Anomaly Detection — Interview Grill

40 questions on AD methods, when each works, evaluation. Drill until you can answer 28+ cold.

A. Setup

1. Three problem variants in AD? Unsupervised (only normal), semi-supervised (mostly normal + some labels), supervised (labeled both classes).

2. Why is AD usually unsupervised in practice? Anomalies are rare. Hand-labeling is expensive. Often you don't even know what new anomaly types exist.

3. Why is AD different from imbalanced classification? Imbalanced classification has labeled examples of both classes. AD has only (or mostly) normal data.

B. Statistical methods

4. Z-score rule of thumb? $|z|>3$ → outlier. Assumes Gaussian.

5. Modified z-score? $M=0.6745(x-\mathrm{median})/\mathrm{MAD}$. Robust to outliers themselves. Threshold $|M|>3.5$.

6. IQR rule? $x<Q_1-1.5\mathrm{IQR}$ or $>Q_3+1.5\mathrm{IQR}$. Box-plot rule.

7. Mahalanobis distance? $D_M=\sqrt{(x-\mu {)}^{\top }{\Sigma }^{-1}(x-\mu )}$. Multivariate; accounts for correlations.

8. Why does Mahalanobis beat per-feature z-score? Captures multivariate anomalies that look "normal" feature-by-feature but anomalous jointly.

C. Density-based

9. KDE for AD? Estimate density via Gaussian kernels around training points. Flag low-density test points.

10. KDE limitation? Curse of dimensionality. Doesn't work for $d>10$ or so.

11. LOF — what does it measure? Local Outlier Factor. Compares point's local density to its $k$-NN's local density. Anomaly = much lower density than neighbors.

12. When is LOF better than global density? Data with varying density across regions. A point can be locally anomalous (sparse for its neighborhood) even if globally typical.

D. Isolation Forest

13. Isolation Forest core idea? Anomalies isolate quickly under random splits. Build random trees; short path = anomaly.

14. How is the tree built? Random feature → random split value in [min, max] → recurse until leaves are single points.

15. Anomaly score formula? $s(x)=2^{-E(h(x))/c(n)}$. $E(h)$ expected path length; $c(n)$ normalization. Score ~1 = anomaly; ~0.5 = normal.

16. Why is IF a strong default? No distance metric (works in high dim); sub-linear training (random subsamples); easy to parallelize; minimal tuning.

17. IF on time-series? Doesn't capture temporal structure. Need feature engineering (lags, rolling stats) or sequential method.

E. One-Class SVM

18. OC-SVM idea? Find boundary in feature space (kernel) separating data from origin with max margin. Inside → normal.

19. $\nu$ parameter? Upper bound on training error fraction. Lower bound on support vectors. Trade-off knob.

20. When use OC-SVM? Roughly compact normal data, low-to-moderate $n$, RBF kernel for non-linear boundary.

21. OC-SVM scaling issue? $O(n^2)$ memory for kernel matrix. Doesn't scale beyond $\sim 10^5$ points.

F. Autoencoder-based

22. AE-based AD principle? Train AE on normal data → minimize reconstruction error. Test point with high reconstruction error → anomaly.

23. Why does AE work for AD? AE learns the manifold of normal data. Anomalies don't fit → poor reconstruction.

24. Risk of over-powerful AE? Reconstructs anomalies too well → no error gap. Regularize: bottleneck size, denoising, ${\ell }_1$ on activations.

25. VAE for AD? Use likelihood under VAE prior + decoder, or reconstruction error. Probabilistic interpretation.

26. AE for images vs text? Same recipe; convolutional architecture for images, transformer/LSTM for sequences.

G. Modern / foundation-model AD

27. Embedding-based AD? Use pretrained encoder (CLIP for images, sentence encoder for text). Compute distance to "normal" centroid. Flag far-from-centroid.

28. Why does this work? Pretrained encoders capture semantically meaningful representations; anomalies often semantically different from normal.

29. Density-ratio approach? Train binary classifier: "this is normal" vs "this might not be." Output probability used as anomaly score.

H. Time-series AD

30. Three types of time-series anomalies? Point (single value), contextual (normal globally, anomalous in context), collective (a pattern of values jointly anomalous).

31. STL decomposition for AD? Decompose into trend + seasonal + residual. Flag outliers in residual (which should be ~iid noise).

32. ARIMA-based AD? Fit ARIMA model. Flag actual values far from forecast (large prediction error).

33. Matrix profile? Cross-correlation across all subsequences. Anomaly = subsequence with low max similarity to all others (no "neighbor").

34. Spectral residual? Signal processing approach. Used by Twitter, Microsoft. Compute spectral residual; anomalies show as spikes.

I. Evaluation

35. Why is AUC misleading for AD? Severe class imbalance (~1% anomalies) → AUC near 1 even for poor classifiers. Most negatives easy.

36. AUPRC — better why? Focuses on positive class. Captures precision-recall trade-off where it matters.

37. Precision @ k? Of top-$k$ flagged, how many are real anomalies? Direct utility metric.

38. Recall at fixed false-alarm rate? What fraction of anomalies caught at, say, 1% false positive rate? Matches operational reality.

39. Cost-asymmetric scoring? Different costs for FP and FN. Optimize threshold for cost minimization, not balanced metric.

40. How to evaluate without labels? Hand-label small subset; inject synthetic anomalies; production validation rate (track flagged → confirmed ratio).

Quick fire

41. Z-score threshold? 3. 42. IQR multiplier? 1.5. 43. Isolation Forest paper year? 2008. 44. OC-SVM scales to? $\sim 10^5$. 45. AE reconstruction error? $\Vert x-g(f(x)){\Vert }^2$. 46. AUPRC vs AUC? Better for severe imbalance. 47. LOF threshold typical? $>1$. 48. DBSCAN for AD? Noise points = anomalies. 49. Time-series anomaly with normal value? Contextual. 50. Embedding-based AD? Distance to normal centroid.

Self-grading

If you can't answer 1-15, you don't know AD methods. If you can't answer 16-30, you'll struggle on AD architecture / time-series questions. If you can't answer 31-40, frontier-lab AD interviews will go past you.

Aim for 30+/50 cold.