix

Let $T \in\left(0,1\right)$, $n\in\mathbb{N}$ and $e_n = [1,\ldots,1]\in\mathbb{R}^n$. Consider the covariance matrix $\mathfrak{A}_n = ...

**0**

votes

**0**answers

27 views

### How to sample from the ratio between two distributions?

I want to sample a lot of $\theta$s from the density function below:
$$ r(\theta) = \frac{prior(\theta)}{Z}\frac{\int p(\theta,z_1)dz_1}{\int q(\theta,z_2)dz_2} $$
where $Z$ is the constant for ...

**0**

votes

**1**answer

215 views

### Continuity of a Functional

A certain functional $T$ is defined as:
$$T(F)=\int_{(0,1)}F^{-1}(s)M(ds)$$
where $M$ is a probability measure with support $[\alpha,1-\alpha]$,for $\alpha>0$.
The result that above functional is ...