Lasso Regression: Why the Solution Lives on a Diamond

A geometric and intuitive explanation of Lasso Regression using vectors, projections, and the concept of a constraint budget. Starting from a simple house price prediction example, the post shows how adding more features than observations leads to overfitting, then explains how Lasso addresses this by restricting the sum of absolute coefficient values. The constraint region forms a diamond shape in coefficient space, and the Lasso solution is found by projecting the target onto the nearest boundary of that diamond. The post walks through data centering, the math of projection onto a constrained line, and demonstrates how Lasso shrinks coefficients and can zero out less important features to improve generalization.