---

name: diffusion_design description: Select and validate scalar diffusion factors for robust or heavy-tailed minimum Stein discrepancy estimators.

Diffusion Choice For Robust Estimation

Use this skill when a Minimum Stein Discrepancy recovery needs to choose the diffusion factor used inside a Stein operator. The skill is appropriate for one-dimensional scalar proxies of the paper's diffusion choices, especially Student-t heavy-tail examples and robust decaying factors for outliers.

Inputs

• Model family or recovery scenario: ordinary, student_t_heavy_tail, or robust_decay.
• Current parameter value and sample points.
• Optional hyperparameters such as scale, degrees of freedom, and decay exponent.

Outputs

• A diffusion function or JSON table of diffusion values.
• Diagnostics: min, max, positivity, finiteness, and monotonicity checks relevant to the chosen family.
• Metadata explaining why the diffusion is mechanism-faithful for the paper.

Workflow

1. Use ordinary when validating baseline Langevin KSD behavior.
2. Use student_t_heavy_tail for Section 4.2-style non-standardised Student-t recovery; values increase with distance from location.
3. Use robust_decay for Section 4.3-style corruption recovery; values decay for large absolute observations.
4. Validate all values before passing the function to a Stein-kernel loss.
5. Save the configuration and diagnostics in the recovery logs.

Validation

Run python tests/test_diffusion_design.py or validate the whole skill tree with tests. The tests check positivity, finiteness, and intended directional behavior.

Limitations

The bundled implementation returns scalar one-dimensional factors. It does not claim to validate all matrix-valued diffusion tensors in the paper.

Refinement cycle 2 note

Robust-decay ablation confirmed outlier downweighting; recovery logs should preserve near_value and far_value when validating robust diffusions.