In this tutorial, we will walk through an example of performing lasso regression on the "carbig" dataset available in MATLAB. The provided code will load the dataset, preprocess the data, perform lasso regression, plot the solution path, and display the resulting coefficients.
lasso regression
Lasso regression, short for least absolute shrinkage and selection operator, is a linear regression method for variable selection and regularization. It is a popular technique in statistics and machine learning, especially when there are a large number of potential predictors.
In traditional linear regression, the goal is to fit a linear model that predicts the relationship between the dependent variable (the variable you want to predict) and the independent variable (the variable used to make the prediction). However, when there are many independent variables, some of them may not contribute much to the prediction, leading to overfitting to new data or poor generalization ability.
Lasso regression solves this problem by introducing a penalty term in the linear regression objective function. The penalty term is based on the sum of the absolute values of the regression coefficients multiplied by a constant (regularization parameter, usually denoted lambda or alpha). The effect of this penalty is that it encourages the coefficients of some variables to go to exactly zero, effectively performing variable selection by shrinking the coefficients of less important variables.
A key feature of lasso regression is its ability to perform variable selection and regularization simultaneously. It automatically removes irrelevant or redundant variables from the model by shrinking some coefficients to zero, which can lead to simpler and more interpretable models. Additionally, the penalty term helps prevent overfitting by discouraging large coefficients, resulting in better generalization to new data.
Lasso regression can be applied to various types of linear models, including ordinary least squares regression, logistic regression, and multiple regression. It is especially useful in situations where there is a high-dimensional feature space and the presence of irrelevant or redundant variables hinders model performance.
MATLAB code for lasso regression
Here is a sample MATLAB code that demonstrates how to perform lasso regression on a dataset using built-in MATLAB functions:
% Load the dataset
load carbig
This line loads in MATLAB a file named