Author: Eiko

Time: 2025-02-17 13:04:14 - 2025-02-17 13:04:14 (UTC)

High Dimensional Statistics

• Concentration and its uses

• Sub-Gaussian random variables

• Sub-Exponential random variables

Concentration

Let \(X_i\) be a sequence of i.i.d random variables

Basic Concentration Inequality

\[ \mathbb{P}\left[ f(|X-\mu|) \ge f(t) \right] \leq \min_f \frac{\mathbb{E}f(|X-\mu|)}{f(t)} \]