# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.regression.linear.lasso

## Class UnconstrainedLASSOProblem

• public class UnconstrainedLASSOProblem
extends LMProblem
A LASSO (least absolute shrinkage and selection operator) problem focuses on solving an RSS (residual sum of squared errors) problem with L1 regularization. The unconstrained form (Lagrangian form) solves $\min_w \left \{ 0.5 * \left \| Xw - y \right \|_2^2 + \lambda * \left \| w \right \|_1 \right \}$
• R. Tibshirani, "Regression shrinkage and selection via the LASSO," Journal of the Royal Statistical Society, Series B, Volume: 58, Issue: 1, 267 - 288, 1996.
• Wikipedia: LASSO method
• ### Constructor Summary

Constructors
Constructor and Description
UnconstrainedLASSOProblem(UnconstrainedLASSOProblem that)
Copy constructor.
UnconstrainedLASSOProblem(Vector y, Matrix X, double lambda)
Constructs a LASSO problem.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double lambda()
Gets the penalization parameter for the unconstrained form of LASSO.
• ### Methods inherited from class com.numericalmethod.suanshu.stats.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

• #### UnconstrainedLASSOProblem

public UnconstrainedLASSOProblem(Vector y,
Matrix X,
double lambda)
Constructs a LASSO problem.
Parameters:
y - the vector of response variable (n * 1), properly demeaned and scaled
X - the design matrix of factors (n * m), properly demeaned and scaled
lambda - the penalization parameter
• #### UnconstrainedLASSOProblem

public UnconstrainedLASSOProblem(UnconstrainedLASSOProblem that)
Copy constructor.
Parameters:
that - another LASSOProblem
• ### Method Detail

• #### lambda

public double lambda()
Gets the penalization parameter for the unconstrained form of LASSO.
Returns:
lambda, the penalization parameter for the unconstrained form of LASSO