Interface Class for One Dimensional fitting in a weighted fashion. More...

#include </scratch/bob/jari/tmp/pristine/yat-0.10.x/yat/regression/OneDimensionalWeighted.h>

Inheritance diagram for theplu::yat::regression::OneDimensionalWeighted:

Public Member Functions
	OneDimensionalWeighted (void)
virtual	~OneDimensionalWeighted (void)
virtual void	fit (const utility::VectorBase &x, const utility::VectorBase &y, const utility::VectorBase &w)=0
virtual double	predict (const double x) const =0
double	prediction_error2 (const double x, const double w=1.0) const
double	r2 (void) const
virtual double	s2 (double w=1) const =0
virtual double	standard_error2 (const double x) const =0

Protected Attributes
statistics::AveragerPairWeighted	ap_
double	chisq_
	Chi-squared.

Detailed Description

Interface Class for One Dimensional fitting in a weighted fashion.

Constructor & Destructor Documentation

theplu::yat::regression::OneDimensionalWeighted::OneDimensionalWeighted ( void )

Default Constructor.

virtual theplu::yat::regression::OneDimensionalWeighted::~OneDimensionalWeighted ( void )

virtual

Destructor

Member Function Documentation

virtual void theplu::yat::regression::OneDimensionalWeighted::fit	(	const utility::VectorBase &	x,
		const utility::VectorBase &	y,
		const utility::VectorBase &	w
	)

pure virtual

This function computes the best-fit given a model (see specific class for details) by minimizing $\sum{w_i(\hat{y_i}-y_i)^2}$ , where $\hat{y}$ is the fitted value. The weight $ w_i $ should be proportional to the inverse of the variance for $ y_i $

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

virtual double theplu::yat::regression::OneDimensionalWeighted::predict ( const double x ) const

pure virtual

Returns:: expected value in x according to the fitted model

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::PolynomialWeighted, and theplu::yat::regression::NaiveWeighted.

double theplu::yat::regression::OneDimensionalWeighted::prediction_error2	(	const double	x,
		const double	w = `1.0`
	)		const

  The prediction error is defined as expected squared deviation a
  new data point (with weight @a w) will be from the model
  value \form#211 and is typically
  divided into the conditional variance ( see s2() )
  given \form#62 and the squared standard error ( see
  standard_error2() ) of the model estimation in \form#62.

$E((Y|x - E(Y|x))^2|w) + E((E(Y|x) - \hat{y}(x))^2)$

  @return expected prediction error for a new data point in @a x
  with weight @a w.

double theplu::yat::regression::OneDimensionalWeighted::r2 ( void ) const

r2 is defined as $\frac{\sum w_i(y_i-\hat{y}_i)^2}{\sum w_i(y_i-m_y)^2}$ or the fraction of the variance explained by the regression model.

virtual double theplu::yat::regression::OneDimensionalWeighted::s2 ( double w = 1 ) const

pure virtual

$ s^2 $ is the estimation of variance of residuals or equivalently the conditional variance of Y.

Returns:: Conditional variance of Y

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

virtual double theplu::yat::regression::OneDimensionalWeighted::standard_error2 ( const double x ) const

pure virtual

The standard error is defined as $E((Y|x,w - \hat{y}(x))^2)$

Returns:: error of model value in x

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

Member Data Documentation

statistics::AveragerPairWeighted theplu::yat::regression::OneDimensionalWeighted::ap_

protected

Averager for pair of x and y

double theplu::yat::regression::OneDimensionalWeighted::chisq_

protected

Chi-squared.

Chi-squared is defined as the $\sum{w_i(\hat{y_i}-y_i)^2}$

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

/scratch/bob/jari/tmp/pristine/yat-0.10.x/yat/regression/OneDimensionalWeighted.h

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation