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Regularization

Ridge regression, lasso, elastic nets

For greater accuracy on low- through medium-dimensional data sets, implement least-squares regression with regularization using `lasso` or `ridge`.

For reduced computation time on high-dimensional data sets that fit in the MATLAB® Workspace, fit a regularized linear regression model using `fitrlinear`.

Classes

 `RegressionLinear` Linear regression model for high-dimensional data `RegressionPartitionedLinear` Cross-validated linear regression model for high-dimensional data

Functions

 `lasso` Regularized least-squares regression using lasso or elastic net algorithms `ridge` Ridge regression `lassoPlot` Trace plot of lasso fit
 `fitrlinear` Fit linear regression model to high-dimensional data `predict` Predict response of linear regression model
 `plotPartialDependence` Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots

Examples and How To

Lasso Regularization

See how `lasso` identifies and discards unnecessary predictors.

Lasso and Elastic Net with Cross-Validation

Predict the mileage (MPG) of a car based on its weight, displacement, horsepower, and acceleration using `lasso` and elastic net.

Wide Data via Lasso and Parallel Computing

Identify important predictors using `lasso` and cross-validation.

Concepts

Introduction to Ridge Regression

Ridge regression addresses the problem of multicollinearity (correlated model terms) in linear regression problems.

Lasso and Elastic Net

The `lasso` algorithm is a regularization technique and shrinkage estimator. The related elastic net algorithm is more suitable when predictors are highly correlated.

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