Bytedance·Machine Learning Engineer·Technical Phone Screen·Senior

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Apr 2026Remote

Summary

Bytedance ML engineer interview that went deep on implementing evaluation metrics from scratch. The AUC-ROC question was the main focus and they wanted both the algorithmic derivation and the probabilistic interpretation, not just code.

Questions Asked (1)

Implement AUC-ROC from scratch given arrays of true binary labels and predicted scores. Walk through two approaches: integrating the ROC curve via sorted thresholds, and the pairwise ranking probability interpretation. Handle tied scores correctly and discuss complexity.

Algorithms & Data StructuresTechnical Trade-offsProduct Analytics & Metrics

Author's notes

This one took longer than I expected to set up cleanly.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and edge cases, then present the two approaches: first, the threshold-based ROC integration using sorted scores, and second, the pairwise ranking probability interpretation. For each, explain the algorithm, handle ties correctly, and analyze time and space complexity. Conclude by comparing the approaches and discussing practical considerations.

Pro tip: Mention that the pairwise approach can be computed in O(n log n) using a Fenwick tree or merge sort, which is more efficient than the naive O(n^2) and often preferred in practice. Also, note that AUC-ROC is equivalent to the Mann-Whitney U statistic, which reinforces the ranking interpretation.

1. Clarify and Define

Restate the problem: given true binary labels and predicted scores, compute AUC-ROC. Define AUC as the area under the ROC curve, which plots TPR vs. FPR across thresholds. Mention that AUC equals the probability that a randomly chosen positive instance is ranked higher than a randomly chosen negative instance.

2. Threshold-Based Approach

Sort instances by predicted score descending. Iterate through thresholds, updating TP, FP, TN, FN, and compute TPR and FPR at each distinct score. Use the trapezoidal rule to integrate the ROC curve. Handle ties by grouping equal scores and updating counts only after processing all instances with the same score.

3. Pairwise Ranking Approach

Compute the number of concordant pairs (positive score > negative score) plus 0.5 times the number of ties (positive score = negative score), divided by the total number of positive-negative pairs. This directly gives the AUC. Explain that this is equivalent to the Mann-Whitney U statistic.

4. Handle Ties Correctly

In the threshold approach, ties are handled by not updating the ROC point until all instances with the same score are processed, ensuring the curve is stepwise. In the pairwise approach, ties contribute 0.5 to the numerator. Emphasize that ignoring ties leads to incorrect AUC.

5. Complexity Analysis and Comparison

For the threshold approach, sorting takes O(n log n) and the scan is O(n), so overall O(n log n) time and O(n) space. For the pairwise approach, the naive implementation is O(n^2), but can be optimized to O(n log n) using a Fenwick tree or merge sort to count inversions. Discuss trade-offs: threshold approach is simpler to implement and interpret, while pairwise approach can be more efficient with the right data structures and directly reflects the ranking interpretation.

Key Points to Mention

AUC-ROC definition and its probabilistic interpretation
ROC curve construction: TPR vs. FPR across thresholds
Trapezoidal rule for area calculation
Handling tied scores: grouping in threshold approach, 0.5 weight in pairwise
Time and space complexity: O(n log n) for both with optimizations
Equivalence to Mann-Whitney U statistic and ranking probability

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