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Meta·Data Scientist·Technical Phone Screen·Senior

Senior
Jul 2026

Summary

Meta data scientist interview with a pretty involved stats/ML question around Bayesian classification. The whole thing centered on a single meaty problem, which I wasn't expecting to go as deep as it did.

Questions Asked (1)

Q1

You have a population of reviewers and limited labels. Propose a classification rule using Bayes' theorem to decide if a reviewer is lazy versus careful, derive the false-positive and false-negative rates for that rule, and then explain how those error rates change if every reviewer is required to complete a large fixed number of reviews.

A/B Testing & ExperimentationProduct Analytics & MetricsTechnical Trade-offs
Author's notes

Took me a minute to get my footing.

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AI HintsAI Generated

Suggested Approach

Start by framing the problem as a binary classification task with a latent variable (lazy vs. careful) and observable features (e.g., review length, time spent, agreement with gold labels). Use Bayes' theorem to derive the posterior probability of laziness given features, then set a decision threshold to minimize expected cost or achieve a desired error trade-off. Derive false-positive and false-negative rates from the distributions of the features under each class, and analyze how increasing the fixed number of reviews per reviewer reduces the variance of the feature estimates, thereby improving classification accuracy and reducing both error rates.

Pro tip: Emphasize that the choice of threshold depends on the business cost of false positives vs. false negatives—e.g., falsely labeling a careful reviewer as lazy may demotivate them, while missing a lazy reviewer harms data quality. Also, note that requiring a large fixed number of reviews can introduce a selection bias if lazy reviewers drop out, so consider the missing data mechanism.

1. Define the classification problem and features

Define 'lazy' vs. 'careful' as a latent binary variable. Choose observable features (e.g., average review length, time per review, agreement with gold labels) that are indicative of the class. Assume prior probabilities P(lazy) and P(careful) based on domain knowledge or historical data.

2. Apply Bayes' theorem to compute posterior

For a given feature vector x, compute P(lazy | x) = P(x | lazy) P(lazy) / P(x). Model the likelihoods P(x | lazy) and P(x | careful) using appropriate distributions (e.g., Gaussian for continuous features). Then decide 'lazy' if P(lazy | x) > threshold, where threshold is chosen based on cost asymmetry.

3. Derive false-positive and false-negative rates

False positive rate (FPR) = P(decide lazy | careful) = ∫ P(decide lazy | x) P(x | careful) dx. False negative rate (FNR) = P(decide careful | lazy) = ∫ P(decide careful | x) P(x | lazy) dx. These integrals can be computed analytically for simple distributions or estimated via simulation.

4. Analyze effect of fixed large number of reviews

If each reviewer completes N reviews, the feature estimates (e.g., mean review length) become more precise, reducing variance. This typically makes the class-conditional distributions more separated, allowing a better threshold and reducing both FPR and FNR. However, if lazy reviewers strategically mimic careful ones when forced to do many reviews, the separation may not improve as much.

5. Discuss practical implications and trade-offs

Summarize how the rule can be implemented, the impact of the fixed N on error rates, and potential pitfalls such as non-stationarity, adversarial behavior, and the cost of misclassification. Suggest validating the model on a held-out set and monitoring performance over time.

Key Points to Mention

  • Bayes' theorem and the need for prior probabilities and likelihood models.
  • Choice of decision threshold based on asymmetric costs of false positives vs. false negatives.
  • How increasing the number of reviews per reviewer reduces variance of feature estimates, improving classification accuracy.
  • Potential for adversarial behavior: lazy reviewers may change behavior when required to do many reviews.
  • The importance of validating the classifier with a confusion matrix and ROC curves.
  • Consideration of selection bias if lazy reviewers drop out when faced with a large fixed number of reviews.

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