Identify Probability of Request Originating from Bad User
Overview
This question evaluates probabilistic reasoning and statistical inference skills, specifically application of Bayes' theorem, handling class imbalance and differing activity rates, estimation of event-origin probabilities, and use of observational features for classification within the Statistics & Math domain.
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Aug 4, 2025, 10:55 AM
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Statistics & Math
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Measuring Abuse in Friend-Requests: Bayes, Identification, and Precision
Scenario
A social-network platform wants to measure and control abuse. Five percent of users are classified as "bad" and, on average, each bad user sends 10× as many friend-requests as a good user.
Tasks
- Compute the probability that a randomly selected friend-request came from a bad user.
- Using only existing event logs, propose a method to identify the likely bad users.
- With additional features (e.g., request timing, acceptance rate), write an expression for P(good | request features) using Bayes' theorem.
- If you must shrink the confidence interval (CI) of that probability estimate to one-tenth its current width, what changes in data collection or analysis would you make?
Hints
- Apply Bayes’ rule and reason about class imbalance and different activity rates.
- Use unsupervised/weakly supervised signals from logs; normalize for exposure (tenure/active days).
- CI width typically shrinks as 1/sqrt(n); consider variance-reduction techniques.
Solution
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