Pinterest·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Pinterest MLE interview with a probability sampling question that looks straightforward until you start thinking about negative scores and numerical overflow. The kind of problem where the math is the easy part and the implementation details are what actually matter.

Questions Asked (1)

Given a list of strings (like user comments) each with a real-valued score that can be negative, sample one string with probability proportional to those scores. How do you handle the mapping and make it numerically stable?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The part I fumbled on first was the negative scores.

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AI HintsAI Generated

Suggested Approach

Start by clarifying that negative scores cannot be used directly as probabilities, so you need a transformation like shifting or exponentiating. Then explain the sampling algorithm (e.g., cumulative distribution or alias method) and emphasize numerical stability techniques such as subtracting the maximum score before exponentiation.

Pro tip: Mention that if all scores are negative, shifting by the minimum makes them non-negative, but be aware that this changes relative weights; alternatively, use softmax with a temperature parameter to control sharpness. Also, note that for large lists, the alias method gives O(1) sampling after O(n) preprocessing.

1. Clarify the problem and constraints

Confirm that scores can be negative and that we need to sample proportionally. Discuss whether the scores are logits or arbitrary real values, as this affects the transformation.

2. Transform scores to non-negative weights

Use a shift (subtract min) or exponentiation (softmax) to ensure all weights are positive. Explain the trade-offs: shifting preserves relative differences but can be dominated by outliers; softmax with temperature controls the distribution.

3. Handle numerical stability

For softmax, subtract the maximum score before exponentiating to avoid overflow/underflow. For shifting, ensure the shift doesn't cause underflow when scores are very negative.

4. Implement sampling algorithm

Describe either the cumulative distribution function (CDF) method with binary search (O(n) preprocessing, O(log n) per sample) or the alias method (O(n) preprocessing, O(1) per sample).

5. Discuss edge cases and complexity

Address cases like all scores equal, all negative, or very large lists. Mention time and space complexity and potential alternatives like rejection sampling.

Key Points to Mention

Negative scores cannot be probabilities; need transformation like shifting or softmax.
Numerical stability: subtract max before exponentiation to prevent overflow.
Cumulative distribution function (CDF) with binary search for sampling.
Alias method for O(1) sampling after O(n) preprocessing.
Trade-offs: shifting vs. softmax, temperature parameter, handling outliers.
Edge cases: all scores equal, all negative, large n, and precision issues.

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