lasso — Fit lasso or elastic-net regularized linear regression models.

lasso(X,y) fits regularized linear regression coefficients for predictor matrix X and response vector y. Columns of B correspond to ascending Lambda values, and [B,FitInfo] = lasso(...) returns MATLAB-compatible fit metadata.

Syntax

B = lasso(X, y)
B = lasso(X, y, Name, Value)
[B, FitInfo] = lasso(X, y)
[B, FitInfo] = lasso(X, y, Name, Value)

Inputs

Returns

Returned values from lasso depend on how many outputs the caller requests.

Errors

How lasso works

• X must be a finite real numeric matrix with observations in rows and predictors in columns. y must be a finite real vector whose length matches size(X,1).
• Lambda accepts a nonnegative scalar or vector. RunMat sorts Lambda values in ascending order for output, matching MATLAB's FitInfo.Lambda convention.
• When Lambda is omitted, RunMat computes a geometric regularization path using NumLambda and LambdaRatio from the largest lambda that gives an all-zero model.
• Alpha supports lasso and elastic-net fits for values in (0,1]. Alpha=1 is lasso; smaller positive values mix in the ridge penalty.
• Standardize and Intercept follow MATLAB's model form. If Intercept is false, RunMat disables standardization and returns zero intercepts.
• Weights accepts a nonnegative observation-weight vector with positive total weight. Weights are normalized internally.
• RelTol and MaxIter control coordinate-descent convergence. The Iterations FitInfo field records iterations per Lambda value.
• CV supports "resubstitution" and positive integer K-fold cross-validation. K-fold fits add SE, LambdaMinMSE, Lambda1SE, IndexMinMSE, and Index1SE fields to FitInfo.
• PredictorNames, DFmax, UseCovariance, CacheSize, MCReps=1, AbsTol, B0, U0, Rho, and Options are accepted for script compatibility. Tall-array ADMM behavior and covariance-matrix acceleration are not implemented; FitInfo.UseCovariance is false because RunMat uses direct coordinate descent.

Examples

Fit a sparse linear model for an explicit Lambda

X = [0 1; 1 1; 2 1; 3 1; 4 1];
y = [1; 3; 5; 7; 9];
B = lasso(X, y, "Lambda", 0, "Standardize", false)

Expected output:

B is approximately [2; 0]. Use FitInfo.Intercept for the constant term.

Return FitInfo for an elastic-net path

[B,FitInfo] = lasso(X, y, "Alpha", 0.5, "Lambda", [0 0.01 0.1]);
coef0 = FitInfo.Intercept(1)

Expected output:

B has one column per Lambda value; FitInfo contains Lambda, Alpha, Intercept, DF, and MSE.

Use K-fold cross-validation

[B,FitInfo] = lasso(X, y, "CV", 5);
idx = FitInfo.IndexMinMSE;
coef = B(:,idx)

Expected output:

FitInfo includes cross-validation MSE, SE, and Lambda selection fields.

Weight observations

w = ones(size(y));
w(1:5) = 2;
[B,FitInfo] = lasso(X, y, "Weights", w)

Expected output:

Rows with larger weights contribute more to the weighted least-squares objective.

Using lasso with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how lasso changes the result.

FAQ

Related Stats functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how lasso is executed, line by line, in Rust.

• View the source for lasso in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

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