#include <itkAdaptiveStochasticVarianceReducedGradientOptimizer.h>

Detailed Description

This class implements a gradient descent optimizer with adaptive gain.

If is a cost function that has to be minimized, the following iterative algorithm is used to find the optimal parameters :

$x(k+1) = x(k) - a(t_k) dC/dx$

The gain at each iteration is defined by:

$a(t_k) = a / (A + t_k + 1)^alpha$

.

And the time is updated according to:

$t_{k+1} = [ t_k + sigmoid( -g_k^T g_{k-1} ) ]^+$

where equals at iteration . For the InitialTime is used, which is defined in the the superclass (StandardGradientDescentOptimizer). Whereas in the superclass this parameter is superfluous, in this class it makes sense.

This method is described in the following references:

[1] P. Cruz, "Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case." Technical Report, 2005. http://hdl.handle.net/2052/74

[2] S. Klein, J.P.W. Pluim, and M. Staring, M.A. Viergever, "Adaptive stochastic gradient descent optimisation for image registration," International Journal of Computer Vision, vol. 81, no. 3, pp. 227-239, 2009. http://dx.doi.org/10.1007/s11263-008-0168-y It is very suitable to be used in combination with a stochastic estimate of the gradient . For example, in image registration problems it is often advantageous to compute the metric derivative ( ) on a new set of randomly selected image samples in each iteration. You may set the parameter NewSamplesEveryIteration to "true" to achieve this effect. For more information on this strategy, you may have a look at:

See also: AdaptiveStochasticVarianceReducedGradient, StandardGradientDescentOptimizer

If is a costfunction that has to be minimised, the following iterative algorithm is used to find the optimal parameters :

$x(k+1) = x(k) - a(t_k) dC/dx$

The gain at each iteration is defined by:

$a(t_k) = a / (A + t_k + 1)^alpha$

.

And the time is updated according to:

$t_{k+1} = [ t_k + sigmoid( -g_k^T g_{k-1} ) ]^+$

where equals at iteration . For the InitialTime is used, which is defined in the the superclass (StandardGradientDescentOptimizer). Whereas in the superclass this parameter is superfluous, in this class it makes sense.

This method is described in the following references:

[1] P. Cruz, "Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case." Technical Report, 2005. http://hdl.handle.net/2052/74

[2] S. Klein, J.P.W. Pluim, and M. Staring, M.A. Viergever, "Adaptive stochastic gradient descent optimisation for image registration," International Journal of Computer Vision, vol. 81, no. 3, pp. 227-239, 2009. http://dx.doi.org/10.1007/s11263-008-0168-y

It is very suitable to be used in combination with a stochastic estimate of the gradient . For example, in image registration problems it is often advantageous to compute the metric derivative ( ) on a new set of randomly selected image samples in each iteration. You may set the parameter NewSamplesEveryIteration to "true" to achieve this effect. For more information on this strategy, you may have a look at:

See also: AdaptiveStochasticVarianceReducedGradient, StandardGradientDescentOptimizer

Definition at line 70 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

Inheritance diagram for itk::AdaptiveStochasticVarianceReducedGradientOptimizer:

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef AdaptiveStochasticVarianceReducedGradientOptimizer	Self

typedef Superclass::StopConditionType	StopConditionType

typedef StandardStochasticVarianceReducedGradientOptimizer	Superclass

Public Types inherited from itk::StandardStochasticVarianceReducedGradientOptimizer
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef StandardStochasticVarianceReducedGradientOptimizer	Self

typedef Superclass::StopConditionType	StopConditionType

typedef StochasticVarianceReducedGradientDescentOptimizer	Superclass

Public Types inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef StochasticVarianceReducedGradientDescentOptimizer	Self

enum	StopConditionType { MaximumNumberOfIterations , MetricError , MinimumStepSize , InvalidDiagonalMatrix , GradientMagnitudeTolerance , LineSearchError }

typedef ScaledSingleValuedNonLinearOptimizer	Superclass

Public Types inherited from itk::ScaledSingleValuedNonLinearOptimizer
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef ScaledCostFunctionType::Pointer	ScaledCostFunctionPointer

typedef ScaledSingleValuedCostFunction	ScaledCostFunctionType

typedef NonLinearOptimizer::ScalesType	ScalesType

typedef ScaledSingleValuedNonLinearOptimizer	Self

typedef SingleValuedNonLinearOptimizer	Superclass

Public Member Functions
virtual const char *	GetClassName () const

virtual double	GetSigmoidMax () const

virtual double	GetSigmoidMin () const

virtual double	GetSigmoidScale () const

virtual bool	GetUseAdaptiveStepSizes () const

virtual void	SetSigmoidMax (double _arg)

virtual void	SetSigmoidMin (double _arg)

virtual void	SetSigmoidScale (double _arg)

virtual void	SetUseAdaptiveStepSizes (bool _arg)

Public Member Functions inherited from itk::StandardStochasticVarianceReducedGradientOptimizer
void	AdvanceOneStep (void) override

virtual const char *	GetClassName () const

virtual double	GetCurrentTime () const

virtual double	GetInitialTime () const

virtual double	GetParam_a () const

virtual double	GetParam_A () const

virtual double	GetParam_alpha () const

virtual double	GetParam_beta () const

virtual void	ResetCurrentTimeToInitialTime (void)

virtual void	SetInitialTime (double _arg)

virtual void	SetParam_a (double _arg)

virtual void	SetParam_A (double _arg)

virtual void	SetParam_alpha (double _arg)

virtual void	SetParam_beta (double _arg)

void	StartOptimization (void) override

Public Member Functions inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
virtual void	AdvanceOneStep (void)

virtual const char *	GetClassName () const

virtual unsigned int	GetCurrentInnerIteration () const

virtual unsigned int	GetCurrentIteration () const

virtual const DerivativeType &	GetGradient ()

virtual unsigned int	GetLBFGSMemory () const

virtual const double &	GetLearningRate ()

virtual const unsigned long &	GetNumberOfInnerIterations ()

virtual const unsigned long &	GetNumberOfIterations ()

virtual const DerivativeType &	GetPreviousGradient ()

virtual const ParametersType &	GetPreviousPosition ()

virtual const DerivativeType &	GetSearchDir ()

virtual const StopConditionType &	GetStopCondition ()

virtual const double &	GetValue ()

virtual void	MetricErrorResponse (ExceptionObject &err)

virtual void	ResumeOptimization (void)

virtual void	SetLearningRate (double _arg)

virtual void	SetNumberOfIterations (unsigned long _arg)

void	SetNumberOfWorkUnits (ThreadIdType numberOfThreads)

virtual void	SetPreviousGradient (DerivativeType _arg)

virtual void	SetPreviousPosition (ParametersType _arg)

virtual void	SetUseEigen (bool _arg)

virtual void	SetUseMultiThread (bool _arg)

virtual void	SetUseOpenMP (bool _arg)

void	StartOptimization (void) override

virtual void	StopOptimization (void)

Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual const char *	GetClassName () const

const ParametersType &	GetCurrentPosition (void) const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales (void) const

virtual void	InitializeScales (void)

virtual void	MaximizeOff ()

virtual void	MaximizeOn ()

void	SetCostFunction (CostFunctionType *costFunction) override

virtual void	SetMaximize (bool _arg)

virtual void	SetUseScales (bool arg)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::StandardStochasticVarianceReducedGradientOptimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
static Pointer	New ()

Protected Member Functions
	AdaptiveStochasticVarianceReducedGradientOptimizer ()

void	UpdateCurrentTime (void) override

	~AdaptiveStochasticVarianceReducedGradientOptimizer () override

Protected Member Functions inherited from itk::StandardStochasticVarianceReducedGradientOptimizer
virtual double	Compute_a (double k) const

virtual double	Compute_beta (double k) const

	StandardStochasticVarianceReducedGradientOptimizer ()

virtual void	UpdateCurrentTime (void)

	~StandardStochasticVarianceReducedGradientOptimizer () override

Protected Member Functions inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
void	PrintSelf (std::ostream &os, Indent indent) const override

	StochasticVarianceReducedGradientDescentOptimizer ()

	~StochasticVarianceReducedGradientDescentOptimizer () override

Protected Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual void	GetScaledDerivative (const ParametersType &parameters, DerivativeType &derivative) const

virtual MeasureType	GetScaledValue (const ParametersType &parameters) const

virtual void	GetScaledValueAndDerivative (const ParametersType &parameters, MeasureType &value, DerivativeType &derivative) const

void	PrintSelf (std::ostream &os, Indent indent) const override

	ScaledSingleValuedNonLinearOptimizer ()

void	SetCurrentPosition (const ParametersType &param) override

virtual void	SetScaledCurrentPosition (const ParametersType &parameters)

	~ScaledSingleValuedNonLinearOptimizer () override

Protected Attributes
DerivativeType	m_PreviousGradient

Protected Attributes inherited from itk::StandardStochasticVarianceReducedGradientOptimizer
double	m_CurrentTime

bool	m_UseConstantStep

Protected Attributes inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
unsigned long	m_CurrentInnerIteration

unsigned long	m_CurrentIteration

DerivativeType	m_Gradient

unsigned long	m_LBFGSMemory

double	m_LearningRate

ParametersType	m_MeanSearchDir

unsigned long	m_NumberOfInnerIterations

unsigned long	m_NumberOfIterations

DerivativeType	m_PreviousGradient

ParametersType	m_PreviousPosition

ParametersType	m_PreviousSearchDir

ParametersType	m_SearchDir

bool	m_Stop

StopConditionType	m_StopCondition

ThreaderType::Pointer	m_Threader

double	m_Value

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction

ParametersType	m_ScaledCurrentPosition

Private Member Functions
	AdaptiveStochasticVarianceReducedGradientOptimizer (const Self &)

void	operator= (const Self &)

Private Attributes
double	m_SigmoidMax

double	m_SigmoidMin

double	m_SigmoidScale

bool	m_UseAdaptiveStepSizes

Additional Inherited Members
Protected Types inherited from itk::StochasticVarianceReducedGradientDescentOptimizer
typedef itk::PlatformMultiThreader	ThreaderType

typedef ThreaderType::WorkUnitInfo	ThreadInfoType

Member Typedef Documentation

◆ ConstPointer

typedef SmartPointer<const Self> itk::AdaptiveStochasticVarianceReducedGradientOptimizer::ConstPointer

Definition at line 80 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ CostFunctionType

typedef Superclass::CostFunctionType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::CostFunctionType

Definition at line 93 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ DerivativeType

typedef Superclass::DerivativeType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::DerivativeType

Definition at line 92 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ MeasureType

typedef Superclass::MeasureType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::MeasureType

Typedefs inherited from the superclass.

Definition at line 90 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ ParametersType

typedef Superclass::ParametersType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::ParametersType

Definition at line 91 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ Pointer

typedef SmartPointer<Self> itk::AdaptiveStochasticVarianceReducedGradientOptimizer::Pointer

Definition at line 79 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionPointer itk::AdaptiveStochasticVarianceReducedGradientOptimizer::ScaledCostFunctionPointer

Definition at line 96 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ ScaledCostFunctionType

typedef Superclass::ScaledCostFunctionType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::ScaledCostFunctionType

Definition at line 95 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ ScalesType

typedef Superclass::ScalesType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::ScalesType

Definition at line 94 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ Self

typedef AdaptiveStochasticVarianceReducedGradientOptimizer itk::AdaptiveStochasticVarianceReducedGradientOptimizer::Self

Standard ITK.

Definition at line 76 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ StopConditionType

typedef Superclass::StopConditionType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::StopConditionType

Definition at line 97 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ Superclass

typedef StandardStochasticVarianceReducedGradientOptimizer itk::AdaptiveStochasticVarianceReducedGradientOptimizer::Superclass

Definition at line 77 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

Constructor & Destructor Documentation

◆ AdaptiveStochasticVarianceReducedGradientOptimizer() [1/2]

itk::AdaptiveStochasticVarianceReducedGradientOptimizer::AdaptiveStochasticVarianceReducedGradientOptimizer ( )

protected

◆ ~AdaptiveStochasticVarianceReducedGradientOptimizer()

itk::AdaptiveStochasticVarianceReducedGradientOptimizer::~AdaptiveStochasticVarianceReducedGradientOptimizer ( )

inlineoverrideprotected

Definition at line 121 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ AdaptiveStochasticVarianceReducedGradientOptimizer() [2/2]

itk::AdaptiveStochasticVarianceReducedGradientOptimizer::AdaptiveStochasticVarianceReducedGradientOptimizer ( const Self & )

private

Member Function Documentation

◆ GetClassName()

virtual const char * itk::AdaptiveStochasticVarianceReducedGradientOptimizer::GetClassName ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::StandardStochasticVarianceReducedGradientOptimizer.

Reimplemented in elastix::AdaptiveStochasticVarianceReducedGradient< TElastix >.

◆ GetSigmoidMax()

virtual double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::GetSigmoidMax ( ) const

virtual

◆ GetSigmoidMin()

virtual double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::GetSigmoidMin ( ) const

virtual

◆ GetSigmoidScale()

virtual double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::GetSigmoidScale ( ) const

virtual

◆ GetUseAdaptiveStepSizes()

virtual bool itk::AdaptiveStochasticVarianceReducedGradientOptimizer::GetUseAdaptiveStepSizes ( ) const

virtual

◆ New()

static Pointer itk::AdaptiveStochasticVarianceReducedGradientOptimizer::New ( )

static

Method for creation through the object factory.

◆ operator=()

void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::operator= ( const Self & )

private

◆ SetSigmoidMax()

virtual void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::SetSigmoidMax ( double _arg )

virtual

Set/Get the maximum of the sigmoid. Should be >0. Default: 1.0

◆ SetSigmoidMin()

virtual void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::SetSigmoidMin ( double _arg )

virtual

Set/Get the maximum of the sigmoid. Should be <0. Default: -0.8

◆ SetSigmoidScale()

virtual void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::SetSigmoidScale ( double _arg )

virtual

Set/Get the scaling of the sigmoid width. Large values cause a more wide sigmoid. Default: 1e-8. Should be >0.

◆ SetUseAdaptiveStepSizes()

virtual void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::SetUseAdaptiveStepSizes ( bool _arg )

virtual

Set/Get whether the adaptive step size mechanism is desired. Default: true

◆ UpdateCurrentTime()

void itk::AdaptiveStochasticVarianceReducedGradientOptimizer::UpdateCurrentTime ( void )

overrideprotectedvirtual

Function to update the current time If UseAdaptiveStepSizes is false this function just increments the CurrentTime by $E_0 = (sigmoid_{max} + sigmoid_{min})/2$ . Else, the CurrentTime is updated according to:
time = max[ 0, time + sigmoid( -gradient*previousgradient) ]
In that case, also the m_PreviousGradient is updated.

Reimplemented from itk::StandardStochasticVarianceReducedGradientOptimizer.

Field Documentation

◆ m_PreviousGradient

DerivativeType itk::AdaptiveStochasticVarianceReducedGradientOptimizer::m_PreviousGradient

protected

The PreviousGradient, necessary for the CruzAcceleration

Definition at line 133 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ m_SigmoidMax

double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::m_SigmoidMax

private

Definition at line 142 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ m_SigmoidMin

double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::m_SigmoidMin

private

Definition at line 143 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ m_SigmoidScale

double itk::AdaptiveStochasticVarianceReducedGradientOptimizer::m_SigmoidScale

private

Definition at line 144 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

◆ m_UseAdaptiveStepSizes

bool itk::AdaptiveStochasticVarianceReducedGradientOptimizer::m_UseAdaptiveStepSizes

private

Settings

Definition at line 141 of file itkAdaptiveStochasticVarianceReducedGradientOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ConstPointer

◆ CostFunctionType

◆ DerivativeType

◆ MeasureType

◆ ParametersType

◆ Pointer

◆ ScaledCostFunctionPointer

◆ ScaledCostFunctionType

◆ ScalesType

◆ Self

◆ StopConditionType

◆ Superclass

Constructor & Destructor Documentation

◆ AdaptiveStochasticVarianceReducedGradientOptimizer() [1/2]

◆ ~AdaptiveStochasticVarianceReducedGradientOptimizer()

◆ AdaptiveStochasticVarianceReducedGradientOptimizer() [2/2]

Member Function Documentation

◆ GetClassName()

◆ GetSigmoidMax()

◆ GetSigmoidMin()

◆ GetSigmoidScale()

◆ GetUseAdaptiveStepSizes()

◆ New()

◆ operator=()

◆ SetSigmoidMax()

◆ SetSigmoidMin()

◆ SetSigmoidScale()

◆ SetUseAdaptiveStepSizes()

◆ UpdateCurrentTime()

Field Documentation

◆ m_PreviousGradient

◆ m_SigmoidMax

◆ m_SigmoidMin

◆ m_SigmoidScale

◆ m_UseAdaptiveStepSizes