rkhs

Reproducing Kernel Hilbert Space primitives for non-parametric statistical testing and kernel methods. Implements kernel matrices, Maximum Mean Discrepancy (MMD), Random Fourier Features, and Nystrom approximation.

Dual-licensed under MIT or Apache-2.0.

crates.io | docs.rs

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

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.

Connections

• logp: KL/JS for discrete distributions; MMD for continuous
• wass: Wasserstein needs ground metric; MMD needs kernel
• lapl: Kernel → similarity graph → Laplacian