cmp::covariance::Covariance Class Reference

Abstract base class for all covariance (kernel) functions. More...

#include <covariance.h>

Inheritance diagram for cmp::covariance::Covariance:

Public Member Functions
virtual	~Covariance ()=default
virtual double	eval (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par) const =0
virtual double	evalGradient (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par, const size_t &i) const =0
virtual double	evalHessian (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par, const size_t &i, const size_t &j) const =0

Detailed Description

Abstract base class for all covariance (kernel) functions.

Mathematical Formulation A covariance function (kernel) \(k: \mathbb{R}^D \times \mathbb{R}^D \to \mathbb{R}\) defines the covariance between GP values at any two inputs \(\mathbf{x}_1, \mathbf{x}_2\):

\[ \text{Cov}(f(\mathbf{x}_1), f(\mathbf{x}_2)) = k(\mathbf{x}_1, \mathbf{x}_2; \boldsymbol{\theta}) \]

where \(\boldsymbol{\theta}\) is the vector of kernel hyperparameters. The function must be symmetric and positive semi-definite:

\[ \sum_{i=1}^n \sum_{j=1}^n c_i c_j k(\mathbf{x}_i, \mathbf{x}_j) \ge 0 \quad \forall c_i \in \mathbb{R} \]

Implementation Algorithm Provides a virtual interface for evaluating the covariance value (eval), its first-order gradient (evalGradient) with respect to a hyperparameter \(\theta_i\), and its second-order Hessian (evalHessian) with respect to hyperparameters \(\theta_i, \theta_j\).

Constructor & Destructor Documentation

~Covariance()

virtual cmp::covariance::Covariance::~Covariance ( )

virtualdefault

Member Function Documentation

eval()

virtual double cmp::covariance::Covariance::eval ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par  ) const

pure virtual

Implemented in cmp::covariance::Sum, cmp::covariance::Product, cmp::covariance::Custom, cmp::covariance::Constant, cmp::covariance::Linear, cmp::covariance::Inverse, cmp::covariance::SquaredExponential, cmp::covariance::Matern52, cmp::covariance::Matern, cmp::covariance::WhiteNoise, and cmp::covariance::ModelClusterCovariance.

evalGradient()

virtual double cmp::covariance::Covariance::evalGradient ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par, const size_t &  i  ) const

pure virtual

Implemented in cmp::covariance::Sum, cmp::covariance::Product, cmp::covariance::Custom, cmp::covariance::Constant, cmp::covariance::Linear, cmp::covariance::Inverse, cmp::covariance::SquaredExponential, cmp::covariance::Matern52, cmp::covariance::Matern, cmp::covariance::WhiteNoise, and cmp::covariance::ModelClusterCovariance.

evalHessian()

virtual double cmp::covariance::Covariance::evalHessian ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par, const size_t &  i, const size_t &  j  ) const

pure virtual

Implemented in cmp::covariance::Sum, cmp::covariance::Product, cmp::covariance::Custom, cmp::covariance::Constant, cmp::covariance::Linear, cmp::covariance::Inverse, cmp::covariance::SquaredExponential, cmp::covariance::Matern52, cmp::covariance::Matern, cmp::covariance::WhiteNoise, and cmp::covariance::ModelClusterCovariance.

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The documentation for this class was generated from the following file:

• include/covariance.h