The 60-second answer
Model y∈{0,1} as Bernoulli with predicted probability p: P(y|p)=p^y(1-p)^(1-y). Take the log likelihood, then negate it to obtain L=−[y log p +(1−y) log(1−p)].
Build the answer in this order
1
Start with intuition
Model y∈{0,1} as Bernoulli with predicted probability p: P(y|p)=p^y(1-p)^(1-y).
2
Write the mathematical object
Take the log likelihood, then negate it to obtain L=−[y log p +(1−y) log(1−p)].
3
State assumptions
Explain why minimizing negative log likelihood is equivalent to maximum likelihood estimation over independent examples.
4
Connect back to ML behavior
Connect logits to the numerically stable implementation: use log-sum-exp/BCE-with-logits instead of manually applying sigmoid then log.
A useful interview mental model
This is the shape of a strong answer—not a script to memorize.
01Definition
02Mechanism
03Trade-offs
04Failure modes
05When to use
Senior-level signal
- Senior answers can derive the gradient with respect to the logit and show the elegant p−y result.
- Discuss class weighting/focal loss as objective changes, not merely metric tweaks.
What the interviewer is really testing
Whether you can connect the math to optimization, uncertainty, model behavior, and a practical engineering decision.
Likely follow-up questions
What assumption makes this approach work?
When would you choose the strongest alternative instead?
What production or data failure mode changes your answer?
Common weak-answer patterns
- Reciting a definition without mechanism or assumptions.
- Claiming one technique is always better without a data regime.
- Stopping before failure modes, validation, or deployment implications.