sin(ωx) — VC = ∞

Parent: examples Prereq: learning-theory — H, h, shattering.

Class $H = \{\, h_\omega : \omega > 0 \,\}$, one parameter:

One real parameter ω, yet by cranking the frequency the wave can be made +/− at any set of points in any pattern → shatters arbitrarily many → VC = ∞.

This is the honest warning of the whole subject: one parameter, infinite VC. Parameter-count is not capacity — and infinite VC means unlearnable.