dev.nm.stat.regression.linear.lasso.lars

Class LARSProblem

java.lang.Object

dev.nm.stat.regression.linear.LMProblem

dev.nm.stat.regression.linear.lasso.lars.LARSProblem

public class LARSProblem
extends LMProblem

Least Angle Regression (LARS) is a regression algorithm for high-dimensional data. Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients. The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.

See Also:

• B. Efron et. al, "Least Angle Regression," The Annals of Statistics, Volume: 32(2), 407 - 499, 2004.
• T. Hastie, R. Tibshirani and J. Friedman, "The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Second Edition)," New York, Springer-Verlag, 2009.
• Wikipedia: Least angle regression

Constructor Summary

Constructors

Constructor and Description
LARSProblem(LARSProblem that) Copy constructor.
LARSProblem(Vector y, Matrix X) Constructs a LASSO variation of the Least Angel Regression (LARS) problem, where an intercept is included in the model and the covariates are normalized first.
LARSProblem(Vector y, Matrix X, boolean lasso) Constructs a Least Angel Regression (LARS) problem, where an intercept is included in the model and the covariates are normalized first.
LARSProblem(Vector y, Matrix X, boolean normalized, boolean lasso) Constructs a Least Angel Regression (LARS) problem, where an intercept is included in the model.
LARSProblem(Vector y, Matrix X, boolean intercept, boolean normalized, boolean lasso) Constructs a Least Angel Regression (LARS) problem.

Method Summary

Modifier and Type	Method and Description
boolean	isLASSO() Checks if the LASSO variation of LARS is used.
int	m() Gets the number of covariates (number of columns of X), excluding the intercept.
Vector	XL2Norm() Gets the L2 norms of the covariates (a vector of ones if no standardization is required).
Matrix	XLARS() Gets the matrix of covariates (possibly demeaned and/or scaled) to be used in LARS.
Vector	XMean() Gets the mean vector to be subtracted from the covariates (a vector of zeros if no intercept is included).
Vector	yLARS() Gets the vector of response variable (possibly demeaned) to be used in LARS.
double	yMean() Gets the mean to be subtracted from the response variable (0 if no intercept is included).

Methods inherited from class dev.nm.stat.regression.linear.LMProblem

A, checkInputs, intercept, invOfwAtwA, nExogenousFactors, nFactors, nObs, wA, weights, wy, X, y

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LARSProblem

public LARSProblem(Vector y,
                   Matrix X,
                   boolean intercept,
                   boolean normalized,
                   boolean lasso)

Constructs a Least Angel Regression (LARS) problem.

Parameters:

y - the vector of response variable (n * 1)

X - the matrix of covariates (n * m)

intercept - an indicator of whether an intercept is included in the model

normalized - an indicator of whether the covariates are first normalized to have unit L2 norm

lasso - an indicator of whether LASSO variation is used

LARSProblem

public LARSProblem(Vector y,
                   Matrix X,
                   boolean normalized,
                   boolean lasso)

Constructs a Least Angel Regression (LARS) problem, where an intercept is included in the model.

Parameters:

y - the vector of response variable (n * 1)

X - the matrix of covariates (n * m)

normalized - an indicator of whether the covariates are first normalized to have unit L2 norm

lasso - an indicator of whether LASSO variation is used

LARSProblem

public LARSProblem(Vector y,
                   Matrix X,
                   boolean lasso)

Constructs a Least Angel Regression (LARS) problem, where an intercept is included in the model and the covariates are normalized first.

Parameters:

y - the vector of response variable (n * 1)

X - the matrix of covariates (n * m)

lasso - an indicator of whether LASSO variation is used

LARSProblem

public LARSProblem(Vector y,
                   Matrix X)

Constructs a LASSO variation of the Least Angel Regression (LARS) problem, where an intercept is included in the model and the covariates are normalized first.

Parameters:

y - the vector of response variable (n * 1)

X - the matrix of covariates (n * m)

LARSProblem

public LARSProblem(LARSProblem that)

Copy constructor.

Parameters:

that - another LeastAngelRegressionProblem

Method Detail

m

public int m()

Gets the number of covariates (number of columns of X), excluding the intercept.

Returns:

the number of covariates

isLASSO

public boolean isLASSO()

Checks if the LASSO variation of LARS is used.

Returns:

true if the LASSO variation of LARS is used

yMean

public double yMean()

Gets the mean to be subtracted from the response variable (0 if no intercept is included).

Returns:

the mean to be subtracted from the response variable

XMean

public Vector XMean()

Gets the mean vector to be subtracted from the covariates (a vector of zeros if no intercept is included).

Returns:

the mean vector to be subtracted from the covariates

XL2Norm

public Vector XL2Norm()

Gets the L2 norms of the covariates (a vector of ones if no standardization is required).

Returns:

the L2 norm of the covariates

yLARS

public Vector yLARS()

Gets the vector of response variable (possibly demeaned) to be used in LARS.

Returns:

the the vector of response variable (possibly demeaned) to be used in LARS

XLARS

public Matrix XLARS()

Gets the matrix of covariates (possibly demeaned and/or scaled) to be used in LARS.

Returns:

the matrix of covariates (possibly demeaned and/or scaled) to be used in LARS