Documentation Center 
Regularized leastsquares regression using lasso or elastic net algorithms
B = lasso(X,Y)
[B,FitInfo]
= lasso(X,Y)
[B,FitInfo]
= lasso(X,Y,Name,Value)
B = lasso(X,Y) returns fitted leastsquares regression coefficients for a set of regularization coefficients Lambda.
[B,FitInfo] = lasso(X,Y) returns a structure containing information about the fits.
[B,FitInfo] = lasso(X,Y,Name,Value) fits regularized regressions with additional options specified by one or more Name,Value pair arguments.
X 
Numeric matrix with n rows and p columns. Each row represents one observation, and each column represents one predictor (variable). 
Y 
Numeric vector of length n, where n is the number of rows of X. Y(i) is the response to row i of X. 
Specify optional commaseparated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
'Alpha' 
Scalar value from 0 to 1 (excluding 0) representing the weight of lasso (L^{1}) versus ridge (L^{2}) optimization. Alpha = 1 represents lasso regression, Alpha close to 0 approaches ridge regression, and other values represent elastic net optimization. See Definitions. Default: 1 
'CV' 
Method lasso uses to estimate mean squared error:
Default: 'resubstitution' 
'DFmax' 
Maximum number of nonzero coefficients in the model. lasso returns results only for Lambda values that satisfy this criterion. Default: Inf 
'Lambda' 
Vector of nonnegative Lambda values. See Definitions.
Default: Geometric sequence of NumLambda values, the largest just sufficient to produce B = 0 
'LambdaRatio' 
Positive scalar, the ratio of the smallest to the largest Lambda value when you do not set Lambda. If you set LambdaRatio = 0, lasso generates a default sequence of Lambda values, and replaces the smallest one with 0. Default: 1e4 
'MCReps' 
Positive integer, the number of Monte Carlo repetitions for cross validation.
Default: 1 
'NumLambda' 
Positive integer, the number of Lambda values lasso uses when you do not set Lambda. lasso can return fewer than NumLambda fits if the if the residual error of the fits drops below a threshold fraction of the variance of Y. Default: 100 
'Options' 
Structure that specifies whether to cross validate in parallel, and specifies the random stream or streams. Create the Options structure with statset. Option fields:

'PredictorNames' 
Cell array of strings representing names of the predictor variables, in the order in which they appear in X. Default: {} 
'RelTol' 
Convergence threshold for the coordinate descent algorithm (see Friedman, Tibshirani, and Hastie [3]). The algorithm terminates when successive estimates of the coefficient vector differ in the L^{2} norm by a relative amount less than RelTol. Default: 1e4 
'Standardize' 
Boolean value specifying whether lasso scales X before fitting the models. Default: true 
'Weights' 
Observation weights, a nonnegative vector of length n, where n is the number of rows of X. lasso scales Weights to sum to 1. Default: 1/n * ones(n,1) 
B 
Fitted coefficients, a pbyL matrix, where p is the number of predictors (columns) in X, and L is the number of Lambda values.  
FitInfo 
Structure containing information about the model fits.
If you set the CV namevalue pair to cross validate, the FitInfo structure contains additional fields.

[1] Tibshirani, R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, Vol 58, No. 1, pp. 267–288, 1996.
[2] Zou, H. and T. Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B, Vol. 67, No. 2, pp. 301–320, 2005.
[3] Friedman, J., R. Tibshirani, and T. Hastie. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, Vol 33, No. 1, 2010. http://www.jstatsoft.org/v33/i01
[4] Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning, 2nd edition. Springer, New York, 2008.