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name: sliced-gaussian-large-scale description: "Fast structured POT alternatives for sliced, Gaussian, GMM, low-rank, BSP, stochastic, semidiscrete, SGOT, COOT, and other large-scale optimal transport workflows." disable-model-invocation: true metadata: disco-role: operating license: MIT

POT sliced, Gaussian, and large-scale alternatives

Use this sub-skill when a POT task asks for a faster or more structured alternative to dense exact optimal transport: sliced or spherical sliced Wasserstein distances and plans, Gaussian or GMM Bures-Wasserstein maps and plans, low-rank/Nystroem/factored approximations, BSP bijections, stochastic or semidiscrete solvers, SGOT, COOT, or one-dimensional DMMOT-style barycenter notes.

Read references/api-reference.md when checking verified signatures, default parameters, input shapes, return values, and module ownership for sliced, Gaussian/GMM, and large-scale APIs.

Read references/workflows.md when replacing dense OT with sliced approximations, controlling projection variance, building sliced transport plans, using spherical sliced distances, or validating a large-problem approximation against a tiny baseline.

Read references/gaussian-gmm.md when inputs are Gaussian means/covariances or GMM component parameters and the goal is a Bures distance, affine Gaussian map, GMM component plan, GMM map, density, or family-level barycenter without discretizing samples.

Read references/large-scale-solvers.md when selecting among low-rank Sinkhorn, Nystroem kernels, factored OT, BSP-OT, semidiscrete OT, stochastic dual solvers, SGOT, COOT, and DMMOT notes for larger or structured problems.

Read references/troubleshooting.md when sliced estimates vary by seed, covariance or GMM shapes fail, optional low-rank/BSP dependencies are missing, stochastic settings diverge, or memory usage grows unexpectedly.

Run scripts/sliced_gaussian_smoke.py with python scripts/sliced_gaussian_smoke.py --mode all to check a local POT install against deterministic tiny sliced, Gaussian, GMM, and low-rank fixtures before adapting these workflows.

Route quickly

• Random projections or high-dimensional samples: prefer ot.sliced.sliced_wasserstein_distance, ot.sliced.max_sliced_wasserstein_distance, spherical variants, or ot.solve_sample(..., method="sliced" | "max_sliced") when a scalar approximation is enough.
• Approximate plans from projections: use ot.sliced.min_sliced_transport_plan or ot.sliced.expected_sliced_plan; validate plan mass and treat projection count/seed as approximation controls.
• Gaussian parameters: use ot.gaussian.bures_wasserstein_distance, ot.gaussian.bures_wasserstein_mapping, high-dimensional Gaussian helpers, or Bures barycenters.
• GMM parameters: use ot.gmm.gmm_ot_plan, ot.gmm.gmm_ot_loss, ot.gmm.gmm_ot_apply_map, and ot.gmm.gmm_barycenter_fixed_point to avoid sample discretization.
• Large sample clouds: compare ot.lowrank.lowrank_sinkhorn, ot.solve_sample(..., method="lowrank" | "nystroem" | "factored" | "bsp"), ot.factored.factored_optimal_transport, and ot.bsp.compute_bspot_bijection against a tiny dense baseline before scaling.
• Structured matrix/operator tasks: use semidiscrete OT for continuous-to-atomic maps, stochastic dual solvers for mini-batch regularized OT, SGOT for spectral operators, COOT for row/feature alignment, and DMMOT only for one-dimensional grid multi-marginal barycenter-style problems.

Boundaries

Route balanced exact EMD/Sinkhorn fundamentals, cost-matrix construction basics, and generic OTResult usage to core-solvers. Route domain adaptation estimator classes to domain-adaptation. Route backend installation, mixed backend arrays, GPU claims, and batch solvers to backend-and-batch. This sub-skill documents large-scale and structured alternatives; it does not claim optional-backend or GPU verification beyond the NumPy-backed evidence summarized here.