Model Selection

Estimation and approximation errors (ERM)

what is Estimation and approximation errors (ERM)?

Preposition

Proposition 4.1 For any sample S, the following inequality holds for the hypothesis returned by ERM:

$\mathbb{P}\left[R\left(h_S^{\text{ERM}}\right)-{\inf }_{h\in \mathcal{H}}R(h)>ϵ\right]\le \mathbb{P}\left[{\sup }_{h\in \mathcal{H}}\left|R(h)-{\hat{R}}_S(h)\right|>\frac{ϵ}{2}\right]$