Choose linear regression or decision tree appropriately
Company: TikTok
Role: Data Scientist
Category: Machine Learning
Difficulty: medium
Interview Round: Technical Screen
You have 100,000 i.i.d. rows with features: x1 (0–100), x2, x3, and y. Unknown to you, the DGP is piecewise linear with a hinge at x1=50 and an interaction y ≈ 3x1 + 20·I[x1>50] + 2·x2x3 + ε, with heteroskedastic noise Var(ε|x1)=0.01·(1+x1). Design an analysis to decide between linear regression and a decision tree. Specify: (1) feature engineering and tests you would run for linearity (e.g., spline basis for x1, x2:x3 interaction) and how you would check residual diagnostics for heteroskedasticity; (2) a fair comparison protocol (CV split, identical preprocessing) and metrics; (3) how you would enforce monotonicity or interaction constraints in a tree-based model to reflect domain knowledge; (4) which model you expect to generalize better here and why, including bias–variance reasoning and how you would quantify it with learning curves.
Quick Answer: This question evaluates model selection and diagnostic skills in supervised learning, specifically assessing feature engineering, interaction detection, handling heteroskedastic residuals, incorporation of monotonicity or interaction constraints in tree-based models, and fair cross-validation-based comparison between linear and tree approaches.