algo::regression::GaussianProcess< K, T > Class Template Reference

Public Member Functions
template<typename... Ts>
	GaussianProcess (const Ts &... args)
template<typename... Ts>
	GaussianProcess (const arma::Mat< T > &inputs, const arma::Row< T > &labels, const T lambda, const Ts &... args)
	GaussianProcess (const arma::Mat< T > &inputs, const arma::Row< T > &labels)
void	Train (const arma::Mat< T > &inputs, const arma::Row< T > &labels)
void	Predict (const arma::Mat< T > &inputs, arma::Row< T > &labels) const
void	PredictVariance (const arma::Mat< T > &inputs, arma::Mat< T > &labels)
T	ComputeError (const arma::Mat< T > &inputs, const arma::Row< T > &labels) const
T	LogLikelihood (const arma::Mat< T > &inputs, const arma::Row< T > &labels) const
void	SamplePrior (const size_t k, const arma::Mat< T > &inputs, arma::Mat< T > &labels) const
void	SamplePosterior (const size_t k, const arma::Mat< T > &inputs, arma::Mat< T > &labels)
const arma::Col< T > &	Parameters () const
arma::Col< T > &	Parameters ()
void	Lambda (const T &lambda)
template<typename Archive >
void	serialize (Archive &ar, const unsigned int)

Detailed Description

template<class K = mlpack::GaussianKernel, class T = DTYPE>
class algo::regression::GaussianProcess< K, T >

Definition at line 20 of file gp.h.

Constructor & Destructor Documentation

GaussianProcess() [1/3]

template<class K = mlpack::GaussianKernel, class T = DTYPE>

template<typename... Ts>

algo::regression::GaussianProcess< K, T >::GaussianProcess ( const Ts &...  args )

inline

Non-working model

Parameters

args	: kernel parameters

Definition at line 29 of file gp.h.

: cov_(args...), lambda_(0.0) { };

GaussianProcess() [2/3]

template<class K , class T >

template<class... Ts>

algo::regression::GaussianProcess< K, T >::GaussianProcess	(	const arma::Mat< T > &	inputs,
		const arma::Row< T > &	labels,
		const T	lambda,
		const Ts &...	args
	)

Parameters

X	: inputs
y	: labels
args	: kernel parameters

Definition at line 19 of file gp_impl.h.

                                                            :
                                        cov_(args...), lambda_(lambda)
{
  Train(inputs, labels);
}

References algo::regression::GaussianProcess< K, T >::Train().

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GaussianProcess() [3/3]

template<class K , class T >

algo::regression::GaussianProcess< K, T >::GaussianProcess	(	const arma::Mat< T > &	inputs,
		const arma::Row< T > &	labels
	)

Parameters

X	: inputs
y	: labels

Definition at line 29 of file gp_impl.h.

                                                                  :
                                        cov_(), lambda_(0.)
{
  Train(inputs, labels);
}

References algo::regression::GaussianProcess< K, T >::Train().

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Member Function Documentation

ComputeError()

template<class K , class T >

T algo::regression::GaussianProcess< K, T >::ComputeError	(	const arma::Mat< T > &	inputs,
		const arma::Row< T > &	labels
	)		const

Calculate the L2 squared error on the given predictors and responses using this linear regression model. This calculation returns

Parameters

X*	: points*
y*	: responses*

Definition at line 71 of file gp_impl.h.

{
  arma::Row<T> temp;
  Predict(inputs, temp);
  const size_t n_points = inputs.n_cols;
 
  temp = labels - temp;
 
  const T cost = arma::dot(temp, temp) / n_points;
 
  return cost;
}

Lambda()

template<class K = mlpack::GaussianKernel, class T = DTYPE>

void algo::regression::GaussianProcess< K, T >::Lambda ( const T &  lambda )

inline

Set Lambda

Parameters

lambda

: lambda

Definition at line 118 of file gp.h.

{ lambda_ = lambda; }

LogLikelihood()

template<class K , class T >

T algo::regression::GaussianProcess< K, T >::LogLikelihood	(	const arma::Mat< T > &	inputs,
		const arma::Row< T > &	labels
	)		const

Calculate the Log Likelihood of the model given data

Parameters

X*	: points*
y*	: responses*

Definition at line 86 of file gp_impl.h.

{
  return -0.5*arma::dot(labels,parameters_) - arma::trace(arma::log(L_))
                                            - 0.5*T(N_)*std::log(2.*M_PI);
}

Parameters()

template<class K = mlpack::GaussianKernel, class T = DTYPE>

const arma::Col<T>& algo::regression::GaussianProcess< K, T >::Parameters ( ) const

inline

Get Parameters

Definition at line 109 of file gp.h.

{ return parameters_; }

Predict()

template<class K , class T >

void algo::regression::GaussianProcess< K, T >::Predict	(	const arma::Mat< T > &	inputs,
		arma::Row< T > &	labels
	)		const

Parameters

X*	: inputs*
y*	: labels*

Definition at line 53 of file gp_impl.h.

{
  arma::Mat<T> k_xpx = cov_.GetMatrix(inputs,train_inp_);
  labels = (k_xpx * parameters_).t();
}

PredictVariance()

template<class K , class T >

void algo::regression::GaussianProcess< K, T >::PredictVariance	(	const arma::Mat< T > &	inputs,
		arma::Mat< T > &	labels
	)

Parameters

X*	: inputs*
y*	: labels*

Definition at line 61 of file gp_impl.h.

{
  arma::Mat<T> k_xpx = cov_.GetMatrix(inputs,train_inp_);
  arma::Mat<T> k_xpxp = cov_.GetMatrix(inputs,inputs);
  arma::Mat<T> v = arma::solve(L_,k_xpx.t());
  labels = arma::conv_to<arma::Mat<T>>::from((k_xpxp - v.t()*v));
}

SamplePosterior()

template<class K , class T >

void algo::regression::GaussianProcess< K, T >::SamplePosterior	(	const size_t	k,
		const arma::Mat< T > &	inputs,
		arma::Mat< T > &	labels
	)

Sample functions from the prior

Parameters

X	: inputs
y	: labels

Definition at line 94 of file gp_impl.h.

{ 
  arma::Row<T> mean;
  arma::Mat<T> cov;
  Predict(inputs, mean);  
  PredictVariance(inputs, cov);  
  cov.diag() += 1e-6; // jitter addition
  labels = arma::mvnrnd(mean.t(), cov, M).t();
}

SamplePrior()

template<class K , class T >

void algo::regression::GaussianProcess< K, T >::SamplePrior	(	const size_t	k,
		const arma::Mat< T > &	inputs,
		arma::Mat< T > &	labels
	)		const

Sample functions from the prior

Parameters

X	: inputs
y	: labels

Definition at line 107 of file gp_impl.h.

{
  size_t N = inputs.n_cols;
  arma::Mat<T> cov = cov_.GetMatrix(inputs,inputs);  
  cov.diag() += 1e-6 + lambda_; // jitter addition
  arma::Col<T> mean(N); 
  labels = arma::mvnrnd(mean, cov, M).t();
}

serialize()

template<class K = mlpack::GaussianKernel, class T = DTYPE>

template<typename Archive >

void algo::regression::GaussianProcess< K, T >::serialize ( Archive &  ar, const unsigned int    )

inline

Serialize the model.

Definition at line 124 of file gp.h.

  {
    ar ( cereal::make_nvp("parameters",parameters_),
         cereal::make_nvp("train_inp",train_inp_),
         cereal::make_nvp("lambda",lambda_),
         cereal::make_nvp("cov",cov_),
         cereal::make_nvp("N",N_),
         cereal::make_nvp("L",L_) );
  }

Train()

template<class K , class T >

void algo::regression::GaussianProcess< K, T >::Train	(	const arma::Mat< T > &	inputs,
		const arma::Row< T > &	labels
	)

Parameters

X	: inputs
y	: labels

Definition at line 37 of file gp_impl.h.

{
  train_inp_ = inputs;
  N_ = inputs.n_cols;
  
  arma::Mat<T> k_xx = cov_.GetMatrix(train_inp_,train_inp_);
 
  arma::Mat<T> KLambda = k_xx+
       (lambda_ + 1.e-6) * arma::eye<arma::Mat<T>>(k_xx.n_rows, k_xx.n_rows);
 
  L_ = arma::chol(KLambda, "lower");
  parameters_ = arma::solve(L_.t(), arma::solve(L_,labels.t()));
}

Referenced by algo::regression::GaussianProcess< K, T >::GaussianProcess().

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

• gp.h
• gp_impl.h