Polynomial Regression in weighted fashion. More...

#include <yat/regression/PolynomialWeighted.h>

Inheritance diagram for theplu::yat::regression::PolynomialWeighted:

Public Member Functions
	PolynomialWeighted (size_t power)

	~PolynomialWeighted (void)
	Destructor.

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

const utility::Vector &	fit_parameters (void) const

double	s2 (const double w=1) const
	Mean Squared Error.

double	predict (const double x) 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. More...

Detailed Description

Polynomial Regression in weighted fashion.

Constructor & Destructor Documentation

theplu::yat::regression::PolynomialWeighted::PolynomialWeighted ( size_t power )

Parameters

power degree of polynomial model

Member Function Documentation

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

virtual

This function computes the best-fit given the polynomial model model 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 $

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

const utility::Vector& theplu::yat::regression::PolynomialWeighted::fit_parameters ( void ) const

Returns: parameters of the model

See Also: MultiDimensional

double theplu::yat::regression::PolynomialWeighted::predict ( const double x ) const

virtual

function predicting in one point.

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 $ .