Lars Algorithm for Solving L1 Regularized Regression Problems (Lasso)

In this article, we explore the Lars (Least Angle Regression) algorithm, an efficient method for solving L1-regularized regression problems commonly known as Lasso. The Lars algorithm operates iteratively, progressively building the Lasso solution path by minimizing residual sum of squares while maintaining the L1 constraint. From an implementation perspective, the algorithm cleverly selects variables to enter the model by making equal angular progress between active predictors, requiring efficient matrix operations and correlation calculations at each step. We will examine the algorithm's underlying principles, computational advantages over traditional methods like forward selection, and its limitations when dealing with highly correlated features. The article includes comparisons with other regression techniques such as ridge regression and elastic net, highlighting scenarios where Lars provides superior performance. Practical applications demonstrate how to implement Lars using statistical software packages, with code snippets showing key parameters like regularization strength adjustment and cross-validation integration for optimal model selection.