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This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Model comment counts and detect anomalies

Quick Overview

This question evaluates competency in statistical modeling of heavy-tailed count data, model selection and comparison, and the formulation of robust monitoring metrics for anomaly detection, testing both theoretical understanding and applied data-science skills.

Modeling Heavy-Tailed Comment Counts and Robust Monitoring

You are analyzing daily comment counts at the post–day level. The distribution is heavy-tailed. From a recent period you observe:

Sample mean = 4
Sample variance = 50

Tasks:

(a) Test whether a Poisson model is appropriate. If not, propose an alternative (negative binomial or discrete lognormal/Poisson–lognormal) and outline how to estimate parameters.

(b) Compare model fits using likelihood-based tests (likelihood ratio for nested models; Vuong test for non-nested models). Explain which tail behavior each model captures.

(c) Define robust monitoring metrics (e.g., trimmed mean, P50/median, Gini) and specify control limits suitable for detecting manipulation (e.g., purchased comments) under heavy tails.

(d) Suppose the daily 99th percentile (P99) suddenly increases 3× while the median (P50) remains stable. Propose a practical rule to trigger investigation while minimizing false alarms.

Quick Overview

Modeling Heavy-Tailed Comment Counts and Robust Monitoring

You are analyzing daily comment counts at the post–day level. The distribution is heavy-tailed. From a recent period you observe:

Sample mean = 4

Sample variance = 50

Tasks:

(a) Test whether a Poisson model is appropriate. If not, propose an alternative (negative binomial or discrete lognormal/Poisson–lognormal) and outline how to estimate parameters.

(b) Compare model fits using likelihood-based tests (likelihood ratio for nested models; Vuong test for non-nested models). Explain which tail behavior each model captures.

(c) Define robust monitoring metrics (e.g., trimmed mean, P50/median, Gini) and specify control limits suitable for detecting manipulation (e.g., purchased comments) under heavy tails.

(d) Suppose the daily 99th percentile (P99) suddenly increases 3× while the median (P50) remains stable. Propose a practical rule to trigger investigation while minimizing false alarms.

Model comment counts and detect anomalies

Quick Overview

Modeling Heavy-Tailed Comment Counts and Robust Monitoring

Solution

Comments (0)

Model comment counts and detect anomalies

Quick Overview

Modeling Heavy-Tailed Comment Counts and Robust Monitoring

Solution

Comments (0)