MML-14-04: Lasso Regression with Absolute-Value Regularization: Sparsity Geometry, Laplace Prior and Subgradient Calculus – Practice Quiz

45 worked single-select and multiselect questions on Lasso Regression ($L_1$): Sparsity Geometry, Laplace Prior & Subgradient Calculus. Cognitive level: Tier 2–4. Prerequisites: QS 14.3, Part 03, Part 13.

Develop conceptual understanding, step-by-step computations, ML diagnostics and the assigned theoretical derivations. Each explanation analyzes every choice by its content.

Learning objectives: Use absolute-value subdifferentials in lasso optimality. Compute soft-thresholds and scaled coordinate updates. Explain sparsity geometry and constrained-penalized equivalence. Derive Laplace-prior MAP with correct normalization factors. Analyze correlated predictors, uniqueness and support selection. Calculate proximal updates and stopping checks. Connect standardization, intercept treatment and regularization paths. Derive dual correlations and shrinkage bias.

Study references: Tibshirani, Proximal Gradient Descent and Acceleration, Soft-thresholding and lasso examples; James et al., An Introduction to Statistical Learning, second edition, Sections 3.1–3.3 and 6.2.