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Two Sigma·Software Engineer·Technical Phone Screen·Senior

Senior
Jun 2026

Summary

Two Sigma research engineer interview with a meaty data analysis problem that blends stats, ML, and feature selection into one question. The kind of problem where you can tell they actually want to see how you think, not just whether you memorized a formula.

Questions Asked (1)

Q1

You're given historical temperature data for NYC and a bunch of small towns. How would you identify which town has the highest volatility, which is most similar to NYC, then use the towns' data to predict NYC temperatures (evaluated with MSE), and finally do greedy forward feature selection to pick the best subset of towns up to some specified count?

Algorithms & Data StructuresProduct Analytics & MetricsTechnical Trade-offs
Author's notes

This is basically four questions stitched together and they just kept going.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the data structure and definitions: volatility as standard deviation of temperature, similarity as correlation or Euclidean distance to NYC. Then outline a modular pipeline: compute volatility, compute similarity, build a regression model using town temperatures to predict NYC, and finally implement greedy forward selection to choose the best subset of towns based on MSE.

Pro tip: Emphasize that greedy forward selection is a heuristic and discuss the trade-off between computational cost and optimality; also mention the importance of cross-validation to avoid overfitting when evaluating MSE.

1. Clarify Data and Metrics

Ask about data format (time series, aligned dates), define volatility (e.g., standard deviation of daily temperatures), and similarity (e.g., correlation or Euclidean distance). Confirm that MSE is the evaluation metric for prediction.

2. Compute Volatility and Similarity

For each town, calculate volatility as the standard deviation of its temperature series. For similarity to NYC, compute correlation or distance between each town's series and NYC's series, then rank towns.

3. Build Predictive Model

Use a regression model (e.g., linear regression) where NYC temperature is the target and town temperatures are features. Train on historical data and evaluate using MSE on a validation set.

4. Greedy Forward Feature Selection

Start with an empty set of towns. Iteratively add the town that most reduces validation MSE until reaching the specified count. Use cross-validation to estimate MSE reliably.

5. Evaluate and Discuss Trade-offs

Compare the selected subset's performance to using all towns or other subsets. Discuss computational complexity (O(k*n) for k features and n candidates) and potential overfitting.

Key Points to Mention

  • Definition of volatility (e.g., standard deviation) and similarity (e.g., correlation, Euclidean distance).
  • Choice of regression model (linear regression, ridge, etc.) and why it's suitable.
  • Use of cross-validation to avoid overfitting and get reliable MSE estimates.
  • Greedy forward selection algorithm: start empty, add best feature iteratively.
  • Computational complexity and trade-offs of greedy selection vs. exhaustive search.
  • Handling of time series aspects: alignment, seasonality, and potential need for normalization.

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