ml::Statistics Namespace Reference

Statistical functions. More...

Functions
template<class Iter >
std::pair< double, double >	sse_and_mean (const Iter begin, const Iter end)
	Calculates the average and sum of squared error for a sample. More...
template<class Iter >
double	sse (const Iter begin, const Iter end)
	Calculates the average and sum of squared error for a sample. More...
template<class Iter >
std::pair< double, unsigned int >	gini_index_and_mode (const Iter begin, const Iter end, const unsigned int K)
	Calculates the Gini index of the sample. More...
template<class Iter >
double	gini_index (const Iter begin, const Iter end, const unsigned int K)
	Calculates the Gini index of the sample. More...
template<class Iter >
unsigned int	mode (const Iter begin, const Iter end, const unsigned int K)
	Calculates the mode (most frequent value) of a sample. More...
template<class R >
R	covariance (const std::vector< R > &xs, const std::vector< R > &ys)
	Calculates sample covariance of two vectors. More...
double	covariance (Eigen::Ref< const Eigen::VectorXd > xs, Eigen::Ref< const Eigen::VectorXd > ys)
	Calculates sample covariance of two vectors. More...

Detailed Description

Statistical functions.

Function Documentation

sse_and_mean()

template<class Iter >

std::pair<double, double> ml::Statistics::sse_and_mean	(	const Iter	begin,
		const Iter	end
	)

Calculates the average and sum of squared error for a sample.

Given a range [begin, end) with N values, calculates

\( \mathrm{SSE} = \sum_{i=1}^{N} (x_i - \bar{x})^2 \)

and

\( \bar{x} = N^{-1} \sum_{i=1}^{N} x_i \).

Parameters

[in]	begin	Iterator pointing to the beginning of the range of sample values.
[in]	end	Iterator pointing one past to the end of the range of sample values.

Template Parameters

Iter	Iterator type.

Returns

( \(\mathrm{SSE}\), \(\bar{x}\)) pair.

sse()

template<class Iter >

double ml::Statistics::sse	(	const Iter	begin,
		const Iter	end
	)

Calculates the average and sum of squared error for a sample.

Given a range [begin, end) with N values, calculates

\( \mathrm{SSE} = \sum_{i=1}^{N} (x_i - \bar{x})^2 \),

where

\( \bar{x} = N^{-1} \sum_{i=1}^{N} x_i \).

Parameters

[in]	begin	Iterator pointing to the beginning of the range of sample values.
[in]	end	Iterator pointing one past to the end of the range of sample values.

Template Parameters

Iter	Iterator type.

Returns

SSE.

gini_index_and_mode()

template<class Iter >

std::pair<double, unsigned int> ml::Statistics::gini_index_and_mode	(	const Iter	begin,
		const Iter	end,
		const unsigned int	K
	)

Calculates the Gini index of the sample.

Gini index is defined as

\( \sum_{k=1}^K \hat{p}_k (1 - \hat{p}_k) \)

where \(\hat{p}_k\) is the frequency of occurrence of class k in data.

Takes as argument a range [begin, end) of class values from 0 to K - 1.

Parameters

[in]	begin	Iterator pointing to the beginning of the range of sample values.
[in]	end	Iterator pointing one past to the end of the range of sample values.
[in]	K	Number of classes, positive.

Template Parameters

Iter	Iterator type.

Returns

Gini index and the most frequent class. If begin == end, mode == K.

gini_index()

template<class Iter >

double ml::Statistics::gini_index	(	const Iter	begin,
		const Iter	end,
		const unsigned int	K
	)

Calculates the Gini index of the sample.

Gini index is defined as

\( \sum_{k=1}^K \hat{p}_k (1 - \hat{p}_k) \)

where \(\hat{p}_k\) is the frequency of occurrence of class k in data.

Takes as argument a range [begin, end) of class values from 0 to K - 1.

Parameters

[in]	begin	Iterator pointing to the beginning of the range of sample values.
[in]	end	Iterator pointing one past to the end of the range of sample values.
[in]	K	Number of classes, positive.

Template Parameters

Iter	Iterator type.

Returns

Gini index.

mode()

template<class Iter >

unsigned int ml::Statistics::mode	(	const Iter	begin,
		const Iter	end,
		const unsigned int	K
	)

Calculates the mode (most frequent value) of a sample.

The sample is assumed to contain values in the [0, K - 1] range.

Parameters

[in]	begin	Iterator pointing to the beginning of the range of sample values.
[in]	end	Iterator pointing one past to the end of the range of sample values.
[in]	K	Positive number of distinct values.

Template Parameters

Iter	Iterator type.

Returns

Mode of the sample.

covariance() [1/2]

template<class R >

R ml::Statistics::covariance	(	const std::vector< R > &	xs,
		const std::vector< R > &	ys
	)

Calculates sample covariance of two vectors.

Parameters

[in]	xs	X values.
[in]	ys	Y values.

Template Parameters

R	Scalar value type.

Returns

Sample covariance (unbiased estimate of population covariance) or NaN if xs.size() < 2.

Exceptions

std::invalid_argument

If xs.size() != ys.size().

covariance() [2/2]

double ml::Statistics::covariance	(	Eigen::Ref< const Eigen::VectorXd >	xs,
		Eigen::Ref< const Eigen::VectorXd >	ys
	)

Calculates sample covariance of two vectors.

Parameters

xs	X values.
ys	Y values.

Returns

Sample covariance (unbiased estimate of population covariance) or NaN if xs.size() < 2.

Exceptions

std::invalid_argument

If xs.size() != ys.size().