cmp::gp::MultiOutputGaussianProcess Class Reference

Manages a collection of independent Gaussian Processes for multi-output regression. More...

#include <multi_gp.h>

Public Member Functions
	MultiOutputGaussianProcess ()
	MultiOutputGaussianProcess (const size_t &nGps, const std::shared_ptr< covariance::Covariance > &kernel, const std::shared_ptr< mean::Mean > &mean, const Eigen::Ref< const Eigen::VectorXd > &params, double nugget=1e-8)
	~MultiOutputGaussianProcess ()=default
	MultiOutputGaussianProcess (const MultiOutputGaussianProcess &other)=default
MultiOutputGaussianProcess &	operator= (const MultiOutputGaussianProcess &other)=default
	MultiOutputGaussianProcess (MultiOutputGaussianProcess &&other) noexcept=default
MultiOutputGaussianProcess &	operator= (MultiOutputGaussianProcess &&other) noexcept=default
void	set (const size_t &nGps, const std::shared_ptr< covariance::Covariance > &kernel, const std::shared_ptr< mean::Mean > &mean, const Eigen::Ref< const Eigen::VectorXd > &params, double nugget=1e-8)
	Set the number of Gaussian Processes and their parameters.
void	condition (const Eigen::Ref< const Eigen::MatrixXd > &xObs, const Eigen::Ref< const Eigen::MatrixXd > &yObs, bool copyData=true)
	Set the values of the observations.
void	fit (const Eigen::Ref< Eigen::MatrixXd > &xObs, const Eigen::Ref< Eigen::MatrixXd > &yObs, const Eigen::Ref< const Eigen::VectorXd > &lb, const Eigen::Ref< const Eigen::VectorXd > &ub, const method &method=MLE, const nlopt::algorithm &alg=nlopt::LN_SBPLX, const double &tol_rel=1e-3, bool copyData=true, const std::shared_ptr< cmp::prior::Prior > &prior=cmp::prior::Uniform::make(), const std::vector< bool > &logScale={})
	Fit the Gaussian Process to the observations.
std::pair< Eigen::VectorXd, Eigen::MatrixXd >	predict (const Eigen::Ref< const Eigen::VectorXd > &x, const type &t=type::POSTERIOR) const
GaussianProcess &	operator[] (const int &i)
size_t	size () const
	Returns the number of output dimensions (the number of GP models).
Eigen::VectorXd	predictMean (const Eigen::Ref< const Eigen::VectorXd > &x, const type &t=type::POSTERIOR) const
	Predicts the output mean vector at the test point x.

Private Attributes
std::vector< GaussianProcess >	gps_
	Collection of single-output Gaussian Process models.
Eigen::MatrixXd	xObs_
	Owning training input matrix.
Eigen::MatrixXd	yObs_
	Owning training output target matrix.
std::optional< Eigen::Ref< const Eigen::MatrixXd > >	pXObs_
	Non-owning reference wrapper to training input matrix.
std::optional< Eigen::Ref< const Eigen::MatrixXd > >	pYObs_
	Non-owning reference wrapper to training output target matrix.

Detailed Description

Manages a collection of independent Gaussian Processes for multi-output regression.

Mathematical Formulation Models a vector-valued function \(\mathbf{f}: \mathbb{R}^D \to \mathbb{R}^M\) using \(M\) independent Gaussian Processes:

\[ f_j(\mathbf{x}) \sim \mathcal{GP}\left(m_j(\mathbf{x}), k_j(\mathbf{x}, \mathbf{x}')\right), \quad j = 0, \dots, M-1 \]

Often used in combination with PCA dimension reduction, where the high-dimensional response vector \(\mathbf{y} \in \mathbb{R}^Q\) is projected onto \(M\) principal components, and each component is modeled by a separate GP.

Implementation Algorithm

1. condition() partitions the multi-column target matrix \(\mathbf{Y}\) to condition each internal GaussianProcess object.
2. fit() sequentially optimizes hyperparameters for each GP in the collection using the specified MLE/LOO objectives.
3. predict() queries predictions from each internal GP to reconstruct the multivariate output mean and variance vectors.

Constructor & Destructor Documentation

MultiOutputGaussianProcess() [1/4]

cmp::gp::MultiOutputGaussianProcess::MultiOutputGaussianProcess

(

)

MultiOutputGaussianProcess() [2/4]

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

~MultiOutputGaussianProcess()

cmp::gp::MultiOutputGaussianProcess::~MultiOutputGaussianProcess ( )

default

MultiOutputGaussianProcess() [3/4]

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

default

MultiOutputGaussianProcess() [4/4]

cmp::gp::MultiOutputGaussianProcess::MultiOutputGaussianProcess ( MultiOutputGaussianProcess &&  other )

defaultnoexcept

Member Function Documentation

condition()

void cmp::gp::MultiOutputGaussianProcess::condition	(	const Eigen::Ref< const Eigen::MatrixXd > &	xObs,
		const Eigen::Ref< const Eigen::MatrixXd > &	yObs,
		bool	copyData = true
	)

Set the values of the observations.

Parameters

xObs	the observation points
yObs	the observation values (each column corresponds to a different output dimension)
copyData	whether to copy the observation data internally (default is true)

fit()

void cmp::gp::MultiOutputGaussianProcess::fit	(	const Eigen::Ref< Eigen::MatrixXd > &	xObs,
		const Eigen::Ref< Eigen::MatrixXd > &	yObs,
		const Eigen::Ref< const Eigen::VectorXd > &	lb,
		const Eigen::Ref< const Eigen::VectorXd > &	ub,
		const method &	method = MLE,
		const nlopt::algorithm &	alg = nlopt::LN_SBPLX,
		const double &	tol_rel = 1e-3,
		bool	copyData = true,
		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 bounds for the hyperparameters
ub	the upper bounds for the hyperparameters
method	the fitting method (default is MLE)
alg	the optimization algorithm (default is nlopt::LN_SBPLX)
tol_rel	the relative tolerance for the optimization (default is 1e-3)
copyData	whether to copy the observation data internally (default is true)
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)

operator=() [1/2]

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

default

operator=() [2/2]

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

defaultnoexcept

operator[]()

GaussianProcess & cmp::gp::MultiOutputGaussianProcess::operator[] ( const int &  i )

inline

predict()

std::pair< Eigen::VectorXd, Eigen::MatrixXd > cmp::gp::MultiOutputGaussianProcess::predict	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		const type &	t = type::POSTERIOR
	)		const

predictMean()

Eigen::VectorXd cmp::gp::MultiOutputGaussianProcess::predictMean	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		const type &	t = type::POSTERIOR
	)		const

Predicts the output mean vector at the test point x.

Parameters

x	The test point.
t	Evaluation type (PRIOR or POSTERIOR).

Returns

Predictive mean vector.

set()

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

Set the number of Gaussian Processes and their parameters.

Parameters

nGps	the number of Gaussian Processes
kernel	the covariance function
mean	the mean function
params	the hyperparameters
nugget	the nugget value

size()

size_t cmp::gp::MultiOutputGaussianProcess::size ( ) const

inline

Returns the number of output dimensions (the number of GP models).

Returns

Size of the GP collection.

Member Data Documentation

gps_

std::vector<GaussianProcess> cmp::gp::MultiOutputGaussianProcess::gps_

private

Collection of single-output Gaussian Process models.

pXObs_

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

private

Non-owning reference wrapper to training input matrix.

pYObs_

std::optional<Eigen::Ref<const Eigen::MatrixXd> > cmp::gp::MultiOutputGaussianProcess::pYObs_

private

Non-owning reference wrapper to training output target matrix.

xObs_

Eigen::MatrixXd cmp::gp::MultiOutputGaussianProcess::xObs_

private

Owning training input matrix.

yObs_

Eigen::MatrixXd cmp::gp::MultiOutputGaussianProcess::yObs_

private

Owning training output target matrix.

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

• include/multi_gp.h
• src/multi_gp.cpp