Iteratively-reweighted least-squares minimization of an M-estimator. More...

#include <rrel_irls.h>

Public Member Functions
	rrel_irls (int max_iterations=dflt_max_iterations_)
	Constructor.
	~rrel_irls ()
	Destructor.
void	set_est_scale (int iterations_for_scale=dflt_iterations_for_scale_, bool use_weighted_scale=false)
	Set scale estimation and parameters.
void	set_scale_lower_bound (double lower_scale)
	Set lower bound of scale estimate.
void	set_no_scale_est ()
	Set for no scale estimation.
void	initialize_scale (double scale)
	Initialize the scale value.
void	reset_scale ()
	Indicate that scale has not been initialized.
double	scale () const
	Get the scale estimate (or the fixed scale value).
void	set_max_iterations (int max_iterations=dflt_max_iterations_)
	Set the maximum number of iterations.
void	set_convergence_test (double convergence_tol=dflt_convergence_tol_)
	Indicate that a convergence test is to be used.
void	set_no_convergence_test ()
	Indicate that no convergence test is to be used.
void	initialize_params (const vnl_vector< double > &init_params)
	Initialize the parameter estimate.
void	reset_params ()
	Reset the parameters.
void	set_trace_level (int level)
bool	estimate (const rrel_estimation_problem problem, const rrel_wls_obj m_estimator)
	Estimate the parameters.
const vnl_vector< double > &	params () const
	Get the parameter estimate.
const vnl_matrix< double > &	cofactor () const
	Get the cofactor matrix (the covariance matrix / scale^2).
bool	converged () const
	Determine if the estimation converged.
int	iterations_used () const
	The number of iterations that were used.
void	trace_residuals (const vcl_vector< double > &residuals) const
	Print the residuals. Used for debugging.
void	trace_weights (const vcl_vector< double > &weights) const
	Print the IRLS weights. Used for debugging.
void	print_params () const
	Print the set of parameters.
Protected Attributes
int	max_iterations_
bool	test_converge_
double	convergence_tol_
bool	est_scale_during_
bool	use_weighted_scale_
int	iterations_for_scale_est_
double	scale_lower_bound_
int	trace_level_
vnl_vector< double >	params_
vnl_matrix< double >	cofact_
bool	params_initialized_
double	scale_
bool	scale_initialized_
double	obj_fcn_
double	prev_obj_fcn_
bool	converged_
int	iteration_
Private Member Functions
bool	has_converged (const vcl_vector< double > &residuals, const rrel_wls_obj m_estimator, const rrel_estimation_problem problem, vnl_vector< double > *params)
Static Private Attributes
static const double	dflt_convergence_tol_ = 1e-4
static const int	dflt_max_iterations_ = 25
static const int	dflt_iterations_for_scale_ = 1

Detailed Description

Iteratively-reweighted least-squares minimization of an M-estimator.

IRLS is a search technique for solving M-estimation problems. The technique is to compute weights from a given parameter estimate, and use those weights to compute a new estimate via weighted least squares.

Several options allow variation in the behavior of estimation:

(1) Scale may be fixed through a parameter setting function or it may be estimated in the first few iterations of IRLS. A parameter called iterations_for_scale_est_ determines the number of iterations during which scale is to be estimated. Scale estimation is either weight-based or median-based.

(2) The maximum number of iterations may be set, either in the constructor or through parameter setting member functions.

(3) The convergence test, which is based on the objective function, may or may not be run. Not running it makes each iteration faster, but may result in more iterations than necessary. The convergence test is not applied until the scale is no longer allowed to change. (The alternative, which was not implemented, is to include a ln(sigma) term to the objective function.)

(4) The parameters, the scale, both or neither may be initialized.

Definition at line 49 of file rrel_irls.h.

Constructor & Destructor Documentation

rrel_irls::rrel_irls ( int max_iterations = dflt_max_iterations_ )

Constructor.

Definition at line 23 of file rrel_irls.cxx.

rrel_irls::~rrel_irls ( ) [inline]

Destructor.

Definition at line 61 of file rrel_irls.h.

Member Function Documentation

const vnl_matrix< double > & rrel_irls::cofactor ( ) const

Get the cofactor matrix (the covariance matrix / scale^2).

Definition at line 252 of file rrel_irls.cxx.

bool rrel_irls::converged ( ) const [inline]

Determine if the estimation converged.

Definition at line 145 of file rrel_irls.h.

bool rrel_irls::estimate	(	const rrel_estimation_problem *	problem,
		const rrel_wls_obj *	m_estimator
	)

Estimate the parameters.

The initial step is to initialize the parameter estimate, if necessary, and then the scale estimate, if necessary. Then the following basic loop is applied:

1. Calculate residuals 2. Test for convergence, if desired. 3. Calculate weights 4. Calculate scale 5. Calculate new estimate

The loop can end in one of three ways: (a) convergence, (b) the maximum number of iterations is reached, (c) the weighted least-squares estimate fails.

Definition at line 118 of file rrel_irls.cxx.

bool rrel_irls::has_converged	(	const vcl_vector< double > &	residuals,
		const rrel_wls_obj *	m_estimator,
		const rrel_estimation_problem *	problem,
		vnl_vector< double > *	params
	)		`[private]`