All Questions

Assume that we have heavy-tailed distribution $F(x)$ such that \begin{align} F(x)=\mathbb{P}[X\geq x]=x^{-0.5}. \end{align} Then, we produce $N$ independent samples $X_1,X_2,\ldots,X_N$ from this ...

I have 2 normal distributions $\mathcal{N}(\mu_1, \mathbb{I}_d)$ where $\mu_1$ is a fixed vector in $\mathbb{R}^d$ and $\mathcal{N}(\mu_2, \mathbb{I}_d)$, where $\mu_2$ is $\mu_1 + V$, where $V$ is ...

I am faced with an information-theoretic upper bound, such as \begin{align} \sqrt{\alpha'}2^{I_\alpha(X;Y)}, \end{align} where $I_\alpha(X;Y)$ is the Rényi mutual information with parameter $\alpha>...

Let $\mathbf{U}$ and $\mathbf{V}$ be random unitary matrices independent of random input vector $\mathbf{x}$. Moreover, $\mathbf{z}$ be random iid complex Gaussian vector with zero mean and identity ...

Assuming the von Mises-Fisher distribution as $$f_{p}(\mathbf{x}; \boldsymbol{\mu}, \kappa) = C_{p}(\kappa) \exp \left( {\kappa \boldsymbol{\mu}^\mathsf{T} \mathbf{x} } \right),$$ where $\kappa \ge 0$,...