turi::optimization::smooth_regularizer_interface Class Reference

#include <ml/optimization/regularizer_interface.hpp>

Public Member Functions
bool	is_smooth ()
virtual	~smooth_regularizer_interface ()
virtual void	compute_hessian (const DenseVector &point, DiagonalMatrix &hessian) const =0
virtual double	compute_function_value (const DenseVector &point) const =0
virtual void	compute_gradient (const DenseVector &point, DenseVector &gradient) const =0
virtual void	apply_proximal_operator (DenseVector &point, const double &_penalty=0) const =0

Detailed Description

Interface for regularizers that separable and smooth.

Definition at line 105 of file regularizer_interface.hpp.

Constructor & Destructor Documentation

~smooth_regularizer_interface()

virtual turi::optimization::smooth_regularizer_interface::~smooth_regularizer_interface ( )

inlinevirtual

Default desctuctor.

Definition at line 118 of file regularizer_interface.hpp.

Member Function Documentation

apply_proximal_operator()

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

pure virtualinherited

Compute the proximal operator for the regularizer at a given point.

Parameters

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

Note

The proximal operator for a convex function f(.) at the point x is defined as prox_f(x) = argmin_v ( f(v) + 0.5 * penalty ||x-v||^2) The idea is an old concept in optimization but it well explained in (1).

References:

(1) Parikh, Neal, and Stephen Boyd. "Foundations and Trends in Optimization." (2014).

Implemented in turi::optimization::elastic_net, turi::optimization::l1_norm, and turi::optimization::l2_norm.

compute_function_value()

virtual double turi::optimization::regularizer_interface::compute_function_value ( const DenseVector &  point ) const

pure virtualinherited

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

Parameters

[in]

point

Point at which we are computing the gradient.

Implemented in turi::optimization::elastic_net, turi::optimization::l1_norm, and turi::optimization::l2_norm.

compute_gradient()

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

pure virtualinherited

Compute the gradient (or subgradient) at the given point.

Parameters

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

Implemented in turi::optimization::elastic_net, turi::optimization::l1_norm, and turi::optimization::l2_norm.

compute_hessian()

virtual void turi::optimization::smooth_regularizer_interface::compute_hessian ( const DenseVector &  point, DiagonalMatrix &  hessian  ) const

pure virtual

Compute the hessian of the regularizer at a given point.

Parameters

[in]	point	Point at which we are computing the gradient.
[in,out]	hessian	Diagonal matrix as the hessian gradient.

Implemented in turi::optimization::l2_norm.

is_smooth()

bool turi::optimization::smooth_regularizer_interface::is_smooth ( )

inline

Function to determine if the regularizer is smooth.

Returns

true

Definition at line 113 of file regularizer_interface.hpp.

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

• ml/optimization/regularizer_interface.hpp