Special "Gaussian-like" kernel function on tasks. More...

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

Inheritance diagram for shark::GaussianTaskKernel< InputTypeT >:

Public Types
typedef InputTypeT	InputType

typedef MultiTaskSample< InputType >	MultiTaskSampleType

typedef AbstractKernelFunction< InputType >	KernelType

Public Types inherited from shark::AbstractKernelFunction< std::size_t >
enum	Feature
	enumerations of kerneland metric features (flags) More...

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

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

typedef base_type::ConstInputReference	ConstInputReference
	Const references to InputType. More...

typedef base_type::ConstBatchInputReference	ConstBatchInputReference
	Const references to BatchInputType. More...

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

typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException

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

typedef Batch< std::size_t >::type	BatchInputType
	batch input type of the kernel More...

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

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

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

Public Member Functions
	GaussianTaskKernel (Data< MultiTaskSampleType > const &data, std::size_t tasks, KernelType &inputkernel, double gamma)
	Construction of a Gaussian kernel on tasks. More...

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

RealVector	parameterVector () const
	Return the parameter vector. More...

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

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

std::size_t	numberOfTasks () const

double	gamma () const
	Kernel bandwidth parameter. More...

double	sigma () const
	Kernel width parameter, equivalent to the bandwidth parameter. More...

void	setGamma (double gamma)

void	setWidth (double sigma)
	Set the kernel width (equivalent to setting the bandwidth). More...

void	read (InArchive &ar)
	From ISerializable. More...

void	write (OutArchive &ar) const
	From ISerializable. More...

Public Member Functions inherited from shark::DiscreteKernel
	DiscreteKernel (RealMatrix const &matrix)
	Construction of the kernel from a positive definite, symmetric matrix. More...

std::size_t	size () const
	Cardinality of the discrete space. More...

boost::shared_ptr< State >	createState () const
	DiscreteKernels don't have a state so they return an EmptyState object. More...

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

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result, State &state) const
	Evaluates the kernel function for every point combination of the two batches. More...

void	eval (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2, RealMatrix &result) const
	Evaluates the kernel function for every point combination of the two batches. More...

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

const Features &	features () const

virtual void	updateFeatures ()

bool	hasFirstParameterDerivative () const

bool	hasFirstInputDerivative () const

bool	isNormalized () const

bool	supportsVariableInputSize () const

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

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

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. More...

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!). More...

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

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

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

virtual	~AbstractMetric ()

virtual double	featureDistanceSqr (ConstInputReference x1, ConstInputReference x2) const=0
	Computes the squared distance in the kernel induced feature space. More...

virtual RealMatrix	featureDistanceSqr (ConstBatchInputReference batchX1, ConstBatchInputReference batchX2) const=0

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

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

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

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

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

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

	BOOST_SERIALIZATION_SPLIT_MEMBER ()

Protected Member Functions
void	computeMatrix ()
	Compute the Gram matrix of the task kernel. More...

Protected Attributes
Data< MultiTaskSampleType > const &	m_data
	multi-task data More...

KernelType *	mpe_inputKernel
	kernel on inputs More...

double	m_gamma
	bandwidth of the Gaussian task kernel More...

Protected Attributes inherited from shark::DiscreteKernel
RealMatrix	m_matrix
	kernel matrix More...

Protected Attributes inherited from shark::AbstractKernelFunction< std::size_t >
Features	m_features

Detailed Description

template<class InputTypeT>
class shark::GaussianTaskKernel< InputTypeT >

Special "Gaussian-like" kernel function on tasks.

: See
Learning Marginal Predictors: Transfer to an Unlabeled Task. G. Blanchard, G. Lee, C. Scott.

: This class computes a Gaussian kernel based on the distance of empirical distributions in feature space induced by yet another kernel. This is useful for multi-task and transfer learning. It reduces the definition of a kernel on tasks to that of a kernel on inputs, plus a single bandwidth parameter for the Gaussian kernel of distributions.

: Given unlabaled data \( x_i, t_i \) where the x-component is an input and the t-component is a task index, the kernel on tasks t and t' is defined as
\[ k(t, t') = \exp \left( -\gamma \cdot \left\| \frac{1}{\ell_{t}\ell{t'}} \sum_{i | t_i = t}\sum_{j | t_j = t'} k'(x_i, x_j) \right\|^2 \right) \]
where k' is an arbitrary kernel on inputs.

Definition at line 129 of file MultiTaskKernel.h.

Member Typedef Documentation

◆ InputType

template<class InputTypeT>

typedef InputTypeT shark::GaussianTaskKernel< InputTypeT >::InputType

Definition at line 134 of file MultiTaskKernel.h.

◆ KernelType

template<class InputTypeT>

typedef AbstractKernelFunction<InputType> shark::GaussianTaskKernel< InputTypeT >::KernelType

Definition at line 136 of file MultiTaskKernel.h.

◆ MultiTaskSampleType

template<class InputTypeT>

typedef MultiTaskSample<InputType> shark::GaussianTaskKernel< InputTypeT >::MultiTaskSampleType

Definition at line 135 of file MultiTaskKernel.h.

Constructor & Destructor Documentation

◆ GaussianTaskKernel()

template<class InputTypeT>

shark::GaussianTaskKernel< InputTypeT >::GaussianTaskKernel	(	Data< MultiTaskSampleType > const &	data,
		std::size_t	tasks,
		KernelType &	inputkernel,
		double	gamma
	)

inline

Construction of a Gaussian kernel on tasks.

Parameters

data	unlabeled data from multiple tasks
tasks	number of tasks in the problem
inputkernel	kernel on inputs based on which task similarity is defined
gamma	Gaussian bandwidth parameter (also refer to the member functions setGamma and setSigma).

Definition at line 144 of file MultiTaskKernel.h.

Member Function Documentation

◆ computeMatrix()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::computeMatrix ( )

inlineprotected

Compute the Gram matrix of the task kernel.

: Here is the real meat. This function implements the kernel function defined in
Learning Marginal Predictors: Transfer to an Unlabeled Task. G. Blanchard, G. Lee, C. Scott.

: In a first step the function computes the inner products of the task-wise empirical distributions, represented by their mean elements in the kernel-induced feature space. In a second step this information is used for the computation of squared distances between empirical distribution, which allows for the straightforward computation of a Gaussian kernel.

Definition at line 236 of file MultiTaskKernel.h.

◆ gamma()

template<class InputTypeT>

double shark::GaussianTaskKernel< InputTypeT >::gamma ( ) const

inline

Kernel bandwidth parameter.

Definition at line 179 of file MultiTaskKernel.h.

◆ name()

template<class InputTypeT>

std::string shark::GaussianTaskKernel< InputTypeT >::name ( ) const

inlinevirtual

From INameable: return the class name.

Reimplemented from shark::DiscreteKernel.

Definition at line 157 of file MultiTaskKernel.h.

◆ numberOfParameters()

template<class InputTypeT>

std::size_t shark::GaussianTaskKernel< InputTypeT >::numberOfParameters ( ) const

inlinevirtual

Return the number of parameters.

Reimplemented from shark::DiscreteKernel.

Definition at line 171 of file MultiTaskKernel.h.

◆ numberOfTasks()

template<class InputTypeT>

std::size_t shark::GaussianTaskKernel< InputTypeT >::numberOfTasks ( ) const

inline

Definition at line 175 of file MultiTaskKernel.h.

◆ parameterVector()

template<class InputTypeT>

RealVector shark::GaussianTaskKernel< InputTypeT >::parameterVector ( ) const

inlinevirtual

Return the parameter vector.

Reimplemented from shark::DiscreteKernel.

Definition at line 160 of file MultiTaskKernel.h.

◆ read()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::read ( InArchive & ar )

inlinevirtual

From ISerializable.

Reimplemented from shark::DiscreteKernel.

Definition at line 205 of file MultiTaskKernel.h.

◆ setGamma()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::setGamma ( double gamma )

inline

Definition at line 189 of file MultiTaskKernel.h.

References SHARK_ASSERT.

◆ setParameterVector()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::setParameterVector ( RealVector const & newParameters )

inlinevirtual

Set the parameter vector.

Reimplemented from shark::DiscreteKernel.

Definition at line 164 of file MultiTaskKernel.h.

◆ setWidth()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::setWidth ( double sigma )

inline

Set the kernel width (equivalent to setting the bandwidth).

The bandwidth gamma and the width sigma are connected: \( gamma = 1 / (2 \cdot sigma^2) \).

Definition at line 198 of file MultiTaskKernel.h.

References SHARK_ASSERT.

◆ sigma()

template<class InputTypeT>

double shark::GaussianTaskKernel< InputTypeT >::sigma ( ) const

inline

Kernel width parameter, equivalent to the bandwidth parameter.

The bandwidth gamma and the width sigma are connected: \( gamma = 1 / (2 \cdot sigma^2) \).

Definition at line 185 of file MultiTaskKernel.h.

◆ write()

template<class InputTypeT>

void shark::GaussianTaskKernel< InputTypeT >::write ( OutArchive & ar ) const

inlinevirtual

From ISerializable.

Reimplemented from shark::DiscreteKernel.

Definition at line 212 of file MultiTaskKernel.h.

Member Data Documentation

◆ m_data

template<class InputTypeT>

Data<MultiTaskSampleType > const& shark::GaussianTaskKernel< InputTypeT >::m_data

protected

multi-task data

Definition at line 281 of file MultiTaskKernel.h.

◆ m_gamma

template<class InputTypeT>

double shark::GaussianTaskKernel< InputTypeT >::m_gamma

protected

bandwidth of the Gaussian task kernel

Definition at line 283 of file MultiTaskKernel.h.

◆ mpe_inputKernel

template<class InputTypeT>

KernelType* shark::GaussianTaskKernel< InputTypeT >::mpe_inputKernel

protected

kernel on inputs

Definition at line 282 of file MultiTaskKernel.h.

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

include/shark/Models/Kernels/MultiTaskKernel.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<class InputTypeT> class shark::GaussianTaskKernel< InputTypeT >

Member Typedef Documentation

◆ InputType

◆ KernelType

◆ MultiTaskSampleType

Constructor & Destructor Documentation

◆ GaussianTaskKernel()

Member Function Documentation

◆ computeMatrix()

◆ gamma()

◆ name()

◆ numberOfParameters()

◆ numberOfTasks()

◆ parameterVector()

◆ read()

◆ setGamma()

◆ setParameterVector()

◆ setWidth()

◆ sigma()

◆ write()

Member Data Documentation

◆ m_data

◆ m_gamma

◆ mpe_inputKernel

template<class InputTypeT>
class shark::GaussianTaskKernel< InputTypeT >