The 60-second answer
For labels y∈{−1,+1}, the functional margin is y(w·x+b); hinge loss max(0,1−margin) penalizes points inside or beyond the wrong side of the margin. The regularized objective balances a large geometric margin (small ||w||) against training violations.
Build the answer in this order
For labels y∈{−1,+1}, the functional margin is y(w·x+b); hinge loss max(0,1−margin) penalizes points inside or beyond the wrong side of the margin.
The regularized objective balances a large geometric margin (small ||w||) against training violations.
Support vectors are the points on/inside the margin that determine the boundary; correctly classified far-away points contribute zero hinge loss.
Explain the role of C/regularization and how kernels replace explicit linear features with similarity in an implicit feature space.
A useful interview mental model
This is the shape of a strong answer—not a script to memorize.
Senior-level signal
- Senior answers distinguish hard-margin assumptions from soft-margin behavior under non-separable/noisy data.
- Discuss calibration: raw SVM scores are margins, not automatically well-calibrated probabilities.
What the interviewer is really testing
Likely follow-up questions
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.