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When is Wasserstein distance appropriate for drift?

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Answer

  • Wasserstein-1 = 'earth mover's distance' — minimal work to move mass from P to Q.
  • Advantages: (1) sensitive to shifts (unlike KL that focuses on mode overlap).
  • (2) Works even when supports differ.
  • (3) Metric (triangle inequality).
  • (4) Meaningful units (same scale as feature).
  • Use for continuous features with ordinal/spatial meaning (prices, temperatures).
  • Drawback: expensive in high-D — use sliced Wasserstein or 1D-per-feature.
Check yourself — multiple choice
  • Random
  • Earth-mover's distance; sensitive to shifts even with different supports; metric with meaningful units; use for ordinal/spatial features; sliced version for high-D
  • Same as KL
  • Not real

Wasserstein: EMD; metric with meaningful units; sensitive to shifts.

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