ml::Crossvalidation Namespace Reference

Methods used for cross-validation. More...

Functions
void	calc_fold_indices (size_t total_len, unsigned int k, unsigned int num_folds, size_t &i0, size_t &i1)
	Calculates indices delimiting a fold. More...
Eigen::Ref< const Eigen::MatrixXd >	only_kth_fold_2d (Eigen::Ref< const Eigen::MatrixXd > data, unsigned int k, unsigned int num_folds)
	Returns k-th fold contents for vector data. More...
Eigen::Ref< const Eigen::VectorXd >	only_kth_fold_1d (Eigen::Ref< const Eigen::VectorXd > data, unsigned int k, unsigned int num_folds)
	Returns k-th fold contents for scalar data. More...
template<class T >
std::vector< T >	only_kth_fold_1d (const std::vector< T > &data, const unsigned int k, const unsigned int num_folds)
	Returns k-th fold contents for scalar data. More...
Eigen::MatrixXd	without_kth_fold_2d (Eigen::Ref< const Eigen::MatrixXd > data, unsigned int k, unsigned int num_folds)
	Returns the contents of all except the k-th fold for vector data. More...
Eigen::VectorXd	without_kth_fold_1d (Eigen::Ref< const Eigen::VectorXd > data, unsigned int k, unsigned int num_folds)
	Returns the contents of all except the k-th fold for scalar data. More...
template<class T >
std::vector< T >	without_kth_fold_1d (const std::vector< T > &data, unsigned int k, unsigned int num_folds)
	Returns the contents of all except the k-th fold for scalar data. More...
template<class Trainer , class Tester >
double	k_fold (Eigen::Ref< const Eigen::MatrixXd > X, Eigen::Ref< const Eigen::VectorXd > y, Trainer train_func, Tester test_func, const unsigned int num_folds)
	Calculates model test error using k-fold cross-validation. More...
template<class Trainer , class Tester >
double	k_fold_scalar (Eigen::Ref< const Eigen::VectorXd > x, Eigen::Ref< const Eigen::VectorXd > y, Trainer train_func, Tester test_func, const unsigned int num_folds)
	Calculates model test error using k-fold cross-validation (scalar X version). More...
template<class Trainer , class Tester >
double	leave_one_out (Eigen::Ref< const Eigen::MatrixXd > X, Eigen::Ref< const Eigen::VectorXd > y, Trainer train_func, Tester test_func)
	Calculates model test error using leave-one-out cross-validation. More...
template<class Trainer , class Tester >
double	leave_one_out_scalar (const Eigen::Ref< const Eigen::VectorXd > x, Eigen::Ref< const Eigen::VectorXd > y, Trainer train_func, Tester test_func)
	Calculates model test error using leave-one-out cross-validation (scalar X version). More...

Detailed Description

Methods used for cross-validation.

Function Documentation

calc_fold_indices()

void ml::Crossvalidation::calc_fold_indices	(	size_t	total_len,
		unsigned int	k,
		unsigned int	num_folds,
		size_t &	i0,
		size_t &	i1
	)

Calculates indices delimiting a fold.

Calculates i0 and i1 such that the k-th fold consists of data points with indices in the [i0, i1) range.

Parameters

[in]	total_len	Total number of data points.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= total_len.
[out]	i0	Lower fold bound (inclusive).
[out]	i1	Upper fold bound (exclusive).

Exceptions

std::invalid_argument

If num_folds > total_len or k >= num_folds.

only_kth_fold_2d()

Eigen::Ref<const Eigen::MatrixXd> ml::Crossvalidation::only_kth_fold_2d	(	Eigen::Ref< const Eigen::MatrixXd >	data,
		unsigned int	k,
		unsigned int	num_folds
	)

Returns k-th fold contents for vector data.

Parameters

[in]	data	Data matrix with data points in columns.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.cols().

Returns

Reference to data from the k-th fold.

Exceptions

std::invalid_argument

If num_folds > data.cols() or k >= num_folds.

only_kth_fold_1d() [1/2]

Eigen::Ref<const Eigen::VectorXd> ml::Crossvalidation::only_kth_fold_1d	(	Eigen::Ref< const Eigen::VectorXd >	data,
		unsigned int	k,
		unsigned int	num_folds
	)

Returns k-th fold contents for scalar data.

Parameters

[in]	data	Data vector.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.size().

Returns

Reference to data from the k-th fold.

Exceptions

std::invalid_argument

If num_folds > data.size() or k >= num_folds.

only_kth_fold_1d() [2/2]

template<class T >

std::vector<T> ml::Crossvalidation::only_kth_fold_1d	(	const std::vector< T > &	data,
		const unsigned int	k,
		const unsigned int	num_folds
	)

Returns k-th fold contents for scalar data.

Parameters

[in]	data	Data vector.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.size().

Template Parameters

T	Scalar data type.

Returns

Data from the k-th fold.

Exceptions

std::invalid_argument

If num_folds > data.size() or k >= num_folds.

without_kth_fold_2d()

Eigen::MatrixXd ml::Crossvalidation::without_kth_fold_2d	(	Eigen::Ref< const Eigen::MatrixXd >	data,
		unsigned int	k,
		unsigned int	num_folds
	)

Returns the contents of all except the k-th fold for vector data.

Parameters

[in]	data	Data matrix with data points in columns.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.size().

Returns

Data from all folds except the k-th one.

Exceptions

std::invalid_argument

If num_folds > data.cols() or k >= num_folds.

without_kth_fold_1d() [1/2]

Eigen::VectorXd ml::Crossvalidation::without_kth_fold_1d	(	Eigen::Ref< const Eigen::VectorXd >	data,
		unsigned int	k,
		unsigned int	num_folds
	)

Returns the contents of all except the k-th fold for scalar data.

Parameters

[in]	data	Data vector.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.size().

Returns

Data from all folds except the k-th one.

Exceptions

std::invalid_argument

If num_folds > data.size() or k >= num_folds.

without_kth_fold_1d() [2/2]

template<class T >

std::vector<T> ml::Crossvalidation::without_kth_fold_1d	(	const std::vector< T > &	data,
		unsigned int	k,
		unsigned int	num_folds
	)

Returns the contents of all except the k-th fold for scalar data.

Parameters

[in]	data	Data vector.
[in]	k	Fold index with 0 <= k < num_folds.
[in]	num_folds	Total number of folds with num_folds <= data.size().

Template Parameters

T	Scalar data type.

Returns

Data from all folds except the k-th one.

Exceptions

std::invalid_argument

If num_folds > data.size() or k >= num_folds.

k_fold()

template<class Trainer , class Tester >

double ml::Crossvalidation::k_fold	(	Eigen::Ref< const Eigen::MatrixXd >	X,
		Eigen::Ref< const Eigen::VectorXd >	y,
		Trainer	train_func,
		Tester	test_func,
		const unsigned int	num_folds
	)

Calculates model test error using k-fold cross-validation.

See https://en.wikipedia.org/wiki/Cross-validation_(statistics)#k-fold_cross-validation

train_func and test_func functors should accept X data as Eigen::Ref<const Eigen::MatrixXd> reference, and y data as Eigen::Ref<const Eigen::VectorXd>.

Parameters

[in]	X	Matrix with all features (data points in columns).
[in]	y	Vector with all responses (scalars).
[in]	train_func	Functor returning a trained model given training features and responses as arguments.
[in]	test_func	Functor calculating test error per data point given the model, test features and test responses as arguments.
[in]	num_folds	Number of folds.

Template Parameters

Trainer	Functor type for model training.
Tester	Functor type for calculating test error.

Returns

Error value per data point.

Exceptions

std::invalid_argument

If num_folds > X.cols() or y.size() != X.cols().

k_fold_scalar()

template<class Trainer , class Tester >

double ml::Crossvalidation::k_fold_scalar	(	Eigen::Ref< const Eigen::VectorXd >	x,
		Eigen::Ref< const Eigen::VectorXd >	y,
		Trainer	train_func,
		Tester	test_func,
		const unsigned int	num_folds
	)

Calculates model test error using k-fold cross-validation (scalar X version).

See https://en.wikipedia.org/wiki/Cross-validation_(statistics)#k-fold_cross-validation

train_func and test_func functors should accept X and y data as Eigen::Ref<const Eigen::VectorXd> references.

Parameters

[in]	x	Vector with all features (scalars).
[in]	y	Vector with all responses (scalars).
[in]	train_func	Functor returning a trained model given training features and responses as arguments.
[in]	test_func	Functor calculating test error per data point given the model, test features and test responses as arguments.
[in]	num_folds	Number of folds.

Template Parameters

Trainer	Functor type for model training.
Tester	Functor type for calculating test error.

Returns

Error value per data point.

Exceptions

std::invalid_argument

If num_folds > X.cols() or y.size() != y.size().

leave_one_out()

template<class Trainer , class Tester >

double ml::Crossvalidation::leave_one_out	(	Eigen::Ref< const Eigen::MatrixXd >	X,
		Eigen::Ref< const Eigen::VectorXd >	y,
		Trainer	train_func,
		Tester	test_func
	)

Calculates model test error using leave-one-out cross-validation.

See https://en.wikipedia.org/wiki/Cross-validation_(statistics)#Leave-one-out_cross-validation

train_func and test_func functors should accept X data as Eigen::Ref<const Eigen::MatrixXd> reference, and y data as Eigen::Ref<const Eigen::VectorXd>.

Parameters

[in]	X	Matrix with all features (data points in columns).
[in]	y	Vector with all responses (scalars).
[in]	train_func	Functor returning a trained model given training features and responses as arguments.
[in]	test_func	Functor calculating test error per data point given the model, test features and test responses as arguments.

Template Parameters

Trainer	Functor type for model training.
Tester	Functor type for calculating test error.

Returns

Error value per data point.

Exceptions

std::invalid_argument

If y.size() < 2 or y.size() != X.cols().

leave_one_out_scalar()

template<class Trainer , class Tester >

double ml::Crossvalidation::leave_one_out_scalar	(	const Eigen::Ref< const Eigen::VectorXd >	x,
		Eigen::Ref< const Eigen::VectorXd >	y,
		Trainer	train_func,
		Tester	test_func
	)

Calculates model test error using leave-one-out cross-validation (scalar X version).

See https://en.wikipedia.org/wiki/Cross-validation_(statistics)#Leave-one-out_cross-validation

train_func and test_func functors should accept X and y data as Eigen::Ref<const Eigen::VectorXd> references.

Parameters

[in]	x	Vector with all features (scalars).
[in]	y	Vector with all responses (scalars).
[in]	train_func	Functor returning a trained model given training features and responses as arguments.
[in]	test_func	Functor calculating test error per data point given the model, test features and test responses as arguments.

Template Parameters

Trainer	Functor type for model training.
Tester	Functor type for calculating test error.

Returns

Error value per data point.

Exceptions

std::invalid_argument

If y.size() < 2 or y.size() != x.size().