TikTok·Data Scientist·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

TikTok data scientist interview with a heavy stats/ML modeling question that felt more like a take-home problem compressed into a live session. One question, very deep, and they clearly wanted to see if you could reason through model selection end to end rather than just recite definitions.

Questions Asked (1)

You have 100k rows with features x1 (ranging 0 to 100), x2, x3, and a target y. The true data-generating process is piecewise linear with a breakpoint at x1=50, an interaction between x2 and x3, and heteroskedastic noise that grows with x1. Walk through how you'd decide between linear regression and a decision tree: what feature engineering and linearity tests you'd run, how you'd check for heteroskedasticity in residuals, how you'd set up a fair model comparison, how you'd enforce monotonicity or interaction constraints in a tree model, and which model you'd expect to generalize better and why using bias-variance reasoning and learning curves.

Technical Trade-offsData ModelingRoot Cause Analysis

Author's notes

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AI HintsAI Generated

Suggested Approach

Start by framing the problem as a bias-variance trade-off driven by the known piecewise linear structure, interaction, and heteroskedastic noise. Walk through a systematic diagnostic and modeling plan: feature engineering to linearize the breakpoint, formal tests for linearity and heteroskedasticity, a fair comparison using proper cross-validation and metrics, and constraints to inject domain knowledge into the tree. Conclude with a reasoned prediction of generalization performance, supported by learning curves and bias-variance decomposition.

Pro tip: Mention that you would use a linear model with a hinge basis for x1 and an explicit x2*x3 interaction as a strong baseline, then compare it to a constrained tree (e.g., monotonic constraints on x1 and interaction constraints) — this shows you can blend statistical rigor with practical ML engineering.

1. Feature engineering and linearity diagnostics

Create a hinge feature max(0, x1-50) to capture the breakpoint and an explicit x2*x3 interaction term. Run linearity tests such as Ramsey RESET, Harvey-Collier, or compare linear vs. spline fits via cross-validated error to check if the piecewise linear structure is adequately captured.

2. Heteroskedasticity assessment

Fit the linear model and plot residuals vs. x1 and fitted values. Use Breusch-Pagan, White, or Goldfeld-Quandt tests to confirm heteroskedasticity. If present, consider weighted least squares, robust standard errors, or transforming the target (e.g., log) if appropriate.

3. Fair model comparison setup

Use repeated k-fold cross-validation with the same folds for both models. Evaluate with metrics robust to heteroskedasticity (e.g., MAE, RMSE) and report mean and standard deviation across folds. Ensure hyperparameter tuning (e.g., tree depth, min samples per leaf) is done inside the CV loop to avoid leakage.

4. Enforcing constraints in tree models

For monotonicity in x1, use monotonic constraints (available in XGBoost, LightGBM, or sklearn's HistGradientBoosting). For the x2*x3 interaction, use interaction constraints to allow only that pair to interact, or engineer the interaction feature and include it as a single feature to encourage the tree to split on it.

5. Generalization prediction with bias-variance and learning curves

Plot learning curves for both models: training and validation error vs. training set size. The linear model with correct features will have lower variance and likely lower bias if the true DGP is piecewise linear; the tree may overfit the heteroskedastic noise and struggle to extrapolate the linear segments. Expect the well-specified linear model to generalize better, but verify empirically.

Key Points to Mention

Piecewise linear structure: use hinge function max(0, x1-50) to linearize the breakpoint.
Interaction term x2*x3 should be explicitly included in the linear model and enforced in the tree via interaction constraints.
Heteroskedasticity: test with Breusch-Pagan/White, and address via weighted least squares or robust standard errors.
Fair comparison: same CV folds, nested hyperparameter tuning, and metrics like MAE/RMSE with uncertainty estimates.
Tree constraints: monotonic constraints on x1 and interaction constraints for x2 and x3.
Bias-variance: linear model has lower variance and correct bias if specified well; tree may overfit noise and extrapolate poorly, so linear likely generalizes better.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.