This class implements a Gaussian Process (GP) regression model for non-parametric Bayesian regression. More...

#include <gp.h>

Collaboration diagram for cmp::gp::GaussianProcess:

[legend]

Public Member Functions
	GaussianProcess ()

	~GaussianProcess ()=default

	GaussianProcess (const std::shared_ptr< covariance::Covariance > &kernel, const std::shared_ptr< mean::Mean > &mean, Eigen::Ref< const Eigen::VectorXd > params, double nugget=1e-8)

	GaussianProcess (const GaussianProcess &other)

GaussianProcess &	operator= (const GaussianProcess &other)

	GaussianProcess (GaussianProcess &&other) noexcept

GaussianProcess &	operator= (GaussianProcess &&other) noexcept

void	set (const std::shared_ptr< covariance::Covariance > &kernel, const std::shared_ptr< mean::Mean > &mean, Eigen::Ref< const Eigen::VectorXd > params, double nugget=1e-8)

void	condition (const Eigen::Ref< const Eigen::MatrixXd > &xObs, const Eigen::Ref< const Eigen::VectorXd > &yObs, bool copyData=true, bool normalizeY=false)
	Condition the GP on a set of observations (allow predictive posterior computation)

void	fit (const Eigen::Ref< const Eigen::MatrixXd > &xObs, const Eigen::Ref< const Eigen::VectorXd > &yObs, const Eigen::Ref< const Eigen::VectorXd > &lb, const Eigen::Ref< const Eigen::VectorXd > &ub, const method &method, const nlopt::algorithm &alg, const double &tol_rel, bool copyData=true, bool normalizeY=false, const std::shared_ptr< cmp::prior::Prior > &prior=cmp::prior::Uniform::make(), const std::vector< bool > &logScale={})
	Fit the Gaussian Process to the observations.

Eigen::VectorXd	getParameters () const
	Get the hyperparameters of the Gaussian Process.

std::shared_ptr< cmp::mean::Mean >	getMean () const
	Gets the shared pointer to the GP prior mean function.

std::shared_ptr< cmp::covariance::Covariance >	getKernel () const
	Gets the shared pointer to the GP covariance kernel.

double	getNugget () const
	Gets the observation noise variance (nugget).

Eigen::MatrixXd	covariance (Eigen::Ref< const Eigen::VectorXd > par) const
	Evaluates the covariance matrix of the Kernel.

Eigen::MatrixXd	covarianceGradient (Eigen::Ref< const Eigen::VectorXd > par, const int &i) const

Eigen::MatrixXd	covarianceHessian (Eigen::Ref< const Eigen::VectorXd > par, const size_t &i, const size_t &j) const

const Eigen::LDLT< Eigen::MatrixXd > &	getCovDecomposition () const

const Eigen::VectorXd &	getAlpha () const

const Eigen::VectorXd &	getDiagCovInverse () const

const Eigen::VectorXd &	getResidualVector () const

const Eigen::Ref< const Eigen::MatrixXd > &	getXObs () const

const Eigen::Ref< const Eigen::VectorXd > &	getYObs () const

size_t	nObs () const
	Returns the number of training observations.

Eigen::VectorXd	priorMean (Eigen::Ref< const Eigen::VectorXd > par) const
	Evaluates the mean on the observations.

Eigen::VectorXd	priorMeanGradient (Eigen::Ref< const Eigen::VectorXd > par, const int &i) const
	Evaluate the gradient of the mean function.

Eigen::VectorXd	residual (Eigen::Ref< const Eigen::VectorXd > par) const
	Evaluate the difference between the observation and the mean function.

std::pair< double, double >	predict (const Eigen::Ref< const Eigen::VectorXd > &x, type predictionType=type::POSTERIOR) const
	Compute the predictive mean and variance at a new point.

double	predictMean (const Eigen::Ref< const Eigen::VectorXd > &x, type predictionType=type::POSTERIOR) const
	Compute the predictive mean at a new point.

std::pair< Eigen::VectorXd, Eigen::MatrixXd >	predictMultiple (const Eigen::Ref< const Eigen::MatrixXd > &x_pts, type predictionType=type::POSTERIOR) const
	Compute the predictive variance at a new set of points.

Eigen::VectorXd	predictMeanMultiple (const Eigen::Ref< const Eigen::MatrixXd > &x_pts, type predictionType=type::POSTERIOR) const
	Compute the predictive mean at a new set of points.

std::pair< double, double >	predictLOO (const size_t &i) const
	Compute the leave-one-out predictive mean and variance at the i-th observation point.

double	logLikelihood () const
	Compute the log-likelihood of the observations given the hyperparameters.

double	logLikelihoodLOO (const size_t &i) const
	Compute the leave-one-out log-likelihood of the observations given the hyperparameters.

Eigen::MatrixXd	expectedVarianceImprovement (const Eigen::Ref< const Eigen::MatrixXd > &x_pts, const Eigen::Ref< const Eigen::MatrixXd > &x_pending, double nu) const

double	objectiveFunction (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::Ref< Eigen::VectorXd > grad, const std::shared_ptr< cmp::prior::Prior > &prior)

double	objectiveFunctionLOO (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::Ref< Eigen::VectorXd > grad, const std::shared_ptr< cmp::prior::Prior > &prior)

double	objectiveFunctionLOOMSE (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::Ref< Eigen::VectorXd > grad, const std::shared_ptr< cmp::prior::Prior > &prior)

Private Member Functions
void	compute (const Eigen::Ref< const Eigen::VectorXd > &par)

Private Attributes
Eigen::VectorXd	par_
	Model hyperparameters.

std::shared_ptr< covariance::Covariance >	pKernel_
	Covariance kernel function.

std::shared_ptr< mean::Mean >	pMean_
	Prior mean function.

double	nugget_
	Observation noise variance (nugget).

std::optional< Eigen::MatrixXd >	xObs_
	Owning storage for training input matrix.

std::optional< Eigen::VectorXd >	yObs_
	Owning storage for training target vector.

std::optional< Eigen::Ref< const Eigen::MatrixXd > >	pXObs_
	Reference wrapper to training input matrix.

std::optional< Eigen::Ref< const Eigen::VectorXd > >	pYObs_
	Reference wrapper to training target vector.

Eigen::LDLT< Eigen::MatrixXd >	covDecomposition_
	LDLT decomposition of the training covariance matrix.

Eigen::VectorXd	alpha_
	GP weights vector: alpha = (K + s^2 I)^-1 (y - m).

Eigen::VectorXd	diagCovInverse_
	Diagonal elements of the inverse covariance matrix.

Eigen::VectorXd	residual_
	Residuals of the mean function: y - m(x).

bool	normalizeY_ = false
	Flag indicating whether target normalization is active.

cmp::scaler::StandardScaler	yScaler_
	Scaler used to normalize the target vector.

Detailed Description

This class implements a Gaussian Process (GP) regression model for non-parametric Bayesian regression.

Mathematical Foundations

A Gaussian Process is a collection of random variables, any finite number of which have a joint Gaussian distribution. It is completely specified by its mean function \(m(\mathbf{x})\) and covariance (kernel) function \(k(\mathbf{x}, \mathbf{x}')\):

\[ f(\mathbf{x}) \sim \mathcal{GP}\left(m(\mathbf{x}), k(\mathbf{x}, \mathbf{x}')\right) \]

Given a training dataset \(\mathcal{D} = \{(\mathbf{x}_i, y_i)\}_{i=1}^N\) where \(\mathbf{X} \in \mathbb{R}^{N \times D}\) and \(\mathbf{y} \in \mathbb{R}^N\), the joint distribution of the training outputs and the predictive function value \(f(\mathbf{x}_*)\) at a test point \(\mathbf{x}_*\) is:

\[ \begin{bmatrix} \mathbf{y} \\ f(\mathbf{x}_*) \end{bmatrix} \sim \mathcal{N}\left( \begin{bmatrix} \mathbf{m}(\mathbf{X}) \\ m(\mathbf{x}_*) \end{bmatrix}, \begin{bmatrix} \mathbf{K}(\mathbf{X}, \mathbf{X}) + \sigma_n^2 \mathbf{I} & \mathbf{k}(\mathbf{X}, \mathbf{x}_*) \\ \mathbf{k}(\mathbf{x}_*, \mathbf{X}) & k(\mathbf{x}_*, \mathbf{x}_*) \end{bmatrix} \right) \]

where \(\sigma_n^2\) is the nugget (representing the observation noise variance).

The conditional posterior distribution at the test point \(\mathbf{x}_*\) is given by:

\[ f(\mathbf{x}_*) | \mathbf{X}, \mathbf{y}, \mathbf{x}_* \sim \mathcal{N}(\mu_*, \sigma_*^2) \]

where the posterior mean \(\mu_*\) and variance \(\sigma_*^2\) are calculated as:

\[ \mu_* = m(\mathbf{x}_*) + \mathbf{k}(\mathbf{x}_*, \mathbf{X}) \left[ \mathbf{K}(\mathbf{X}, \mathbf{X}) + \sigma_n^2 \mathbf{I} \right]^{-1} (\mathbf{y} - \mathbf{m}(\mathbf{X})) \]

\[ \sigma_*^2 = k(\mathbf{x}_*, \mathbf{x}_*) - \mathbf{k}(\mathbf{x}_*, \mathbf{X}) \left[ \mathbf{K}(\mathbf{X}, \mathbf{X}) + \sigma_n^2 \mathbf{I} \right]^{-1} \mathbf{k}(\mathbf{X}, \mathbf{x}_*) \]

Implementation Algorithms

LDLT Decomposition: Directly inverting \(\mathbf{K}_y = \mathbf{K}(\mathbf{X}, \mathbf{X}) + \sigma_n^2 \mathbf{I}\) is numerically unstable and computationally expensive ( \(O(N^3)\)). We construct \(\mathbf{K}_y\) and compute its LDLT decomposition:
\[ \mathbf{K}_y = \mathbf{L} \mathbf{D} \mathbf{L}^T \]
Backsubstitution: We precompute the weight vector \(\boldsymbol{\alpha}\) by solving:
\[ \mathbf{L} \mathbf{D} \mathbf{L}^T \boldsymbol{\alpha} = \mathbf{y} - \mathbf{m}(\mathbf{X}) \]
The predictive posterior mean is then efficiently evaluated as:
\[ \mu_* = m(\mathbf{x}_*) + \mathbf{k}(\mathbf{x}_*, \mathbf{X}) \boldsymbol{\alpha} \]
Hyperparameter Optimization: The hyperparameters \(\boldsymbol{\theta}\) of the covariance and mean functions are optimized by maximizing the marginal log-likelihood:
\[ \log p(\mathbf{y} | \mathbf{X}, \boldsymbol{\theta}) = -\frac{1}{2} (\mathbf{y} - \mathbf{m}(\mathbf{X}))^T \mathbf{K}_y^{-1} (\mathbf{y} - \mathbf{m}(\mathbf{X})) - \frac{1}{2} \log |\mathbf{K}_y| - \frac{N}{2} \log (2\pi) \]
using gradient-free (e.g., Subplex) or gradient-based NLopt algorithms.

Constraints & Invariants

**Nugget ( \(\sigma_n^2\))**: Must be strictly positive ( \(\ge 10^{-12}\), default \(10^{-8}\)) to ensure the covariance matrix remains strictly positive-definite.
Training Inputs: Pre-conditions require that the dataset is non-empty ( \(N \ge 1\)).
Hyperparameter bounds: Must satisfy the user-specified bounds \(\mathbf{lb} \le \boldsymbol{\theta} \le \mathbf{ub}\).

Constructor & Destructor Documentation

◆ GaussianProcess() [1/4]

cmp::gp::GaussianProcess::GaussianProcess ( )

◆ ~GaussianProcess()

cmp::gp::GaussianProcess::~GaussianProcess ( )

default

◆ GaussianProcess() [2/4]

cmp::gp::GaussianProcess::GaussianProcess	(	const std::shared_ptr< covariance::Covariance > &	kernel,
		const std::shared_ptr< mean::Mean > &	mean,
		Eigen::Ref< const Eigen::VectorXd >	params,
		double	nugget = `1e-8`
	)

◆ GaussianProcess() [3/4]

cmp::gp::GaussianProcess::GaussianProcess ( const GaussianProcess & other )

◆ GaussianProcess() [4/4]

cmp::gp::GaussianProcess::GaussianProcess ( GaussianProcess && other )

noexcept

Member Function Documentation

◆ compute()

void GaussianProcess::compute ( const Eigen::Ref< const Eigen::VectorXd > & par )

private

◆ condition()

void cmp::gp::GaussianProcess::condition	(	const Eigen::Ref< const Eigen::MatrixXd > &	xObs,
		const Eigen::Ref< const Eigen::VectorXd > &	yObs,
		bool	copyData = `true`,
		bool	normalizeY = `false`
	)

Condition the GP on a set of observations (allow predictive posterior computation)

Parameters

xObs	The observation points
yObs	The observation values
copyData	Decide whether or not to make a deep copy of the data
normalizeY	Whether to normalize the observation values

Note: if copyData is false, and normalizeY is true the function will throw an exception, since it cannot normalize the data without owning it.

◆ covariance()

Eigen::MatrixXd GaussianProcess::covariance ( Eigen::Ref< const Eigen::VectorXd > par ) const

Evaluates the covariance matrix of the Kernel.

FUNCTIONS FOR THE KERNEL
Parameters

par The vector of hyperparameters

Returns
a matrix containing the evaluation of the Kernel on the observation points

◆ covarianceGradient()

Eigen::MatrixXd GaussianProcess::covarianceGradient	(	Eigen::Ref< const Eigen::VectorXd >	par,
		const int &	i
	)		const

Evaluate the i-th component of the gradient of the covariance matrix.

Parameters

par	The vector of hyperparameters
i	The component of the gradient required

◆ covarianceHessian()

Eigen::MatrixXd GaussianProcess::covarianceHessian	(	Eigen::Ref< const Eigen::VectorXd >	par,
		const size_t &	i,
		const size_t &	j
	)		const

Evaluate the ij component of the hessian of the covariance matrix.

Parameters

par	The vector of hyperparameters
i	row of the hessian matrix
j	colum of the hessian matrix

◆ expectedVarianceImprovement()

Eigen::MatrixXd GaussianProcess::expectedVarianceImprovement	(	const Eigen::Ref< const Eigen::MatrixXd > &	x_pts,
		const Eigen::Ref< const Eigen::MatrixXd > &	x_pending,
		double	nu
	)		const

FUNCTIONS FOR THE EXPECTED VARIANCE IMPROVEMENT

◆ fit()

void GaussianProcess::fit	(	const Eigen::Ref< const Eigen::MatrixXd > &	xObs,
		const Eigen::Ref< const Eigen::VectorXd > &	yObs,
		const Eigen::Ref< const Eigen::VectorXd > &	lb,
		const Eigen::Ref< const Eigen::VectorXd > &	ub,
		const method &	method,
		const nlopt::algorithm &	alg,
		const double &	tol_rel,
		bool	copyData = `true`,
		bool	normalizeY = `false`,
		const std::shared_ptr< cmp::prior::Prior > &	prior = `cmp::prior::Uniform::make()`,
		const std::vector< bool > &	logScale = `{}`
	)

Fit the Gaussian Process to the observations.

Parameters

xObs	the observation points
yObs	the observation values
lb	the lower bound for the hyperparameters
ub	the upper bound for the hyperparameters
method	the method to be used for the optimization
alg	the algorithm to be used for the optimization
tol_rel	the relative tolerance for the optimization
copyData	whether to copy the observation data internally (default is true)
normalizeY	whether to normalize the observation values (default is false)
prior	the prior distribution for the hyperparameters (default is uniform prior)
logScale	a vector indicating which hyperparameters should be optimized in log scale (default is all false)

FIT THE GP

◆ getAlpha()

const Eigen::VectorXd & cmp::gp::GaussianProcess::getAlpha ( ) const

inline

◆ getCovDecomposition()

const Eigen::LDLT< Eigen::MatrixXd > & cmp::gp::GaussianProcess::getCovDecomposition ( ) const

inline

◆ getDiagCovInverse()

const Eigen::VectorXd & cmp::gp::GaussianProcess::getDiagCovInverse ( ) const

inline

◆ getKernel()

std::shared_ptr< cmp::covariance::Covariance > cmp::gp::GaussianProcess::getKernel ( ) const

inline

Gets the shared pointer to the GP covariance kernel.

Returns: Shared pointer to the Covariance object.

◆ getMean()

std::shared_ptr< cmp::mean::Mean > cmp::gp::GaussianProcess::getMean ( ) const

inline

Gets the shared pointer to the GP prior mean function.

Returns: Shared pointer to the Mean object.

◆ getNugget()

double cmp::gp::GaussianProcess::getNugget ( ) const

inline

Gets the observation noise variance (nugget).

Returns: Nugget value.

◆ getParameters()

Eigen::VectorXd cmp::gp::GaussianProcess::getParameters ( ) const

inline

Get the hyperparameters of the Gaussian Process.

Returns: the value of the hyperparameters

◆ getResidualVector()

const Eigen::VectorXd & cmp::gp::GaussianProcess::getResidualVector ( ) const

inline

◆ getXObs()

const Eigen::Ref< const Eigen::MatrixXd > & cmp::gp::GaussianProcess::getXObs ( ) const

inline

◆ getYObs()

const Eigen::Ref< const Eigen::VectorXd > & cmp::gp::GaussianProcess::getYObs ( ) const

inline

◆ logLikelihood()

double GaussianProcess::logLikelihood ( ) const

Compute the log-likelihood of the observations given the hyperparameters.

LOG LIKELIHOOD FUNCTIONS
Returns
The value of the log-likelihood

Exceptions

runtime_error if the GP is not conditioned

◆ logLikelihoodLOO()

double GaussianProcess::logLikelihoodLOO ( const size_t & i ) const

Compute the leave-one-out log-likelihood of the observations given the hyperparameters.

Returns: The value of the leave-one-out log-likelihood

Exceptions

runtime_error if the GP is not conditioned or out_of_range if i is out of range [0, nObs_)

◆ nObs()

size_t cmp::gp::GaussianProcess::nObs ( ) const

inline

Returns the number of training observations.

Returns: Number of training data rows.

◆ objectiveFunction()

double GaussianProcess::objectiveFunction	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		Eigen::Ref< Eigen::VectorXd >	grad,
		const std::shared_ptr< cmp::prior::Prior > &	prior
	)

* OBJECTIVE FUNCTIONS FOR THE OPTIMIZATION

◆ objectiveFunctionLOO()

double GaussianProcess::objectiveFunctionLOO	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		Eigen::Ref< Eigen::VectorXd >	grad,
		const std::shared_ptr< cmp::prior::Prior > &	prior
	)

◆ objectiveFunctionLOOMSE()

double GaussianProcess::objectiveFunctionLOOMSE	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		Eigen::Ref< Eigen::VectorXd >	grad,
		const std::shared_ptr< cmp::prior::Prior > &	prior
	)

◆ operator=() [1/2]

GaussianProcess & cmp::gp::GaussianProcess::operator= ( const GaussianProcess & other )

◆ operator=() [2/2]

GaussianProcess & cmp::gp::GaussianProcess::operator= ( GaussianProcess && other )

noexcept

◆ predict()

std::pair< double, double > GaussianProcess::predict	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		type	predictionType = `type::POSTERIOR`
	)		const

Compute the predictive mean and variance at a new point.

FUNCTIONS FOR THE PREDICTIVE DISTRIBUTION

Parameters

x	The new prediction point
predictionType	The type of prediction (prior or posterior)

Returns: A pair containing the mean and variance of the prediction

MAKING PREDICTIONS

◆ predictLOO()

std::pair< double, double > cmp::gp::GaussianProcess::predictLOO ( const size_t & i ) const

Compute the leave-one-out predictive mean and variance at the i-th observation point.

Parameters

i	The index of the observation point

Returns: A pair containing the mean and variance of the leave-one-out prediction

Exceptions

std::out_of_range if i is out of range [0, nObs_) and runtime error if the GP is not conditioned

◆ predictMean()

double GaussianProcess::predictMean	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		type	predictionType = `type::POSTERIOR`
	)		const

Compute the predictive mean at a new point.

Note: The predictive mean can be computed in O(n) time for the posterior and O(1) time for the prior. Hence it is better to use this function if only the mean is required.

Parameters

x	The new prediction point
predictionType	The type of prediction (prior or posterior)

Returns: The predictive mean

◆ predictMeanMultiple()

Eigen::VectorXd cmp::gp::GaussianProcess::predictMeanMultiple	(	const Eigen::Ref< const Eigen::MatrixXd > &	x_pts,
		type	predictionType = `type::POSTERIOR`
	)		const

Compute the predictive mean at a new set of points.

Parameters

x_pts	The new prediction points
predictionType	The type of prediction (prior or posterior)

Returns: The predictive mean

Note: The predictive mean can be computed in O(n*m) time for the posterior and O(m) time for the prior, where n is the number of observations and m is the number of prediction points. Hence it is better to use this function if only the mean is required.

◆ predictMultiple()

std::pair< Eigen::VectorXd, Eigen::MatrixXd > cmp::gp::GaussianProcess::predictMultiple	(	const Eigen::Ref< const Eigen::MatrixXd > &	x_pts,
		type	predictionType = `type::POSTERIOR`
	)		const

Compute the predictive variance at a new set of points.

Parameters

x_pts	The new prediction points
predictionType	The type of prediction (prior or posterior)

Returns: A pair containing the mean and variance of the predictions

◆ priorMean()

Eigen::VectorXd GaussianProcess::priorMean ( Eigen::Ref< const Eigen::VectorXd > par ) const

Evaluates the mean on the observations.

FUNCTIONS FOR THE MEAN
Parameters

par The vector of hyperparameters

Returns
The mean of the points.

◆ priorMeanGradient()

Eigen::VectorXd GaussianProcess::priorMeanGradient	(	Eigen::Ref< const Eigen::VectorXd >	par,
		const int &	i
	)		const

Evaluate the gradient of the mean function.

Parameters

par	The vector of hyperparameters
i	the index of the hyperparameter

Returns: a vector containing the computation of the gradient

◆ residual()

Eigen::VectorXd GaussianProcess::residual ( Eigen::Ref< const Eigen::VectorXd > par ) const

Evaluate the difference between the observation and the mean function.

Parameters

par	The vector of hyperparameters

Returns: a vector containing the computation of the residual

◆ set()

void cmp::gp::GaussianProcess::set	(	const std::shared_ptr< covariance::Covariance > &	kernel,
		const std::shared_ptr< mean::Mean > &	mean,
		Eigen::Ref< const Eigen::VectorXd >	params,
		double	nugget = `1e-8`
	)

A GP is defined by a Kernel function, a mean function, a nugget and its hyperparameters.

Parameters

kernel	The Kernel function
mean	The mean function
params	The vector of hyperparameters
nugget	The nugget value (default is 1e-8)

Note: This function is used to set the Kernel and mean functions of the GP.

Member Data Documentation

◆ alpha_

Eigen::VectorXd cmp::gp::GaussianProcess::alpha_

private

GP weights vector: alpha = (K + s^2 I)^-1 (y - m).

◆ covDecomposition_

Eigen::LDLT<Eigen::MatrixXd> cmp::gp::GaussianProcess::covDecomposition_

private

LDLT decomposition of the training covariance matrix.

◆ diagCovInverse_

Eigen::VectorXd cmp::gp::GaussianProcess::diagCovInverse_

private

Diagonal elements of the inverse covariance matrix.

◆ normalizeY_

bool cmp::gp::GaussianProcess::normalizeY_ = false

private

Flag indicating whether target normalization is active.

◆ nugget_

double cmp::gp::GaussianProcess::nugget_

private

Observation noise variance (nugget).

◆ par_

Eigen::VectorXd cmp::gp::GaussianProcess::par_

private

Model hyperparameters.

◆ pKernel_

std::shared_ptr<covariance::Covariance> cmp::gp::GaussianProcess::pKernel_

private

Covariance kernel function.

◆ pMean_

std::shared_ptr<mean::Mean> cmp::gp::GaussianProcess::pMean_

private

Prior mean function.

◆ pXObs_

std::optional<Eigen::Ref<const Eigen::MatrixXd> > cmp::gp::GaussianProcess::pXObs_

private

Reference wrapper to training input matrix.

◆ pYObs_

std::optional<Eigen::Ref<const Eigen::VectorXd> > cmp::gp::GaussianProcess::pYObs_

private

Reference wrapper to training target vector.

◆ residual_

Eigen::VectorXd cmp::gp::GaussianProcess::residual_

private

Residuals of the mean function: y - m(x).

◆ xObs_

std::optional<Eigen::MatrixXd> cmp::gp::GaussianProcess::xObs_

private

Owning storage for training input matrix.

◆ yObs_

std::optional<Eigen::VectorXd> cmp::gp::GaussianProcess::yObs_

private

Owning storage for training target vector.

◆ yScaler_

cmp::scaler::StandardScaler cmp::gp::GaussianProcess::yScaler_

private

Scaler used to normalize the target vector.

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

include/gp.h
src/gp.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Mathematical Foundations

Implementation Algorithms

Constraints & Invariants

Constructor & Destructor Documentation

◆ GaussianProcess() [1/4]

◆ ~GaussianProcess()

◆ GaussianProcess() [2/4]

◆ GaussianProcess() [3/4]

◆ GaussianProcess() [4/4]

Member Function Documentation

◆ compute()

◆ condition()

◆ covariance()

◆ covarianceGradient()

◆ covarianceHessian()

◆ expectedVarianceImprovement()

◆ fit()

◆ getAlpha()

◆ getCovDecomposition()

◆ getDiagCovInverse()

◆ getKernel()

◆ getMean()

◆ getNugget()

◆ getParameters()

◆ getResidualVector()

◆ getXObs()

◆ getYObs()

◆ logLikelihood()

◆ logLikelihoodLOO()

◆ nObs()

◆ objectiveFunction()

◆ objectiveFunctionLOO()

◆ objectiveFunctionLOOMSE()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ predict()

◆ predictLOO()

◆ predictMean()

◆ predictMeanMultiple()

◆ predictMultiple()

◆ priorMean()

◆ priorMeanGradient()

◆ residual()

◆ set()

Member Data Documentation

◆ alpha_

◆ covDecomposition_

◆ diagCovInverse_

◆ normalizeY_

◆ nugget_

◆ par_

◆ pKernel_

◆ pMean_

◆ pXObs_

◆ pYObs_

◆ residual_

◆ xObs_

◆ yObs_

◆ yScaler_