shark::HingeLoss Class Reference

Hinge-loss for large margin classification. More...

#include <shark/ObjectiveFunctions/Loss/HingeLoss.h>

Inheritance diagram for shark::HingeLoss:

Public Member Functions
	HingeLoss ()
	constructor
std::string	name () const
	Returns class name "HingeLoss".
double	eval (BatchLabelType const &labels, BatchOutputType const &predictions) const
	calculates the sum of all
double	evalDerivative (BatchLabelType const &labels, BatchOutputType const &predictions, BatchOutputType &gradient) const
	evaluate the loss and the derivative w.r.t. the prediction
Public Member Functions inherited from shark::AbstractLoss< unsigned int, RealVector >
	AbstractLoss ()
virtual double	eval (ConstLabelReference target, ConstOutputReference prediction) const
	evaluate the loss for a target and a prediction
double	eval (Data< LabelType > const &targets, Data< OutputType > const &predictions) const
virtual double	evalDerivative (ConstLabelReference target, ConstOutputReference prediction, OutputType &gradient) const
	evaluate the loss and its derivative for a target and a prediction
virtual double	evalDerivative (ConstLabelReference target, ConstOutputReference prediction, OutputType &gradient, MatrixType &hessian) const
	evaluate the loss and its first and second derivative for a target and a prediction
double	operator() (LabelType const &target, OutputType const &prediction) const
	evaluate the loss for a target and a prediction
double	operator() (BatchLabelType const &target, BatchOutputType const &prediction) const
Public Member Functions inherited from shark::AbstractCost< LabelT, OutputT >
virtual	~AbstractCost ()
const Features &	features () const
virtual void	updateFeatures ()
bool	hasFirstDerivative () const
	returns true when the first parameter derivative is implemented
bool	isLossFunction () const
	returns true when the cost function is in fact a loss function
virtual double	eval (Data< LabelType > const &targets, Data< OutputType > const &predictions) const =0
double	operator() (Data< LabelType > const &targets, Data< OutputType > const &predictions) const
Public Member Functions inherited from shark::INameable
virtual	~INameable ()

Additional Inherited Members
Public Types inherited from shark::AbstractLoss< unsigned int, RealVector >
typedef RealVector	OutputType
typedef unsigned int	LabelType
typedef RealMatrix	MatrixType
typedef Batch< OutputType >::type	BatchOutputType
typedef Batch< LabelType >::type	BatchLabelType
typedef ConstProxyReference< LabelTypeconst >::type	ConstLabelReference
	Const references to LabelType.
typedef ConstProxyReference< OutputTypeconst >::type	ConstOutputReference
	Const references to OutputType.
Public Types inherited from shark::AbstractCost< LabelT, OutputT >
enum	Feature { HAS_FIRST_DERIVATIVE = 1 , HAS_SECOND_DERIVATIVE = 2 , IS_LOSS_FUNCTION = 4 }
	list of features a cost function can have More...
typedef OutputT	OutputType
typedef LabelT	LabelType
typedef Batch< OutputType >::type	BatchOutputType
typedef Batch< LabelType >::type	BatchLabelType
typedef TypedFlags< Feature >	Features
typedef TypedFeatureNotAvailableException< Feature >	FeatureNotAvailableException
Protected Attributes inherited from shark::AbstractCost< LabelT, OutputT >
Features	m_features

Detailed Description

Hinge-loss for large margin classification.

The hinge loss for two class problems is defined as \( L_i = \max \{ 0 , 1- y_i f(x_i) \} \) where \( y_i \in \{-1,1} \) is the label and \( f(x_i) \) is the prediction of the model for the ith input. The loss introduces the concept of a margin, that is, the point should not only be correctly classified but also not too close to the decision boundary. Therefore even correctly classified points are getting punished.

for multi class problems the concept of sums of the relative margin is used: \( L_i = \sum_{c \neq y_i} \max \{ 0 , 1- 1/2 (f_{y_i}(x_i)- f_c(x_i) \} \). This loss requires that there is a margin between the different class outputs and the functions needs as many outputs as classes. the pre-factor 1/2 ensures that in the 2 class 2 output case with a linear function the value of loss is the same as in the single output version.

The loss is implemented for class labels 0,1,...,n, even in the binary cases.

The hinge-loss is differentiable except on one point. For points violating the margin, the derivative is -1, for points that are not violating it, it is 0. Boundary counts as non-violating.

Definition at line 58 of file HingeLoss.h.

Constructor & Destructor Documentation

HingeLoss()

shark::HingeLoss::HingeLoss ( )

inline

constructor

Definition at line 62 of file HingeLoss.h.

References shark::AbstractCost< LabelT, OutputT >::m_features.

Member Function Documentation

eval()

double shark::HingeLoss::eval ( BatchLabelType const &  labels, BatchOutputType const &  predictions  ) const

inlinevirtual

calculates the sum of all

Implements shark::AbstractLoss< unsigned int, RealVector >.

Definition at line 72 of file HingeLoss.h.

References SIZE_CHECK.

evalDerivative()

double shark::HingeLoss::evalDerivative ( BatchLabelType const &  target, BatchOutputType const &  prediction, BatchOutputType &  gradient  ) const

inlinevirtual

evaluate the loss and the derivative w.r.t. the prediction

The default implementations throws an exception. If you overwrite this method, don't forget to set the flag HAS_FIRST_DERIVATIVE.

Parameters

target	target value
prediction	prediction, typically made by a model
gradient	the gradient of the loss function with respect to the prediction

Reimplemented from shark::AbstractLoss< unsigned int, RealVector >.

Definition at line 100 of file HingeLoss.h.

References SIZE_CHECK.

name()

std::string shark::HingeLoss::name ( ) const

inlinevirtual

Returns class name "HingeLoss".

Reimplemented from shark::INameable.

Definition at line 67 of file HingeLoss.h.

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

• include/shark/ObjectiveFunctions/Loss/HingeLoss.h