Design a Work-Together Distance Between Any Two Employees of a Company

Design a "people distance" `d(u1, u2)` between any two users in a company that quantifies how much the two of them work together. A smaller distance should mean a closer working relationship. This was a 60-minute ML design round for a machine learning engineer role. The prompt gives no more detail, so you drive the framing: decide what the distance is for, which signals it can use, how to learn and evaluate it, and how to serve it for every pair of employees. ```hint Define "working together" first Before choosing a model, list the observable events inside a company that show two people work together, and decide whether you have any labels at all or must build proxy labels. ``` ```hint Evaluating without ground truth Think about which future behaviour a good distance computed today should predict, and how you would hold that behaviour out in time. ``` ### Clarifying Questions - What consumes the distance: ranking search results or documents, people suggestions, expertise finding, or something else? Does the consumer need a true metric (symmetric, satisfying the triangle inequality) or only a ranking score? - Which signals is the system permitted to use (org chart, calendar metadata, document co-editing, comments and mentions, chat or email metadata), and is message content off limits? - How large are the companies, in employees per customer, and how fresh must the distance be? - Should the distance be symmetric, and should recent collaboration count more than old collaboration? ### What a Strong Answer Covers - A framing tied to a concrete consumer and an explicit definition of closeness - A signal inventory with normalization for event size, time decay, and privacy and permission limits - A graph-based baseline and a learned model, with proxy labels and a leakage-free time split - Offline and online evaluation that does not depend on ground truth that does not exist - Serving every pair without computing all N^2 distances, plus cold start for new hires - Monitoring for reorganizations and drift ### Follow-up Questions - How do you assign distances for a new hire with no interactions yet? - Two people never interact directly, but both work closely with the same third person. How does your design handle that? - How do you keep the distance from exposing private relationships, such as a confidential one-on-one or a private channel? - After a reorganization, how quickly does your distance adapt, and how would you detect that it has gone stale?