Automatic relevance detection kernel for unconstrained parameter optimization. More...

#include <shark/Models/Kernels/ArdKernel.h>

Inheritance diagram for shark::ARDKernelUnconstrained< InputType >:

Public Types
typedef base_type::BatchInputType	BatchInputType

typedef base_type::ConstInputReference	ConstInputReference

typedef base_type::ConstBatchInputReference	ConstBatchInputReference

Public Types inherited from shark::AbstractKernelFunction< InputTypeT >
enum	Feature { HAS_FIRST_PARAMETER_DERIVATIVE = 1 , HAS_FIRST_INPUT_DERIVATIVE = 2 , IS_NORMALIZED = 4 , SUPPORTS_VARIABLE_INPUT_SIZE = 8 }
	enumerations of kerneland metric features (flags) More...

typedef base_type::InputType	InputType
	Input type of the Kernel.

typedef base_type::BatchInputType	BatchInputType
	batch input type of the kernel

typedef base_type::ConstInputReference	ConstInputReference
	Const references to InputType.

typedef base_type::ConstBatchInputReference	ConstBatchInputReference
	Const references to BatchInputType.

typedef TypedFlags< Feature >	Features
	This statement declares the member m_features. See Core/Flags.h for details.

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

Public Types inherited from shark::AbstractMetric< InputTypeT >
typedef InputTypeT	InputType
	Input type of the Kernel.

typedef Batch< InputTypeT >::type	BatchInputType
	batch input type of the kernel

typedef ConstProxyReference< InputTypeconst >::type	ConstInputReference
	Const references to InputType.

typedef ConstProxyReference< BatchInputTypeconst >::type	ConstBatchInputReference
	Const references to BatchInputType.

Public Types inherited from shark::IParameterizable< VectorType >
typedef VectorType	ParameterVectorType

Public Member Functions
	ARDKernelUnconstrained (unsigned int dim, double gamma_init=1.0)

std::string	name () const
	From INameable: return the class name.

RealVector	parameterVector () const
	Return the parameter vector.

void	setParameterVector (RealVector const &newParameters)
	Set the parameter vector.

std::size_t	numberOfParameters () const
	Return the number of parameters.

boost::shared_ptr< State >	createState () const
	creates the internal state of the kernel

RealVector	gammaVector () const
	convenience methods for setting/getting the actual gamma values

void	setGammaVector (RealVector const &newGammas)

double	eval (ConstInputReference x1, ConstInputReference x2) const
	evaluates \( k(x,z)\)

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result) const
	evaluates \( k(x,z)\) for a whole batch

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const
	evaluates \( k(x,z)\) for a whole batch

void	weightedParameterDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficients, State const &state, RealVector &gradient) const
	evaluates \( \frac {\partial k(x,z)}{\partial \sqrt{\gamma_i}}\) weighted over a whole batch

void	weightedInputDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficientsX2, State const &state, BatchInputType &gradient) const
	evaluates \( \frac {\partial k(x,z)}{\partial x}\)

void	read (InArchive &ar)
	From ISerializable, reads a metric from an archive.

void	write (OutArchive &ar) const
	From ISerializable, writes a metric to an archive.

Public Member Functions inherited from shark::AbstractKernelFunction< InputTypeT >
	AbstractKernelFunction ()

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstParameterDerivative () const

bool	hasFirstInputDerivative () const

bool	isNormalized () const

bool	supportsVariableInputSize () const

virtual double	eval (ConstInputReference x1, ConstInputReference x2) const
	Evaluates the kernel function.

double	operator() (ConstInputReference x1, ConstInputReference x2) const
	Convenience operator which evaluates the kernel function.

virtual void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const =0
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns).

virtual void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result) const
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns).

RealMatrix	operator() (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const
	Evaluates the subset of the KernelGram matrix which is defined by X1(rows) and X2 (columns).

virtual void	weightedParameterDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficients, State const &state, RealVector &gradient) const
	Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the batch.

virtual void	weightedInputDerivative (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix const &coefficientsX2, State const &state, BatchInputType &gradient) const
	Calculates the derivative of the inputs X1 (only x1!).

virtual double	featureDistanceSqr (ConstInputReference x1, ConstInputReference x2) const
	Computes the squared distance in the kernel induced feature space.

virtual RealMatrix	featureDistanceSqr (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const
	Computes the squared distance in the kernel induced feature space.

Public Member Functions inherited from shark::AbstractMetric< InputTypeT >
	AbstractMetric ()

virtual	~AbstractMetric ()

double	featureDistance (ConstInputReference x1, ConstInputReference x2) const
	Computes the distance in the kernel induced feature space.

Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Public Member Functions inherited from shark::IParameterizable< VectorType >
virtual	~IParameterizable ()

Public Member Functions inherited from shark::ISerializable
virtual	~ISerializable ()
	Virtual d'tor.

void	load (InArchive &archive, unsigned int version)
	Versioned loading of components, calls read(...).

void	save (OutArchive &archive, unsigned int version) const
	Versioned storing of components, calls write(...).

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Protected Attributes
RealVector	m_gammas
	kernel bandwidth parameters, one for each input dimension.

std::size_t	m_inputDimensions
	how many input dimensions = how many bandwidth parameters

Protected Attributes inherited from shark::AbstractKernelFunction< InputTypeT >
Features	m_features

Detailed Description

template<class InputType = RealVector>
class shark::ARDKernelUnconstrained< InputType >

Automatic relevance detection kernel for unconstrained parameter optimization.

The automatic relevance detection (ARD) kernel is a general Gaussian kernel with diagonal covariance matrix: \( k(x, z) = \exp(-\sum_i \gamma_i (x_i - z_i)^2) \). The ARD kernel holds one real-valued parameter \( \gamma_i \) per input dimension. The parameters \( p_i \) are encoded as \( p_i = log(\gamma_i) \), allowing for unconstrained optimization. Here, the exposed/visible parameters are transformed by an exp before being used in the actual computations.

Note that, like all or most models/kernels designed for unconstrained optimization, the argument to the constructor corresponds to the value of the true weights, while the set and get methods for the parameter vector set the parameterized values and not the true weights.

Definition at line 59 of file ArdKernel.h.

Member Typedef Documentation

◆ BatchInputType

template<class InputType = RealVector>

typedef base_type::BatchInputType shark::ARDKernelUnconstrained< InputType >::BatchInputType

Definition at line 72 of file ArdKernel.h.

◆ ConstBatchInputReference

template<class InputType = RealVector>

typedef base_type::ConstBatchInputReference shark::ARDKernelUnconstrained< InputType >::ConstBatchInputReference

Definition at line 74 of file ArdKernel.h.

◆ ConstInputReference

template<class InputType = RealVector>

typedef base_type::ConstInputReference shark::ARDKernelUnconstrained< InputType >::ConstInputReference

Definition at line 73 of file ArdKernel.h.

Constructor & Destructor Documentation

◆ ARDKernelUnconstrained()

template<class InputType = RealVector>

shark::ARDKernelUnconstrained< InputType >::ARDKernelUnconstrained	(	unsigned int	dim,
		double	gamma_init = `1.0`
	)

inline

Constructor

Parameters

dim	input dimension
gamma_init	initial gamma value for all dimensions (true value, used as passed into ctor)

Definition at line 79 of file ArdKernel.h.

References shark::AbstractKernelFunction< InputType >::HAS_FIRST_INPUT_DERIVATIVE, shark::AbstractKernelFunction< InputType >::HAS_FIRST_PARAMETER_DERIVATIVE, shark::AbstractKernelFunction< InputType >::IS_NORMALIZED, shark::AbstractKernelFunction< InputTypeT >::m_features, shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, and SHARK_RUNTIME_CHECK.

Member Function Documentation

◆ createState()

template<class InputType = RealVector>

boost::shared_ptr< State > shark::ARDKernelUnconstrained< InputType >::createState ( ) const

inlinevirtual

creates the internal state of the kernel

Reimplemented from shark::AbstractKernelFunction< InputTypeT >.

Definition at line 111 of file ArdKernel.h.

◆ eval() [1/3]

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::eval	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix &	result
	)		const

inline

evaluates \( k(x,z)\) for a whole batch

ARD kernel evaluation

\[ k(x, z) = \exp(-\sum_i \gamma_i (x_i - z_i)^2) \]

Definition at line 144 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, and SIZE_CHECK.

◆ eval() [2/3]

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::eval	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix &	result,
		State &	state
	)		const

inline

evaluates \( k(x,z)\) for a whole batch

ARD kernel evaluation

\[ k(x, z) = \exp(-\sum_i \gamma_i (x_i - z_i)^2) \]

Definition at line 165 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, SIZE_CHECK, and shark::State::toState().

◆ eval() [3/3]

template<class InputType = RealVector>

double shark::ARDKernelUnconstrained< InputType >::eval	(	ConstInputReference	x1,
		ConstInputReference	x2
	)		const

inline

evaluates \( k(x,z)\)

ARD kernel evaluation

\[ k(x, z) = \exp(-\sum_i \gamma_i (x_i - z_i)^2) \]

Definition at line 133 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, and SIZE_CHECK.

◆ gammaVector()

template<class InputType = RealVector>

RealVector shark::ARDKernelUnconstrained< InputType >::gammaVector ( ) const

inline

convenience methods for setting/getting the actual gamma values

Definition at line 116 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas.

Referenced by run_one_trial().

◆ name()

template<class InputType = RealVector>

std::string shark::ARDKernelUnconstrained< InputType >::name ( ) const

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::INameable.

Definition at line 96 of file ArdKernel.h.

◆ numberOfParameters()

template<class InputType = RealVector>

std::size_t shark::ARDKernelUnconstrained< InputType >::numberOfParameters ( ) const

inlinevirtual

Return the number of parameters.

Reimplemented from shark::IParameterizable< VectorType >.

Definition at line 106 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_inputDimensions.

◆ parameterVector()

template<class InputType = RealVector>

RealVector shark::ARDKernelUnconstrained< InputType >::parameterVector ( ) const

inlinevirtual

Return the parameter vector.

Reimplemented from shark::IParameterizable< VectorType >.

Definition at line 99 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas.

Referenced by run_one_trial().

◆ read()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::read ( InArchive & archive )

inlinevirtual

From ISerializable, reads a metric from an archive.

Reimplemented from shark::AbstractMetric< InputTypeT >.

Definition at line 247 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, and shark::ARDKernelUnconstrained< InputType >::m_inputDimensions.

◆ setGammaVector()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::setGammaVector ( RealVector const & newGammas )

inline

Definition at line 119 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, RANGE_CHECK, and SIZE_CHECK.

◆ setParameterVector()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::setParameterVector ( RealVector const & newParameters )

inlinevirtual

Set the parameter vector.

Reimplemented from shark::IParameterizable< VectorType >.

Definition at line 102 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, and SIZE_CHECK.

◆ weightedInputDerivative()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::weightedInputDerivative	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix const &	coefficientsX2,
		State const &	state,
		BatchInputType &	gradient
	)		const

inline

evaluates \( \frac {\partial k(x,z)}{\partial x}\)

first derivative of ARD kernel wrt the first input pattern

\[ \frac {\partial k(x,z)}{\partial x} = -2 \gamma_i \left( x_i - z_i \right)\cdot k(x,z) \]

Definition at line 221 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, SIZE_CHECK, and shark::State::toState().

◆ weightedParameterDerivative()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::weightedParameterDerivative	(	ConstBatchInputReference	batchX1,
		ConstBatchInputReference	batchX2,
		RealMatrix const &	coefficients,
		State const &	state,
		RealVector &	gradient
	)		const

inline

evaluates \( \frac {\partial k(x,z)}{\partial \sqrt{\gamma_i}}\) weighted over a whole batch

Since the ARD kernel is parametrized for unconstrained optimization, we return the derivative w.r.t. the parameters \( p_i \), where \( p_i^2 = \gamma_i \).

\[ \frac {\partial k(x,z)}{\partial p_i} = -2 p_i (x_i - z_i)^2 \cdot k(x,z) \]

Definition at line 192 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, shark::ARDKernelUnconstrained< InputType >::m_inputDimensions, SIZE_CHECK, shark::sqr(), and shark::State::toState().

◆ write()

template<class InputType = RealVector>

void shark::ARDKernelUnconstrained< InputType >::write ( OutArchive & archive ) const

inlinevirtual

From ISerializable, writes a metric to an archive.

The default implementation just saves the parameters.

Reimplemented from shark::AbstractMetric< InputTypeT >.

Definition at line 252 of file ArdKernel.h.

References shark::ARDKernelUnconstrained< InputType >::m_gammas, and shark::ARDKernelUnconstrained< InputType >::m_inputDimensions.

Member Data Documentation

◆ m_gammas

template<class InputType = RealVector>

RealVector shark::ARDKernelUnconstrained< InputType >::m_gammas

protected

kernel bandwidth parameters, one for each input dimension.

Definition at line 258 of file ArdKernel.h.

◆ m_inputDimensions

template<class InputType = RealVector>

std::size_t shark::ARDKernelUnconstrained< InputType >::m_inputDimensions

protected

how many input dimensions = how many bandwidth parameters

Definition at line 259 of file ArdKernel.h.

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

include/shark/Models/Kernels/ArdKernel.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ BatchInputType

◆ ConstBatchInputReference

◆ ConstInputReference

Constructor & Destructor Documentation

◆ ARDKernelUnconstrained()

Member Function Documentation

◆ createState()

◆ eval() [1/3]

◆ eval() [2/3]

◆ eval() [3/3]

◆ gammaVector()

◆ name()

◆ numberOfParameters()

◆ parameterVector()

◆ read()

◆ setGammaVector()

◆ setParameterVector()

◆ weightedInputDerivative()

◆ weightedParameterDerivative()

◆ write()

Member Data Documentation

◆ m_gammas

◆ m_inputDimensions