Build kernel pdf objects. More...

#include <pdf1d_kernel_pdf_builder.h>

Inheritance diagram for pdf1d_kernel_pdf_builder:

Public Types
enum	build_type { fixed_width, select_equal, width_from_sep, adaptive }
Public Member Functions
	pdf1d_kernel_pdf_builder ()
	Dflt ctor.
virtual	~pdf1d_kernel_pdf_builder ()
	Destructor.
void	set_use_fixed_width (double width)
	Use fixed width kernels of given width when building.
void	set_use_equal_width ()
	Use equal width kernels of width depending on number of samples.
void	set_use_width_from_separation ()
	Kernel width proportional to distance to nearby samples.
void	set_use_adaptive ()
	Build adaptive kernel estimate.
virtual void	set_min_var (double min_var)
	Define lower threshold on variance for built models.
virtual double	min_var () const
	Get lower threshold on variance for built models.
virtual void	build_from_array (pdf1d_pdf &model, const double *data, int n) const
	Build from n elements in data[i].
virtual void	build (pdf1d_pdf &model, double mean) const
	Build default model with given mean.
virtual void	build (pdf1d_pdf &model, mbl_data_wrapper< double > &data) const
	Build model from data.
virtual void	weighted_build (pdf1d_pdf &model, mbl_data_wrapper< double > &data, const vcl_vector< double > &wts) const
	Build model from weighted data.
void	build_fixed_width (pdf1d_kernel_pdf &kpdf, const double *data, int n, double width) const
	Build from n elements in data[i]. Fixed kernel width.
void	build_select_equal_width (pdf1d_kernel_pdf &kpdf, const double *data, int n) const
	Build from n elements in data[i]. Chooses width.
void	build_width_from_separation (pdf1d_kernel_pdf &kpdf, const double *data, int n) const
	Kernel width proportional to distance to nearby samples.
void	build_adaptive (pdf1d_kernel_pdf &kpdf, const double *data, int n) const
	Build adaptive kernel estimate.
short	version_no () const
	Version number for I/O.
virtual vcl_string	is_a () const
	Name of the class.
virtual bool	is_class (vcl_string const &s) const
	Does the name of the class match the argument?.
virtual void	print_summary (vcl_ostream &os) const
	Print class to os.
virtual void	b_write (vsl_b_ostream &bfs) const
	Save class to binary file stream.
virtual void	b_read (vsl_b_istream &bfs)
	Load class from binary file stream.
virtual pdf1d_pdf *	new_model () const =0
	Create empty model.
virtual vcl_string	new_model_type () const =0
	Name of the model class returned by new_model().
virtual pdf1d_builder *	clone () const =0
	Create a copy on the heap and return base class pointer.
Private Member Functions
pdf1d_kernel_pdf &	kernel_pdf (pdf1d_pdf &model) const
Private Attributes
double	min_var_
	Minimum variance of whole model.
build_type	build_type_
	Type of building to be performed.
double	fixed_width_
	Width set if fixed_width option on build used.

Detailed Description

Build kernel pdf objects.

Contains algorithms for selecting kernel widths.

Simplest is to use equal widths (set_use_equal_width()).

More interesting is an adaptive kernel estimate (set_use_adaptive()). This tends to get results comparable with the equal width method for simple cases, but can match to more complex distributions more easily. In particular, it tends to approximate the tails more accurately.

See book on Density Estimation by B.W.Silverman (Pub. Chapman and Hall, 1986) for details.

Definition at line 29 of file pdf1d_kernel_pdf_builder.h.

Member Enumeration Documentation

enum pdf1d_kernel_pdf_builder::build_type

Enumerator:

fixed_width
select_equal
width_from_sep
adaptive

Definition at line 32 of file pdf1d_kernel_pdf_builder.h.

Constructor & Destructor Documentation

pdf1d_kernel_pdf_builder::pdf1d_kernel_pdf_builder ( )

Dflt ctor.

Definition at line 21 of file pdf1d_kernel_pdf_builder.cxx.

pdf1d_kernel_pdf_builder::~pdf1d_kernel_pdf_builder ( ) [virtual]

Destructor.

Definition at line 28 of file pdf1d_kernel_pdf_builder.cxx.

Member Function Documentation

void pdf1d_kernel_pdf_builder::b_read ( vsl_b_istream & bfs ) [virtual]

Load class from binary file stream.

Implements pdf1d_builder.

Definition at line 308 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::b_write ( vsl_b_ostream & bfs ) const [virtual]

Save class to binary file stream.

Implements pdf1d_builder.

Definition at line 300 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build	(	pdf1d_pdf &	model,
		double	mean
	)		const `[virtual]`

Build default model with given mean.

Implements pdf1d_builder.

Definition at line 80 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build	(	pdf1d_pdf &	model,
		mbl_data_wrapper< double > &	data
	)		const `[virtual]`

Build model from data.

The kernel centres in the pdf will have same value and order as the training data

Implements pdf1d_builder.

Definition at line 126 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build_adaptive	(	pdf1d_kernel_pdf &	kpdf,
		const double *	data,
		int	n
	)		const

Build adaptive kernel estimate.

Use equal widths to create a pilot estimate, then use the prob at each data point to modify the widths. Uses Silverman's equation 5.8 with alpha = 0.5 as suggested, and based on a pilot estimate as calculated by build_select_equal_width(). The kernel centres in the pdf will have same value and order as the training data.

This method gives a significantly higher density near the edges of the distribution than suggested by the cumulative histogram of the training data, pushing the cdf estimate closer to 0.5 at the edges. If you want to approximate the cumulative histogram more closely, then build_select_equal_width() may be more effective.

Use equal widths to create a pilot estimate, then use the prob at each data point to modify the widths

Definition at line 244 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build_fixed_width	(	pdf1d_kernel_pdf &	kpdf,
		const double *	data,
		int	n,
		double	width
	)		const

Build from n elements in data[i]. Fixed kernel width.

Build from n elements in data[i].

The kernel centres in the pdf will have same value and order as the training data

Definition at line 167 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build_from_array	(	pdf1d_pdf &	model,
		const double *	data,
		int	n
	)		const `[virtual]`

Build from n elements in data[i].

Build kernel_pdf from n elements in data[i].

Reimplemented from pdf1d_builder.

Definition at line 90 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build_select_equal_width	(	pdf1d_kernel_pdf &	kpdf,
		const double *	data,
		int	n
	)		const

Build from n elements in data[i]. Chooses width.

Same width selected for all points, using $w=(3n/4)^{-0.2}\sigma$ , as suggested by Silverman

The kernel centres in the pdf will have same value and order as the training data

Same width selected for all points, using $w=(3n/4)^{-0.2}\sigma$ , as suggested by Silverman

Definition at line 177 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::build_width_from_separation	(	pdf1d_kernel_pdf &	kpdf,
		const double *	data,
		int	n
	)		const

Kernel width proportional to distance to nearby samples.

The kernel centres in the pdf will have same value and order as the training data

Definition at line 220 of file pdf1d_kernel_pdf_builder.cxx.

virtual pdf1d_builder* pdf1d_builder::clone ( ) const [pure virtual, inherited]

Create a copy on the heap and return base class pointer.

Implemented in pdf1d_mixture_builder, pdf1d_exponential_builder, pdf1d_flat_builder, pdf1d_gaussian_builder, pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

vcl_string pdf1d_kernel_pdf_builder::is_a ( ) const [virtual]

Name of the class.

Reimplemented from pdf1d_builder.

Reimplemented in pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

Definition at line 272 of file pdf1d_kernel_pdf_builder.cxx.

bool pdf1d_kernel_pdf_builder::is_class ( vcl_string const & s ) const [virtual]

Does the name of the class match the argument?.

Reimplemented from pdf1d_builder.

Reimplemented in pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

Definition at line 279 of file pdf1d_kernel_pdf_builder.cxx.

pdf1d_kernel_pdf & pdf1d_kernel_pdf_builder::kernel_pdf ( pdf1d_pdf & model ) const [private]

Definition at line 34 of file pdf1d_kernel_pdf_builder.cxx.

double pdf1d_kernel_pdf_builder::min_var ( ) const [virtual]

Get lower threshold on variance for built models.

Implements pdf1d_builder.

Definition at line 75 of file pdf1d_kernel_pdf_builder.cxx.

virtual pdf1d_pdf* pdf1d_builder::new_model ( ) const [pure virtual, inherited]

Create empty model.

Implemented in pdf1d_mixture_builder, pdf1d_exponential_builder, pdf1d_flat_builder, pdf1d_gaussian_builder, pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

virtual vcl_string pdf1d_builder::new_model_type ( ) const [pure virtual, inherited]

Name of the model class returned by new_model().

Implemented in pdf1d_mixture_builder, pdf1d_exponential_builder, pdf1d_flat_builder, pdf1d_gaussian_builder, pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

void pdf1d_kernel_pdf_builder::print_summary ( vcl_ostream & os ) const [virtual]

Print class to os.

Implements pdf1d_builder.

Reimplemented in pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

Definition at line 293 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::set_min_var ( double min_var ) [virtual]

Define lower threshold on variance for built models.

Implements pdf1d_builder.

Definition at line 68 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::set_use_adaptive ( )

Build adaptive kernel estimate.

Definition at line 61 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::set_use_equal_width ( )

Use equal width kernels of width depending on number of samples.

This method appears to give a lower density near the tails

Definition at line 49 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::set_use_fixed_width ( double width )

Use fixed width kernels of given width when building.

Definition at line 42 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::set_use_width_from_separation ( )

Kernel width proportional to distance to nearby samples.

Definition at line 55 of file pdf1d_kernel_pdf_builder.cxx.

short pdf1d_kernel_pdf_builder::version_no ( ) const

Version number for I/O.

Reimplemented from pdf1d_builder.

Reimplemented in pdf1d_epanech_kernel_pdf_builder, and pdf1d_gaussian_kernel_pdf_builder.

Definition at line 286 of file pdf1d_kernel_pdf_builder.cxx.

void pdf1d_kernel_pdf_builder::weighted_build	(	pdf1d_pdf &	model,
		mbl_data_wrapper< double > &	data,
		const vcl_vector< double > &	wts
	)		const `[virtual]`