`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

Name	Type	Required	Default	Description
`X`	`NumericArray`	Yes	—	Predictor matrix with observations in rows and predictors in columns.
`y`	`NumericArray`	Yes	—	Response vector with one value per row of X.
`options`	`Any`	Variadic	—	Name-value options such as Lambda, Alpha, Standardize, Intercept, Weights, CV, NumLambda, LambdaRatio, MaxIter, and RelTol.

Returns

Name	Type	Description
`B`	`NumericArray`	Coefficient matrix with one column per Lambda value.
`FitInfo`	`Any`	Fit information structure containing Lambda, Alpha, Intercept, DF, MSE, and related fields.

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

Errors

Identifier	When	Message
`RunMat:lasso:InvalidArgument`	Inputs, option names, option values, dimensions, or tolerances are malformed.	`lasso: invalid argument`
`RunMat:lasso:Convergence`	Coordinate descent cannot make numerical progress for the supplied data.	`lasso: convergence failure`
`RunMat:lasso:Internal`	RunMat cannot construct lasso outputs.	`lasso: internal error`

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, and MCReps=1 are accepted for script compatibility. Tall-array ADMM behavior, covariance-matrix acceleration, and the currently unimplemented CacheSize, AbsTol, B0, U0, Rho, and Options forms reject explicitly; FitInfo.UseCovariance is false because RunMat uses direct coordinate descent.
Typed-integer X, y, floating parameters, and structural or logical controls are independently classified RunMat-only extensions. Integer data remains exact until a checked double solver boundary; values not exactly representable as double reject rather than round.

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.

Run a small lasso example, explain the result, then change one input and compare the output.

FAQ

Where is the intercept stored?⌄

The coefficient matrix B contains only predictor coefficients. Intercepts are returned in FitInfo.Intercept, one value per Lambda.

Does RunMat implement covariance-matrix acceleration?⌄

No. RunMat accepts UseCovariance for script compatibility, but fitting uses the direct coordinate-descent path and FitInfo.UseCovariance is false.

How are Lambda values ordered?⌄

RunMat returns Lambda values in ascending order in FitInfo.Lambda, and the columns of B use the same order.

Does cross-validation match MATLAB's random partitions exactly?⌄

No. RunMat currently uses deterministic round-robin K-fold partitions. The returned fields and selection semantics are MATLAB-compatible, but fold assignment is deterministic.

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.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

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

Syntax

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

Inputs

Name	Type	Required	Default	Description
`X`	`NumericArray`	Yes	—	Predictor matrix with observations in rows and predictors in columns.
`y`	`NumericArray`	Yes	—	Response vector with one value per row of X.
`options`	`Any`	Variadic	—	Name-value options such as Lambda, Alpha, Standardize, Intercept, Weights, CV, NumLambda, LambdaRatio, MaxIter, and RelTol.

Returns

Name	Type	Description
`B`	`NumericArray`	Coefficient matrix with one column per Lambda value.
`FitInfo`	`Any`	Fit information structure containing Lambda, Alpha, Intercept, DF, MSE, and related fields.

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

Errors

Identifier	When	Message
`RunMat:lasso:InvalidArgument`	Inputs, option names, option values, dimensions, or tolerances are malformed.	`lasso: invalid argument`
`RunMat:lasso:Convergence`	Coordinate descent cannot make numerical progress for the supplied data.	`lasso: convergence failure`
`RunMat:lasso:Internal`	RunMat cannot construct lasso outputs.	`lasso: internal error`

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, and MCReps=1 are accepted for script compatibility. Tall-array ADMM behavior, covariance-matrix acceleration, and the currently unimplemented CacheSize, AbsTol, B0, U0, Rho, and Options forms reject explicitly; FitInfo.UseCovariance is false because RunMat uses direct coordinate descent.
Typed-integer X, y, floating parameters, and structural or logical controls are independently classified RunMat-only extensions. Integer data remains exact until a checked double solver boundary; values not exactly representable as double reject rather than round.

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.

Run a small lasso example, explain the result, then change one input and compare the output.

FAQ

Where is the intercept stored?⌄

The coefficient matrix B contains only predictor coefficients. Intercepts are returned in FitInfo.Intercept, one value per Lambda.

Does RunMat implement covariance-matrix acceleration?⌄

No. RunMat accepts UseCovariance for script compatibility, but fitting uses the direct coordinate-descent path and FitInfo.UseCovariance is false.

How are Lambda values ordered?⌄

RunMat returns Lambda values in ascending order in FitInfo.Lambda, and the columns of B use the same order.

Does cross-validation match MATLAB's random partitions exactly?⌄

No. RunMat currently uses deterministic round-robin K-fold partitions. The returned fields and selection semantics are MATLAB-compatible, but fold assignment is deterministic.

Ml

Summary

Random

binornd · bootstrp · datasample · dividerand · exprnd · gamrnd · lhsdesign · mvnrnd · normrnd · random · randsample · rng · trnd · unidrnd · unifrnd · wblrnd

Hist

histc · histcounts · histcounts2

Options

statget · statset

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.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

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

Syntax

Inputs

Returns

Errors

How lasso works

Examples

Fit a sparse linear model for an explicit Lambda

Return FitInfo for an elastic-net path

Use K-fold cross-validation

Weight observations

Using lasso with coding agents

FAQ

Related Stats functions

Ml

Summary

Random

Hist

Options

Open-source implementation

About RunMat

Download RunMat

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

Syntax

Inputs

Returns

Errors

How lasso works

Examples

Fit a sparse linear model for an explicit Lambda

Return FitInfo for an elastic-net path

Use K-fold cross-validation

Weight observations

Using lasso with coding agents

FAQ

Related Stats functions

Ml

Summary

Random

Hist

Options

Open-source implementation

About RunMat

Download RunMat

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

How `lasso` works

Using `lasso` with coding agents

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

How `lasso` works

Using `lasso` with coding agents