The SLOPE model. More...

#include <slope.h>

Public Member Functions
	Slope ()=default

void	setSolver (const std::string &solver)
	Sets the numerical solver used to fit the model.

void	setIntercept (bool intercept)
	Sets the intercept flag.

void	setNormalization (const std::string &type)
	Sets normalization type for the design matrix.

void	setUpdateClusters (bool update_clusters)
	Sets the update clusters flag.

void	setReturnClusters (const bool return_clusters)
	Sets the return clusters flag.

void	setAlphaMinRatio (double alpha_min_ratio)
	Sets the alpha min ratio.

void	setAlphaType (const std::string &alpha_type)
	Sets the alpha type.

void	setLearningRateDecr (double learning_rate_decr)
	Sets the learning rate decrement.

void	setQ (double q)
	Sets the q value.

void	setOscarParameters (const double theta1, const double theta2)
	Sets OSCAR parameters.

void	setTol (double tol)
	Sets the tolerance value.

void	setRelaxTol (double tol)
	Sets the tolerance value for the relaxed SLOPE solver.

void	setRelaxMaxOuterIterations (int max_it)
	Sets the maximum number of outer (IRLS) iterations for the relaxed solver.

void	setRelaxMaxInnerIterations (int max_it)
	Sets the maximum number of inner iterations for the relaxed solver.

void	setMaxIterations (int max_it)
	Sets the maximum number of iterations.

void	setPathLength (int path_length)
	Sets the path length.

void	setHybridCdIterations (int cd_iterations)
	Sets the frequence of proximal gradient descent steps.

void	setHybridCdType (const std::string &cd_type)
	Sets the frequence of proximal gradient descent steps.

void	setLambdaType (const std::string &lambda_type)
	Sets the lambda type for regularization weights.

void	setLoss (const std::string &loss_type)
	Sets the loss function type.

void	setScreening (const std::string &screening_type)
	Sets the type of feature screening used, which discards predictors that are unlikely to be active.

void	setModifyX (const bool modify_x)
	Controls if `x` should be modified-in-place.

void	setDevChangeTol (const double dev_change_tol)
	Sets tolerance in deviance change for early stopping.

void	setDevRatioTol (const double dev_ratio_tol)
	Sets tolerance in deviance change for early stopping.

void	setMaxClusters (const int max_clusters)
	Sets the maximum number of clusters.

void	setCentering (const std::string &type)
	Sets the center points for feature normalization.

void	setCentering (const Eigen::VectorXd &x_centers)
	Sets the center points for feature normalization.

void	setScaling (const std::string &type)
	Sets the scaling type.

void	setDiagnostics (const bool collect_diagnostics)
	Toggles collection of diagnostics.

void	setScaling (const Eigen::VectorXd &x_scales)
	Sets the scaling factors for feature normalization.

void	setAlphaEstimationMaxIterations (const int alpha_est_maxit)
	Sets the maximum number of iterations for the alpha estimation procedure.

void	setRandomSeed (const int seed)
	Sets the random seed.

void	setRandomSeed (std::optional< int > seed)
	Sets the random seed.

bool	hasRandomSeed () const
	Checks if a random seed is set.

int	getRandomSeed () const
	Gets the random seed.

int	getAlphaEstimationMaxIterations () const
	Gets the maximum number of iterations allowed for the alpha estimation procedure.

bool	getFitIntercept () const
	Returns the intercept flag.

const std::string &	getLossType ()
	Get currently defined loss type.

template<typename T >
SlopePath	path (Eigen::EigenBase< T > &x, const Eigen::MatrixXd &y_in, Eigen::ArrayXd alpha=Eigen::ArrayXd::Zero(0), Eigen::ArrayXd lambda=Eigen::ArrayXd::Zero(0))
	Computes SLOPE regression solution path for multiple alpha and lambda values.

template<typename T >
SlopeFit	fit (Eigen::EigenBase< T > &x, const Eigen::MatrixXd &y_in, const double alpha=1.0, Eigen::ArrayXd lambda=Eigen::ArrayXd::Zero(0))
	Fits a single SLOPE regression model for given alpha and lambda values.

template<typename T >
SlopePath	estimateAlpha (Eigen::EigenBase< T > &x, Eigen::MatrixXd &y)
	Estimates the regularization parameter alpha for SLOPE regression.

template<typename T >
SlopeFit	relax (const SlopeFit &fit, T &x, const Eigen::VectorXd &y_in, const double gamma=0.0, Eigen::VectorXd beta0=Eigen::VectorXd(0), Eigen::VectorXd beta=Eigen::VectorXd(0))
	Relaxes a fitted SLOPE model.

template<typename T >
SlopePath	relax (const SlopePath &path, T &x, const Eigen::VectorXd &y, const double gamma=0.0)
	Relaxes a fitted SLOPE path.

Detailed Description

The SLOPE model.

This class implements the SLOPE algorithm for regularized regression problems. It supports different loss functions (quadratic, logistic, poisson) and provides functionality for fitting models with sorted L1 regularization along a path of regularization parameters.

Definition at line 45 of file slope.h.

Constructor & Destructor Documentation

◆ Slope()

slope::Slope::Slope ( )

default

Default constructor for the Slope class.

Initializes the Slope object with default parameter values.

Member Function Documentation

◆ estimateAlpha()

template<typename T >

SlopePath slope::Slope::estimateAlpha	(	Eigen::EigenBase< T > &	x,
		Eigen::MatrixXd &	y
	)

inline

Estimates the regularization parameter alpha for SLOPE regression.

This function implements an algorithm to estimate an appropriate regularization parameter (alpha) for SLOPE, which is a generalization of the lasso. When n >= p + 30, it directly estimates alpha from OLS residuals. Otherwise, it uses an iterative procedure that alternates between estimating alpha and fitting the SLOPE model.

The iterative procedure works by:

Starting with an empty set of selected variables
Estimating alpha based on the selected variables
Fitting a SLOPE model with that alpha
Updating the selected variables based on non-zero coefficients
Repeating until convergence or maximum iterations reached

Template Parameters

MatrixType The type of matrix used to store the design matrix

Parameters

x	Design matrix with n observations and p predictors
y	Response matrix

Returns: A SlopePath object containing the fitted model with estimated alpha

Exceptions

std::runtime_error If maximum iterations reached or if too many variables selected

Definition at line 734 of file slope.h.

◆ fit()

template<typename T >

SlopeFit slope::Slope::fit	(	Eigen::EigenBase< T > &	x,
		const Eigen::MatrixXd &	y_in,
		const double	alpha = `1.0`,
		Eigen::ArrayXd	lambda = `Eigen::ArrayXd::Zero(0)`
	)

inline

Fits a single SLOPE regression model for given alpha and lambda values.

Template Parameters

T	Matrix type for feature input (supports dense or sparse matrices)

Parameters

x	Feature matrix of size n x p
y_in	Response matrix of size n x m
alpha	Mixing parameter for elastic net regularization
lambda	Vector of regularization parameters (if empty, computed automatically)

Returns: SlopeFit Object containing fitted model and optimization metrics

Fits a single SLOPE model with specified regularization parameters, returning coefficients and optimization details in a SlopeFit object.

Definition at line 698 of file slope.h.

◆ getLossType()

const std::string & slope::Slope::getLossType ( )

Get currently defined loss type.

Returns: The loss type as a string

◆ path()

template<typename T >

SlopePath slope::Slope::path	(	Eigen::EigenBase< T > &	x,
		const Eigen::MatrixXd &	y_in,
		Eigen::ArrayXd	alpha = `Eigen::ArrayXd::Zero(0)`,
		Eigen::ArrayXd	lambda = `Eigen::ArrayXd::Zero(0)`
	)

inline

Computes SLOPE regression solution path for multiple alpha and lambda values.

Template Parameters

T	Matrix type for feature input (supports dense or sparse matrices)

Parameters

x	Feature matrix of size n x p
y_in	Response matrix of size n x m
alpha	Sequence of mixing parameters for elastic net regularization
lambda	Sequence of regularization parameters (if empty, computed automatically)

Returns: SlopePath object containing full solution path and optimization metrics

Fits SLOPE models for each combination of alpha and lambda values, storing all solutions and optimization metrics in a SlopePath object.

Definition at line 376 of file slope.h.

◆ relax() [1/2]

template<typename T >

SlopeFit slope::Slope::relax	(	const SlopeFit &	fit,
		T &	x,
		const Eigen::VectorXd &	y_in,
		const double	gamma = `0.0`,
		Eigen::VectorXd	beta0 = `Eigen::VectorXd(0)`,
		Eigen::VectorXd	beta = `Eigen::VectorXd(0)`
	)

inline

Relaxes a fitted SLOPE model.

Template Parameters

T	Matrix type for feature input (supports dense or sparse matrices)

Parameters

fit	Previously fitted SLOPE model containing coefficient estimates
x	Feature matrix of size n x p
y_in	Response vector of size n
gamma	Relaxation parameter, proportion of SLOPE-penalized fit. Must be between 0 and 1. Default is 0.0 which means fully relaxed.
beta0	Warm start intercept values (optional)
beta	Warm start coefficient values (optional)

Returns: SlopeFit Object containing the relaxed model with unpenalized coefficients

Definition at line 804 of file slope.h.

◆ relax() [2/2]

template<typename T >

SlopePath slope::Slope::relax	(	const SlopePath &	path,
		T &	x,
		const Eigen::VectorXd &	y,
		const double	gamma = `0.0`
	)

inline

Relaxes a fitted SLOPE path.

Template Parameters

T	Matrix type for feature input (supports dense or sparse matrices)

Parameters

path	Previously fitted SLOPE path
x	Feature matrix of size n x p
y	Response vector of size n
gamma	Relaxation parameter, proportion of SLOPE-penalized fit. Must be between 0 and 1. Default is 0.0 which means fully relaxed.

Returns: SlopePath Object containing the relaxed model with unpenalized coefficients

Definition at line 974 of file slope.h.

◆ setAlphaEstimationMaxIterations()

void slope::Slope::setAlphaEstimationMaxIterations ( const int alpha_est_maxit )

Sets the maximum number of iterations for the alpha estimation procedure.

The current stopping criterion for this solver is that the sets of selected features between two consecutive iterations is identical, but users have experienced instances where these sets will cycle back on forth between two sets, which would make the algorithm fail to converge.

Parameters

alpha_est_maxit The maximum number of allowed iterations

◆ setAlphaMinRatio()

void slope::Slope::setAlphaMinRatio ( double alpha_min_ratio )

Sets the alpha min ratio.

Parameters

alpha_min_ratio The value to set for the alpha min ratio. A negative value means that the program automatically chooses 1e-4 if the number of observations is larger than the number of features and 1e-2 otherwise.

◆ setAlphaType()

void slope::Slope::setAlphaType ( const std::string & alpha_type )

Sets the alpha type.

If "path", values of "alpha" are automatically selected to span a range from completele penalization to the almost-unpenalized case: the SLOPE path. If "estimate", which is only available for the quadratic loss, the alpha value is estimated by using the scaled L2 norm of the residuals vector from an OLS fit. In case the number of features exceeds the number of observations plus 30, then this is done iteratively starting at the null (or intercept-only) models, and proceeding by refitting slope with these estimations until the set of selected features no longer changes.

Parameters

alpha_type The type of alpha, one of "path" and "estimate".

◆ setCentering() [1/2]

void slope::Slope::setCentering ( const Eigen::VectorXd & x_centers )

Sets the center points for feature normalization.

Parameters

x_centers Vector containing center values for each feature Used in feature normalization: x_normalized = (x - center) / scale

◆ setCentering() [2/2]

void slope::Slope::setCentering ( const std::string & type )

Sets the center points for feature normalization.

Parameters

type	Type of centering, one of: "mean", "none"

◆ setDevChangeTol()

void slope::Slope::setDevChangeTol ( const double dev_change_tol )

Sets tolerance in deviance change for early stopping.

Parameters

dev_change_tol The tolerance for the change in deviance.

◆ setDevRatioTol()

void slope::Slope::setDevRatioTol ( const double dev_ratio_tol )

Sets tolerance in deviance change for early stopping.

Parameters

dev_ratio_tol The tolerance for the dev ratio. If the deviance exceeds this value, the path will terminate.

◆ setDiagnostics()

void slope::Slope::setDiagnostics ( const bool collect_diagnostics )

Toggles collection of diagnostics.

Parameters

collect_diagnostics Whether to collect diagnostics, i.e. dual gap, objective value, etc. These will be stored in the SlopeFit and SlopePath objects.

◆ setHybridCdIterations()

void slope::Slope::setHybridCdIterations ( int cd_iterations )

Sets the frequence of proximal gradient descent steps.

Parameters

cd_iterations Number of inner coordinate descent iterations to perform in each iteration of the hybrid solver. If set to 0, the solver will resolve into pure PGD.

◆ setHybridCdType()

void slope::Slope::setHybridCdType ( const std::string & cd_type )

Sets the frequence of proximal gradient descent steps.

Parameters

cd_type The type of coordinate descent to use in the hybrid solver.

◆ setIntercept()

void slope::Slope::setIntercept ( bool intercept )

Sets the intercept flag.

Parameters

intercept Should an intercept be fitted?

◆ setLambdaType()

void slope::Slope::setLambdaType ( const std::string & lambda_type )

Sets the lambda type for regularization weights.

Parameters

lambda_type The method used to compute regularization weights. Currently "bh" (Benjamini-Hochberg), "quadratic", "oscar", and "lasso" are supported.

◆ setLearningRateDecr()

void slope::Slope::setLearningRateDecr ( double learning_rate_decr )

Sets the learning rate decrement.

Parameters

learning_rate_decr The value to set for the learning rate decrement for the proximal gradient descent step.

◆ setLoss()

void slope::Slope::setLoss ( const std::string & loss_type )

Sets the loss function type.

Parameters

loss_type

The type of loss function to use. Supported values are:

"quadratic": Quadratic regression
"logistic": Logistic regression
"poisson": Poisson regression
"multinomial": Multinomial logistic regression

◆ setMaxClusters()

void slope::Slope::setMaxClusters ( const int max_clusters )

Sets the maximum number of clusters.

Parameters

max_clusters The maximum number of clusters. SLOPE can (theoretically) select at most min(n, p) clusters (unique non-zero betas). By default, this is set to -1, which means that the number of clusters will be automatically set to the number of observations + 1.

◆ setMaxIterations()

void slope::Slope::setMaxIterations ( int max_it )

Sets the maximum number of iterations.

Parameters

max_it The value to set for the maximum number of iterations. Must be positive. If negative (the default), then the value will be decided by the solver.

◆ setModifyX()

void slope::Slope::setModifyX ( const bool modify_x )

Controls if x should be modified-in-place.

If true, then x will be modified in place if it is normalized. In case when x is dense, it will be both centered and scaled. If x is sparse, it will be only scaled.

Parameters

modify_x Whether to modfiy x in place or not

◆ setNormalization()

void slope::Slope::setNormalization ( const std::string & type )

Sets normalization type for the design matrix.

Parameters

type	Type of normalization: one of "standardization" or "none".

See also: setCentering() For setting centers, specifically; setScaling() For setting scales, specifically

◆ setOscarParameters()

void slope::Slope::setOscarParameters	(	const double	theta1,
		const double	theta2
	)

Sets OSCAR parameters.

Parameters

theta1	Parameter for OSCAR.
theta2	Parameter for OSCAR.

◆ setPathLength()

void slope::Slope::setPathLength ( int path_length )

Sets the path length.

Parameters

path_length The value to set for the path length.

◆ setQ()

void slope::Slope::setQ ( double q )

Sets the q value.

Parameters

q	The value to set for the q value for use in automatically generating the lambda sequence. values between 0 and 1 are allowed..

◆ setRandomSeed() [1/2]

void slope::Slope::setRandomSeed ( const int seed )

Sets the random seed.

Parameters

seed	The value to set for the path length.

◆ setRandomSeed() [2/2]

void slope::Slope::setRandomSeed ( std::optional< int > seed )

Sets the random seed.

Parameters

seed	The value to set for the path length.

◆ setRelaxMaxInnerIterations()

void slope::Slope::setRelaxMaxInnerIterations ( int max_it )

Sets the maximum number of inner iterations for the relaxed solver.

Parameters

max_it The value to set for the maximum number of iterations. Must be positive.

◆ setRelaxMaxOuterIterations()

void slope::Slope::setRelaxMaxOuterIterations ( int max_it )

Sets the maximum number of outer (IRLS) iterations for the relaxed solver.

Parameters

max_it The value to set for the maximum number of iterations. Must be positive.

◆ setRelaxTol()

void slope::Slope::setRelaxTol ( double tol )

Sets the tolerance value for the relaxed SLOPE solver.

Parameters

tol	The value to set for the tolerance value. Must be positive.

◆ setReturnClusters()

void slope::Slope::setReturnClusters ( const bool return_clusters )

Sets the return clusters flag.

Parameters

return_clusters Selects whether the fitted model should return cluster information.

◆ setScaling() [1/2]

void slope::Slope::setScaling ( const Eigen::VectorXd & x_scales )

Sets the scaling factors for feature normalization.

Parameters

x_scales Vector containing scale values for each feature Used in feature normalization: x_normalized = (x - center) / scale

◆ setScaling() [2/2]

void slope::Slope::setScaling ( const std::string & type )

Sets the scaling type.

Parameters

type	Type of scaling, one of: "sd", "l1", "none"

◆ setScreening()

void slope::Slope::setScreening ( const std::string & screening_type )

Sets the type of feature screening used, which discards predictors that are unlikely to be active.

Parameters

screening_type

Type of screening. Supported values are: are:

"strong": Strong screening rule ()
"none": No screening

◆ setSolver()

void slope::Slope::setSolver ( const std::string & solver )

Sets the numerical solver used to fit the model.

Parameters

solver One of "auto", "pgd", "fista", or "hybrid". In the first case (the default), the solver is automatically selected based on availability of the hybrid solver, which currently means that the hybrid solver is used everywhere except for the multinomial loss.

◆ setTol()

void slope::Slope::setTol ( double tol )

Sets the tolerance value.

Parameters

tol	The value to set for the tolerance value. Must be positive.

◆ setUpdateClusters()

void slope::Slope::setUpdateClusters ( bool update_clusters )

Sets the update clusters flag.

Parameters

update_clusters Selects whether the coordinate descent keeps the clusters updated.

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

include/slope/slope.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Slope()

Member Function Documentation

◆ estimateAlpha()

◆ fit()

◆ getLossType()

◆ path()

◆ relax() [1/2]

◆ relax() [2/2]

◆ setAlphaEstimationMaxIterations()

◆ setAlphaMinRatio()

◆ setAlphaType()

◆ setCentering() [1/2]

◆ setCentering() [2/2]

◆ setDevChangeTol()

◆ setDevRatioTol()

◆ setDiagnostics()

◆ setHybridCdIterations()

◆ setHybridCdType()

◆ setIntercept()

◆ setLambdaType()

◆ setLearningRateDecr()

◆ setLoss()

◆ setMaxClusters()

◆ setMaxIterations()

◆ setModifyX()

◆ setNormalization()

◆ setOscarParameters()

◆ setPathLength()

◆ setQ()

◆ setRandomSeed() [1/2]

◆ setRandomSeed() [2/2]

◆ setRelaxMaxInnerIterations()

◆ setRelaxMaxOuterIterations()

◆ setRelaxTol()

◆ setReturnClusters()

◆ setScaling() [1/2]

◆ setScaling() [2/2]

◆ setScreening()

◆ setSolver()

◆ setTol()

◆ setUpdateClusters()