---

name: bbvi_variance_reduction description: Compute BBVI Rao-Blackwellized and score-function control-variate gradient estimators with variance diagnostics.

BBVI Variance Reduction

When To Use

Use this skill after forming BBVI score-function terms when you can identify local model terms for a variational factor or want to apply the paper's score-function control variate. It preserves black-box behavior because it requires only local log-density values and score functions.

Do not use it to update parameters or to claim variance reduction without numeric diagnostics.

Inputs

• score: sample-by-parameter score values for one variational factor.
• local_signal: per-sample local learning signal for that factor.
• full_signal: optional per-sample full learning signal for naive comparison.

Outputs

• rao_blackwell_terms and rao_blackwell_estimate.
• control_variate_scale and control_variate_estimate.
• variance: naive, Rao-Blackwellized, and control-variate empirical variances.
• variance_reduction_ratio: naive variance divided by control-variate variance when available.

Workflow

1. Normalize scores and validate sample counts.
2. Compute Rao-Blackwellized local terms as score * local_signal.
3. Estimate the control-variate scale by aggregated covariance divided by aggregated score variance.
4. Compute corrected terms as local terms minus a_hat * score.
5. Report variance diagnostics over per-sample term norms.

Validation

Run:

python tests/test_variance_reduction.py

Limitations

The caller must supply valid local terms. This skill does not infer a Markov blanket from an arbitrary model graph.