This is a straight Bayes calculation but I fumbled the setup for a minute because I kept second-guessing the base rate.
Use Bayes' theorem with the law of total probability. Define the prior probability of a bad user as 5%, and the likelihood ratio of friend requests as 10:1. Compute the posterior probability that a randomly chosen friend request came from a bad user.
Pro tip: Clearly state the assumption that all users send at least one friend request or that the rates are proportional; otherwise, the problem is underspecified. Also, mention that this is a classic base rate problem and the answer is not simply 5% × 10.
Let B be the event that a user is bad, and G be the event that a user is good. Given P(B) = 0.05 and P(G) = 0.95. Let R be the event that a randomly chosen friend request is from a user.
Assume each good user sends r friend requests, so each bad user sends 10r friend requests. The total expected friend requests from good users is 0.95 * r, and from bad users is 0.05 * 10r = 0.5r.
Total expected friend requests = 0.95r + 0.5r = 1.45r.
The probability that a randomly chosen friend request came from a bad user is (0.5r) / (1.45r) = 0.5 / 1.45 ≈ 0.3448 or 34.48%.
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I went straight to aggregating request volume per user and flagging statistical outliers, which felt obvious in retrospect.
Start by clarifying what 'bad actor' means in the context of the product and available event logs, then propose a framework that combines rule-based heuristics with unsupervised anomaly detection and supervised classification if labels exist. Emphasize feature engineering from raw event logs (e.g., frequency, sequence, timing) and validation via manual review or A/B testing.
Pro tip: Highlight the importance of defining a clear, measurable proxy for 'bad actor' (e.g., spam reports, account bans) and stress that any detection method must be evaluated for precision at scale to avoid alienating legitimate users.
Clarify with stakeholders what behaviors constitute bad acting (e.g., spam, fraud, abuse) and how they manifest in event logs. Establish evaluation metrics like precision@k, recall, or lift over baseline.
Analyze log data to extract user-level features such as action frequency, session patterns, sequence anomalies, time-of-day activity, and content-based signals. Consider aggregations over sliding windows.
If labeled data exists, train supervised models (e.g., gradient boosting, logistic regression). Otherwise, use unsupervised techniques like isolation forests, clustering, or autoencoders to flag outliers. Combine with rule-based filters for known patterns.
Evaluate model performance using holdout sets or manual review of top-scored users. Incorporate feedback to reduce false positives and adapt to evolving bad actor tactics.
Integrate the detection system into production with monitoring for drift and performance. Set up alerts for anomalous spikes and a process for human review and action.
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Start by defining what 'good' means in this context (e.g., a user who is likely to accept requests) and identify the relevant events: sending a request and having features like request timing and acceptance rate. Then apply Bayes' theorem to compute P(good | sent request) using prior P(good), likelihood P(sent request | good), and evidence P(sent request), incorporating the additional features as conditional probabilities or by modeling them as part of the likelihood.
Pro tip: Emphasize that the prior P(good) should be estimated from historical data or business context, and that features like request timing and acceptance rate can be used to refine the likelihood, but be cautious about assuming independence if features are correlated.
Clarify what constitutes a 'good' user (e.g., high acceptance rate, reliable) and define the events: G = user is good, R = user sent a request. Also identify additional features F1 = request timing, F2 = acceptance rate.
Write Bayes' theorem: P(G | R, F1, F2) = P(R, F1, F2 | G) * P(G) / P(R, F1, F2). Explain that we want the posterior probability of G given the request and features.
Assume conditional independence of features given G to simplify: P(R, F1, F2 | G) = P(R | G) * P(F1 | G) * P(F2 | G). Estimate each from data (e.g., P(R | G) from historical request rates of good users).
Compute P(R, F1, F2) by summing over G and not G: P(R, F1, F2) = P(R, F1, F2 | G)P(G) + P(R, F1, F2 | ¬G)P(¬G). Use the same independence assumption for ¬G.
Plug in the numbers to get P(G | R, F1, F2). Discuss how the additional features update the probability compared to using only R, and consider potential correlations or need for more sophisticated models.
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Knew the answer involved sample size but blanked on the exact relationship between width and n for a second.
Start by explaining that the width of a confidence interval is proportional to 1/√n, so reducing it to one-tenth requires a 100-fold increase in sample size. Then discuss practical ways to achieve this, such as increasing traffic allocation, extending the experiment duration, or using variance reduction techniques like CUPED, while acknowledging trade-offs.
Pro tip: Mention that simply increasing sample size may not be feasible, so combining it with variance reduction techniques (e.g., CUPED) and ensuring proper randomization can achieve the goal more efficiently. Also, highlight the importance of checking for novelty effects and ensuring the metric is stable over time.
Recall that the width of a confidence interval is inversely proportional to the square root of the sample size. To reduce the width by a factor of 10, you need 100 times more data.
Consider increasing the proportion of users exposed to the experiment, extending the experiment duration, or increasing the overall user base if possible. Also, consider running the experiment on a larger fraction of traffic.
Use methods like CUPED (Controlled-experiment Using Pre-Experiment Data) to reduce variance by using pre-experiment covariates. This can effectively increase the signal-to-noise ratio without increasing sample size.
Choose a more sensitive metric or transform the metric (e.g., log transformation) to reduce variance. Ensure proper randomization and avoid peeking to maintain validity.
Discuss the trade-offs: longer experiments may introduce seasonality effects, larger traffic allocation may impact user experience, and variance reduction techniques require additional data and assumptions.
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