Exercise 9.15

Answers

Rotational invariance:
$E_{hint} (h) = \frac{1}{N} \sum_{n = 1}^{N} {(h (x_{n}) - h (x_{n}^{'}))}^{2} 1 [h (x_{n}) \neq h (x_{n}^{'})] .$
Convexity hint:
$E_{hint} (h) = \frac{1}{N} \sum_{n = 1}^{N} {(h (x_{n}) - h (x_{n}^{'}))}^{2} 1 [h (η x_{n} + (1 - η) x_{n}^{'}) > ηh (x_{n}) + (1 - η) h (x_{n}^{'})],$
where $0 \leq η \leq 1$ .
Perturbation hint:
$E_{hint} (h) = \frac{1}{N} \sum_{n = 1}^{N} {(h (x_{n}) - g (x_{n}))}^{2} 1 [| h (x_{n}) - g (x_{n}) | > δh (x_{n})],$
where $g (x)$ is the known function that the target function is close to.

niuers

2021-12-08 10:29