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Boston Consulting Group·Data Scientist·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
Jun 2026

Summary

BCG data scientist technical screen, one big multi-part question about loss functions for regression. Dense enough that I left unsure if I'd actually nailed it or just sounded like I knew what I was talking about.

Questions Asked (1)

Q1

You're building a regression model to predict car prices in USD with an unscaled target. Walk through when and why you'd choose MSE over MAE, covering optimization behavior, convexity, outlier sensitivity, probabilistic assumptions, business fit, and how leaving the target unscaled affects training.

Technical Trade-offsData ModelingProduct Analytics & Metrics
Author's notes

This was basically six questions duct-taped together and they just...

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AI HintsAI Generated

Suggested Approach

Structure your answer around the trade-offs between MSE and MAE, explicitly addressing each dimension the interviewer listed: optimization, convexity, outliers, probabilistic assumptions, business fit, and unscaled target effects. Use a decision framework that ties the choice to the business objective and data characteristics, and conclude with a clear recommendation for the car price scenario.

Pro tip: Emphasize that MSE's sensitivity to outliers can be a feature or a bug depending on whether large errors are disproportionately costly in the business context; for car prices, a $10k error on a luxury car may matter less than a $2k error on a budget car, so consider relative error or a weighted loss.

1. Define the business objective and error cost

Clarify what matters: is a $1k error equally bad for all cars, or do large errors on expensive cars matter more? This determines whether to penalize large errors heavily (MSE) or treat all errors linearly (MAE).

2. Analyze optimization and convexity

Explain that MSE is smooth and convex, leading to stable gradient-based optimization, while MAE is non-smooth at zero and may require subgradient methods, but is more robust to outliers.

3. Connect to probabilistic assumptions

MSE corresponds to Gaussian noise, MAE to Laplacian noise. Choose based on the assumed error distribution; car price errors often have heavier tails, favoring MAE.

4. Assess outlier sensitivity and unscaled target impact

MSE squares errors, so outliers dominate; MAE is linear. With unscaled target, MSE gradients scale with target magnitude, potentially causing unstable training; MAE gradients are scale-robust but may converge slowly.

5. Make a recommendation and consider alternatives

For car prices, if outliers are rare and large errors are costly, MSE is fine; otherwise MAE or Huber loss. Also mention that unscaled target may require learning rate tuning or target normalization for MSE.

Key Points to Mention

  • MSE is differentiable and convex, enabling efficient optimization; MAE is non-differentiable at zero but robust to outliers.
  • MSE assumes Gaussian errors, MAE assumes Laplacian errors; check residual distribution.
  • Outliers: MSE penalizes large errors quadratically, MAE linearly; car price data often has outliers (e.g., luxury cars).
  • Business fit: MSE aligns with minimizing large errors if they are disproportionately costly; MAE aligns with minimizing typical error.
  • Unscaled target: MSE gradients scale with target magnitude, affecting learning rate and convergence; MAE is scale-invariant but may need more iterations.
  • Alternatives: Huber loss combines benefits; consider log-transform or normalization for MSE.

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