rkhs 0.2.1

Reproducing Kernel Hilbert Space: kernels, MMD, and kernel quantile embeddings (re-exports hopfield for AM)
Documentation

rkhs

crates.io Documentation CI

Kernel methods.

Dual-licensed under MIT or Apache-2.0.

crates.io | docs.rs

Quickstart

[dependencies]
rkhs = "0.1.3"

use rkhs::{rbf, mmd_unbiased, mmd_permutation_test};

let x = vec![vec![0.0, 0.0], vec![0.1, 0.1], vec![0.2, 0.0]];
let y = vec![vec![5.0, 5.0], vec![5.1, 5.1], vec![5.2, 5.0]];

// MMD: kernel distance between distributions
let mmd = mmd_unbiased(&x, &y, |a, b| rbf(a, b, 1.0));

// Permutation test for significance
let (_, p_value) = mmd_permutation_test(&x, &y, |a, b| rbf(a, b, 1.0), 1000);

Functions

Function Purpose
rbf Gaussian/RBF kernel
polynomial Polynomial kernel
kernel_matrix n x n Gram matrix
mmd_biased Biased MMD estimate
mmd_unbiased Unbiased MMD U-statistic
mmd_permutation_test Two-sample test with p-value
median_bandwidth Bandwidth selection heuristic
energy_lse Log-Sum-Exp energy (Dense AM with RBF)
energy_lsr Log-Sum-ReLU energy (Dense AM with Epanechnikov)
retrieve_memory Memory retrieval via energy descent

Why MMD

MMD (Maximum Mean Discrepancy) measures distance between distributions using kernel mean embeddings. Given samples from P and Q, it tests whether P = Q.

  • Two-sample testing (detect distribution shift)
  • Domain adaptation (minimize source/target divergence)
  • GAN evaluation
  • Model criticism

Why "rkhs"

Every positive-definite kernel k(x,y) uniquely defines a Reproducing Kernel Hilbert Space (Moore-Aronszajn theorem). MMD, kernel PCA, SVM, Gaussian processes -- all operate in this space. The name reflects the unifying structure.