Struct VCDimension 

pub struct VCDimension {
    pub dim: usize,
}

VC dimension and growth function calculations.

Fields

dim: usize

The claimed VC dimension.

Implementations

impl VCDimension

pub fn new(dim: usize) -> Self

Create a new VCDimension.

pub fn sauer_shelah_bound(&self, m: usize) -> usize

Sauer-Shelah bound: Π_H(m) ≤ Σ_{i=0}^{d} C(m,i).

pub fn can_shatter(&self, m: usize) -> bool

Check if d-dimensional threshold classifier can shatter m points.

For the canonical 1D threshold classifier H = {h_θ : θ ∈ ℝ}, VC dim = 1. This checks whether the bound is consistent with shattering.

pub fn fundamental_theorem_pac(&self) -> bool

Fundamental theorem of PAC learning: finite VC dim ↔ PAC learnability.