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name: unbalanced-partial description: "Use POT unbalanced and partial optimal transport solvers when masses may differ, outliers should be ignored, or only part of the mass should move." disable-model-invocation: true metadata: disco-role: operating license: MIT

POT unbalanced and partial optimal transport

Use this sub-skill when a POT task is about relaxed marginals, unequal total mass, explicit transported mass, outlier rejection, unbalanced barycenters, or regularization paths for unbalanced OT.

Route the request

• Read references/api-reference.md when choosing between ot.unbalanced.*, ot.partial.*, ot.regpath.*, and unified ot.solve(..., unbalanced=...) APIs or when checking signatures, return shapes, and parameter meanings.
• Read references/workflows.md when implementing an end-to-end recipe: compare UOT against partial OT for outliers, stabilize entropic partial OT, build an unbalanced barycenter, use 1D helpers, or sample an L2-UOT regularization path.
• Read references/troubleshooting.md when a plan has unexpected mass, m is infeasible, reg/reg_m are confused, a divergence name is rejected, small entropic regularization produces NaNs, or optional backend behavior is unclear.
• Run scripts/unbalanced_partial_smoke.py after installing POT to check deterministic NumPy UOT/partial/barycenter/regpath behavior; the legacy --include-optional-uot-1d flag attempts the optional autodiff-backed 1D UOT check and records a structured skip when that backend is unavailable.

Boundaries

This sub-skill owns unbalanced and partial OT semantics: sinkhorn_unbalanced, sinkhorn_unbalanced2, mm_unbalanced, lbfgsb_unbalanced, uot_1d, barycenter_unbalanced, partial_wasserstein, entropic_partial_wasserstein, partial_wasserstein_1d, unbalanced/partial GW routing notes, and ot.regpath L2-UOT paths.

Route balanced exact OT, balanced Sinkhorn basics, distance matrix construction basics, and OTResult fundamentals to core-solvers. Route detailed Gromov-Wasserstein and fused GW modeling to gromov. Route sliced high-dimensional UOT variants and Gaussian/GMM approximations to sliced-gaussian-large-scale. Route optional backend installation, batch solvers, and mixed-array backend issues to backend-and-batch.

Operating checklist

1. Validate that weights are one-dimensional, nonnegative, finite, and aligned with the rows/columns of the cost matrix.
2. Decide the mass model: UOT relaxes marginal constraints with reg_m/unbalanced; partial OT fixes transported mass with m.
3. Scale or inspect the cost matrix before choosing reg and reg_m; the same numeric parameters mean different things after cost rescaling.
4. Validate the returned plan: shape (len(a), len(b)), finite nonnegative entries, transported mass, and row/column sums appropriate to UOT or partial constraints.
5. For entropic partial OT at small reg, prefer method="sinkhorn_log" and confirm finite output plus plan.sum() ≈ m.