LARS

An implementation of Least Angle Regression (Stagewise/laSso), also known as LARS.

:- use_module('path/to/.../src/methods/lars/lars.pl').

%% usage example
TrainData = [5.1,3.5,1.4, 4.9,3.0,1.4, 4.7,3.2,1.3, 4.6,3.1,1.5],
TestData = [3,2,0, 5,1,4, 0,0,4, 3,3,5, 0,5,5, 2,5,5],
lars_initAndTrainModel(0, 0.0, 0.0, 1.0e-16, TrainData, 3, [0,1,0,1], 0, _),
lars_predict(TestData, 3, PredictList, 1).

Available Predicates

links/resources

lars_initAndTrainModel/9

Only initialize the LARS model.

%% predicate definition 
lars_initAndTrainModel(UseCholesky, Lambda1, Lambda2, Tolerance, DataList, DataPointsDim, ResponsesList, RowMajor, Error) :-
        Tolerance > 0, 
        convert_list_to_float_array(DataList, DataPointsDim, array(Xsize, Xrownum, X)),
        convert_list_to_float_array(ResponsesList, array(Ysize, Y)),
        initAndTrainModelI(UseCholesky, Lambda1, Lambda2, Tolerance, X, Xsize, Xrownum, Y, Ysize, RowMajor, Error).

%% foreign c++ predicate definition 
foreign(initAndTrainModel, c, initAndTrainModelI( +integer, 
                                                  +float32, +float32, +float32,
                                                  +pointer(float_array), +integer, +integer,
                                                  +pointer(float_array), +integer, 
                                                  +integer, -float32)).

Parameters

Name	Type	Description	Default
useCholesky	+integer(bool)	Whether or not to use Cholesky decomposition when solving linear system (as opposed to using the full Gram matrix).	(0)false
lambda1	+float	Regularization parameter for l1-norm penalty.	0.0
lambda2	+float	Regularization parameter for l2-norm penalty.	0.0
tolerance	+float	Run until the maximum correlation of elements in (X^T y) is less than this.	1e-16
data	+matrix	Column-major input data (or row-major input data if rowMajor = true).	-
responses	+vector	A vector of targets.	-
rowMajor	+integer(bool)	Set to false if the data is row-major.	(1)true
error	-float	minimum cost error	-

lars_activeSet/1

Get the set of active dimensions

%% predicate definition 
lars_activeSet(ActiveSetList) :-
        activeSetI(Y, Ysize),
        convert_float_array_to_list(Y, Ysize, ActiveSetList).

%% foreign c++ predicate definition 
foreign(activeSet, c, activeSetI(-pointer(float_array), -integer)).

Parameters

Name	Type	Description	Default
activeSet	-vector	Get the set of active dimensions	-

lars_beta/1

Get the solution coefficients.

%% predicate definition 
lars_beta(BetaList) :-
        betaI(Y, Ysize),
        convert_float_array_to_list(Y, Ysize, BetaList).

%% foreign c++ predicate definition 
foreign(beta, c, betaI(-pointer(float_array), -integer)).

Parameters

Name	Type	Description	Default
beta	-vector	Get the solution coefficients.	-

lars_betaPath/2

Get the set of coefficients after each iteration. The solution is the last element.

%% predicate definition 
lars_betaPath(BetaList, XCols) :-
        betaPathI(X, XCols, XRows),
        convert_float_array_to_2d_list(X, XCols, XRows, BetaList).

%% foreign c++ predicate definition 
foreign(betaPath, c, betaPathI(-pointer(float_array), -integer, -integer)).

Parameters

Name	Type	Description	Default
betaPath	-matrix	Get the set of coefficients after each iteration. The solution is the last element.	-

lars_computeError/5

Compute cost error of the given data matrix using the currently-trained LARS model.

Only ||y-beta*X||2 is used to calculate cost error.

%% predicate definition 
lars_computeError(DataList, DataRows, ResponsesList, RowMajor, Error) :-
        convert_list_to_float_array(DataList, DataRows, array(Xsize, Xrownum, X)),
        convert_list_to_float_array(ResponsesList, array(Ysize, Y)),
        computeErrorI(X, Xsize, Xrownum, Y, Ysize, RowMajor, Error).

%% foreign c++ predicate definition 
foreign(computeError, c, computeErrorI( +pointer(float_array), +integer, +integer, 
                                        +pointer(float_array), +integer, 
                                        +integer, 
                                        [-float32])).

Parameters

Name	Type	Description	Default
matX	+matrix	Column-major input data (or row-major input data if rowMajor = true).	-
y	+vector	responses A vector of targets.	-
rowMajor	+integer(bool)	Should be true if the data points matrix is row-major and false otherwise.	(0)false
error	-float	The minimum cost error.	-

lars_lambdaPath/1

Get the set of values for lambda1 after each iteration; the solution is the last element.

%% predicate definition 
lars_lambdaPath(LambdaPathList) :-
        lambdaPathI(Y, Ysize),
        convert_float_array_to_list(Y, Ysize, LambdaPathList).

%% foreign c++ predicate definition 
foreign(lambdaPath, c, lambdaPathI(-pointer(float_array), -integer)).

Parameters

Name	Type	Description	Default
lambdaPath	-vector	Get the set of values for lambda1 after each iteration; the solution is the last element.	-

lars_matUtriCholFactor/2

Get the upper triangular cholesky factor.

%% predicate definition 
lars_matUtriCholFactor(FactorList, XCols) :-
        matUtriCholFactorI(X, XCols, XRows),
        convert_float_array_to_2d_list(X, XCols, XRows, FactorList).

%% foreign c++ predicate definition 
foreign(matUtriCholFactor, c, matUtriCholFactorI(-pointer(float_array), -integer, -integer)).

Parameters

Name	Type	Description	Default
factor	-matrix	Get the upper triangular cholesky factor.	-

lars_predict/4

Predict y_i for each data point in the given data matrix using the currently-trained LARS model.

%% predicate definition 
lars_predict(PointsList, PointsRows, PredicList, RowMajor) :-
        convert_list_to_float_array(PointsList, PointsRows, array(Xsize, Xrownum, X)),
        predictI(X, Xsize, Xrownum, Y, Ysize, RowMajor),
        convert_float_array_to_list(Y, Ysize, PredicList).

%% foreign c++ predicate definition 
foreign(predict, c, predictI( +pointer(float_array), +integer, +integer, 
                              -pointer(float_array), -integer, 
                              +integer)).

Parameters

Name	Type	Description	Default
points	+matrix	The data points to regress on.	-
predictions	-vector	y, which will contained calculated values on completion.	-
rowMajor	+integer(bool)	Should be true if the data points matrix is row-major and false otherwise.	(0)false

Connected Links/Resources

If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.

added some of the links from the python documentation

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