turi::optimization::l1_norm Class Reference

#include <ml/optimization/regularizers-inl.hpp>

Public Member Functions
	l1_norm (const DenseVector &_lambda)
	~l1_norm ()
double	compute_function_value (const DenseVector &point) const
void	compute_gradient (const DenseVector &point, DenseVector &gradient) const
void	apply_proximal_operator (DenseVector &point, const double &_penalty=0) const
bool	is_smooth ()

Protected Attributes
DenseVector	lambda
size_t	variables

Detailed Description

Interface for the regularizer (Scaled L1-norm)

 f(x) = \sum_{i} lambda_i * |x_i|

Definition at line 129 of file regularizers-inl.hpp.

Constructor & Destructor Documentation

l1_norm()

turi::optimization::l1_norm::l1_norm ( const DenseVector &  _lambda )

inline

Default constructor.

Definition at line 141 of file regularizers-inl.hpp.

~l1_norm()

turi::optimization::l1_norm::~l1_norm ( )

inline

Default desctuctor. Do nothing.

Definition at line 149 of file regularizers-inl.hpp.

Member Function Documentation

apply_proximal_operator()

void turi::optimization::l1_norm::apply_proximal_operator ( DenseVector &  point, const double &  _penalty = 0  ) const

inlinevirtual

Compute the proximal operator for the l2-regularizer

Parameters

[in,out]	point	Point at which we are computing the gradient.
[in]	penalty	Penalty

Note

The proximal operator for lambda * ||x||_1 at the point v is given by soft(x, lambda) = (x - lambda)_+ - (-x - lambda)_+

Implements turi::optimization::regularizer_interface.

Definition at line 191 of file regularizers-inl.hpp.

compute_function_value()

double turi::optimization::l1_norm::compute_function_value ( const DenseVector &  point ) const

inlinevirtual

Compute the function value of the regularizer at a given point.

Parameters

[in]

point

Point at which we are computing the gradient.

Implements turi::optimization::regularizer_interface.

Definition at line 157 of file regularizers-inl.hpp.

compute_gradient()

void turi::optimization::l1_norm::compute_gradient ( const DenseVector &  point, DenseVector &  gradient  ) const

inlinevirtual

Compute the subgradient at the given point.

Parameters

[in]	point	Point at which we are computing the gradient.
[out]	gradient	Dense sub-gradient

Implements turi::optimization::regularizer_interface.

Definition at line 170 of file regularizers-inl.hpp.

is_smooth()

bool turi::optimization::regularizer_interface::is_smooth ( )

inlineinherited

Function to determine if the regularizer is smooth.

Returns

false

Definition at line 56 of file regularizer_interface.hpp.

Member Data Documentation

lambda

DenseVector turi::optimization::l1_norm::lambda

protected

Penalty on the regularizer

Definition at line 133 of file regularizers-inl.hpp.

variables

size_t turi::optimization::l1_norm::variables

protected

Variables in the problem

Definition at line 134 of file regularizers-inl.hpp.

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

• ml/optimization/regularizers-inl.hpp