Theories of Deep Learning MT25, Vapnik-Chervonenkis dimension

Suppose $f _ \theta : \mathcal D \to {0,1}$ is a binary classifier parameterised by $\theta$. @Define what it means for $f$ to shatter a set $X \subseteq \mathcal D$.

Recall that a binary classifier $f _ \theta : \mathcal D \to {0,1}$ parameterised by $\theta$ is said to shatter a set $X \subseteq \mathcal D$ if for every assignment of labels to those data, there exists a $\theta$ such that $f$ makes no errors when classifying those data.

In this context, @define the VC (Vapnik-Chervonenkis) dimension of $f$.