LARS

class LARS(*args)

Least Angle Regression.

Refer to Sparse least squares polynomial metamodel.

Notes

LARS inherits from BasisSequenceFactory.

If the size P of the PC basis is of similar size to N, or even possibly significantly larger than N , then the following ordinary least squares problem is ill-posed:

\vect{a} = \argmin_{\vect{b} \in \Rset^P} E_{\mu} \left[ \left( g \circ T^{-1}
        (\vect{U}) - \vect{b}^{\intercal} \vect{\Psi}(\vect{U}) \right)^2 \right]

The sparse least squares approaches may be employed instead. Eventually a sparse PC representation is obtained, that is an approximation which only contains a small number of active basis functions.

This class is not usable as is because it has sense only whithin the FunctionalChaosAlgorithm.

Methods

build(self, x, y, psi, indices)

Run the algorithm.

getClassName(self)

Accessor to the object’s name.

getId(self)

Accessor to the object’s id.

getMaximumRelativeConvergence(self)

Accessor to the stopping criterion on the L1-norm of the coefficients.

getName(self)

Accessor to the object’s name.

getShadowedId(self)

Accessor to the object’s shadowed id.

getVerbose(self)

Accessor to the verbosity.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasVisibleName(self)

Test if the object has a distinguishable name.

setMaximumRelativeConvergence(self, …)

Accessor to the stopping criterion on the L1-norm of the coefficients.

setName(self, name)

Accessor to the object’s name.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setVerbose(self, verbose)

Accessor to the verbosity.

setVisibility(self, visible)

Accessor to the object’s visibility state.

__init__(self, *args)

Initialize self. See help(type(self)) for accurate signature.

build(self, x, y, psi, indices)

Run the algorithm.

Parameters
x2-d sequence of float

Input sample

y2-d sequence of float

Output sample

psisequence of Function

Basis

indicessequence of int

Current indices of the basis

Returns
measureBasisSequence

Fitting measure

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getMaximumRelativeConvergence(self)

Accessor to the stopping criterion on the L1-norm of the coefficients.

Returns
efloat

Stopping criterion.

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getVerbose(self)

Accessor to the verbosity.

Returns
vbool.

Verbosity

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

setMaximumRelativeConvergence(self, coefficientsPaths)

Accessor to the stopping criterion on the L1-norm of the coefficients.

Parameters
efloat

Stopping criterion.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVerbose(self, verbose)

Accessor to the verbosity.

Parameters
vbool

Enable or disable the verbosity.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.