Module anisotropic_rbf 

Anisotropic RBF Kernel Approximations

This module implements anisotropic RBF kernels and their approximations. Anisotropic kernels use different length scales for different dimensions, allowing the kernel to adapt to the varying importance of features.

Key Features

• Anisotropic RBF Sampler: Random features for anisotropic RBF kernels
• Automatic Relevance Determination (ARD): Learn feature relevance
• Mahalanobis Distance: Use learned covariance matrix
• Robust Anisotropic RBF: Outlier-resistant anisotropic kernels
• Adaptive Length Scales: Automatic length scale optimization

Mathematical Background

Anisotropic RBF kernel: k(x, x’) = σ² exp(-0.5 * (x - x’)ᵀ Λ⁻¹ (x - x’))

Where Λ = diag(l₁², l₂², …, lₐ²) is the diagonal matrix of squared length scales.

References

Structs

AnisotropicRBFSampler

Anisotropic RBF kernel sampler using random Fourier features AnisotropicRBFSampler

FittedAnisotropicRBF

Fitted anisotropic RBF sampler FittedAnisotropicRBF

FittedMahalanobisRBF

Fitted Mahalanobis RBF sampler FittedMahalanobisRBF

FittedRobustAnisotropicRBF

Fitted robust anisotropic RBF sampler FittedRobustAnisotropicRBF

MahalanobisRBFSampler

Mahalanobis distance-based RBF sampler MahalanobisRBFSampler

RobustAnisotropicRBFSampler

Robust anisotropic RBF sampler with outlier resistance RobustAnisotropicRBFSampler

Enums

RobustEstimator

Types of robust estimators for covariance RobustEstimator