theplu::yat::regression::LinearWeighted Class Reference

#include <yat/regression/LinearWeighted.h>

Inheritance diagram for theplu::yat::regression::LinearWeighted:

List of all members.

Public Member Functions

LinearWeighted (void)

The default constructor.

virtual ~LinearWeighted (void)

The destructor.

double alpha (void) const

double alpha_var (void) const

double beta (void) const

double beta_var (void) const

void fit (const utility::VectorBase &x, const utility::VectorBase &y, const utility::VectorBase &w)

double predict (const double x) const

double s2 (double w=1) const

double standard_error2 (const double x) const

double prediction_error2 (const double x, const double w=1.0) const

double r2 (void) const

Protected Attributes

statistics::AveragerPairWeighted ap_

double chisq_

Chi-squared.

Detailed Description

linear regression.

Member Function Documentation

double theplu::yat::regression::LinearWeighted::alpha ( void ) const

$ alpha $ is estimated as $\frac{\sum w_iy_i}{\sum w_i}$

Returns:: the parameter $\alpha$

double theplu::yat::regression::LinearWeighted::alpha_var ( void ) const

Variance is estimated as $\frac{s^2}{\sum w_i}$

See also:: s2()

Returns:: variance of parameter $\alpha$

double theplu::yat::regression::LinearWeighted::beta ( void ) const

$ beta $ is estimated as $\frac{\sum w_i(y_i-m_y)(x_i-m_x)}{\sum w_i(x_i-m_x)^2}$

Returns:: the parameter $\beta$

double theplu::yat::regression::LinearWeighted::beta_var ( void ) const

Variance is estimated as $\frac{s^2}{\sum w_i(x_i-m_x)^2}$

See also:: s2()

Returns:: variance of parameter $\beta$

void theplu::yat::regression::LinearWeighted::fit	(	const utility::VectorBase &	x,
		const utility::VectorBase &	y,
		const utility::VectorBase &	w
	)			`[virtual]`

This function computes the best-fit linear regression coefficients $(\alpha, \beta)$ of the model $y = \alpha + \beta (x-m_x)$ from vectors x and y, by minimizing $\sum{w_i(y_i - \alpha - \beta (x-m_x))^2}$ , where $ m_x $ is the weighted average. By construction $\alpha$ and $\beta$ are independent.

Implements theplu::yat::regression::OneDimensionalWeighted.

double theplu::yat::regression::LinearWeighted::predict ( const double x ) const [virtual]

Function predicting value using the linear model: $y =\alpha + \beta (x - m)$

Implements theplu::yat::regression::OneDimensionalWeighted.

double theplu::yat::regression::LinearWeighted::s2 ( double w = 1 ) const [virtual]

Noise level for points with weight w.

Implements theplu::yat::regression::OneDimensionalWeighted.

double theplu::yat::regression::LinearWeighted::standard_error2 ( const double x ) const [virtual]

estimated error $y_{err} = \sqrt{ Var(\alpha) + Var(\beta)*(x-m)}$ .

Implements theplu::yat::regression::OneDimensionalWeighted.

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

The prediction error is defined as expected squared deviation a new data point (with weight w) will be from the model value $E((Y|x - \hat{y}(x))^2|w)$ and is typically divided into the conditional variance ( see s2() ) given $ x $ and the squared standard error ( see standard_error2() ) of the model estimation in $ x $ .

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

Returns:: expected prediction error for a new data point in x with weight w.

double theplu::yat::regression::OneDimensionalWeighted::r2 ( void ) const [inherited]

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.

Member Data Documentation

statistics::AveragerPairWeighted theplu::yat::regression::OneDimensionalWeighted::ap_ [protected, inherited]

Averager for pair of x and y

double theplu::yat::regression::OneDimensionalWeighted::chisq_ [protected, inherited]

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:

yat/regression/LinearWeighted.h


Public Member Functions
	LinearWeighted (void)
	The default constructor.
virtual	~LinearWeighted (void)
	The destructor.
double	alpha (void) const
double	alpha_var (void) const
double	beta (void) const
double	beta_var (void) const
void	fit (const utility::VectorBase &x, const utility::VectorBase &y, const utility::VectorBase &w)
double	predict (const double x) const
double	s2 (double w=1) const
double	standard_error2 (const double x) const
double	prediction_error2 (const double x, const double w=1.0) const
double	r2 (void) const
Protected Attributes
statistics::AveragerPairWeighted	ap_
double	chisq_
	Chi-squared.