# 05.Least Angle Regression

Least angle regression, aka, LAR

## Least Angle Regression

- Algorithm 3.2
- We want to change $\beta$ so that the prediction is closer to data $y$, i.e., we require the change of $\beta$ decreases $X\beta = y - r$. So the change should be $\propto X^T r $.
- Why this works? It reduces the MSE.
- LAR is similar to lasso.
- Modified LAR Algorithm 3.2a leads to lasso result.
- LAR(lasso) is efficient. It takes $\mathrm{min}(p,N-1)$ steps where lasso itself might take more than p steps.
- LAR and lasso are almost identical if we use the geometric meaning of the algorithms. But when some coefficient crosses 0, the differences pop up.

Planted:
by OctoMiao;

## Table of Contents

**Current Ref:**

- esl/05.least-angle-regression.md