Struct NegEntropy 

pub struct NegEntropy;

Negative-entropy Bregman generator: (F(x) = \sum_i x_i \ln x_i), (\nabla F(x)_i = 1 + \ln x_i).

The Bregman divergence with this generator is the (unnormalized) KL divergence: (B_F(p, q) = \sum_i p_i \ln(p_i / q_i) - \sum_i (p_i - q_i)). When (p) and (q) are normalized (simplex), the second sum vanishes and (B_F = D_{KL}(p | q)).

This connects the information-theoretic (f-divergence) and geometric (Bregman) views of KL divergence. The dually-flat structure of the probability simplex under this generator is the foundation of information geometry (Amari & Nagaoka, 2000).

Trait Implementations

impl BregmanGenerator for NegEntropy

fn f(&self, x: &[f64]) -> Result<f64>

Evaluate the potential (F(x)).

fn grad_into(&self, x: &[f64], out: &mut [f64]) -> Result<()>

Write (\nabla F(x)) into out.

impl Clone for NegEntropy

fn clone(&self) -> NegEntropy

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for NegEntropy

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for NegEntropy

fn default() -> NegEntropy

Returns the “default value” for a type.

impl Copy for NegEntropy