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name: bbvi_score_function_gradient description: Compute black-box variational inference score-function ELBO gradient estimates from samples, log-density values, and variational score functions.

BBVI Score-Function Gradient

When To Use

Use this skill when implementing or auditing the core Black Box Variational Inference estimator from Ranganath, Gerrish, and Blei. It applies when you can sample from q(z | lambda), evaluate log p(x,z), evaluate log q(z | lambda), and compute grad_lambda log q(z | lambda).

Do not use it for pathwise/reparameterization gradients or for optimizer updates.

Inputs

• logp: list of scalar log-joint values, one per sample.
• logq: list of scalar variational log-density values, one per sample.
• score: list of score values. A one-dimensional list represents one scalar parameter; a two-dimensional list represents sample-by-parameter scores.

Outputs

• learning_signal: logp - logq for each sample.
• gradient_terms: per-sample score-function gradient terms.
• gradient_estimate: Monte Carlo average over samples.
• diagnostics: sample count, parameter dimension, and finite-value status.

Workflow

1. Normalize score arrays to sample-by-parameter shape.
2. Validate matching sample counts and finite numeric values.
3. Compute per-sample learning signals.
4. Multiply each score row by its learning signal.
5. Average across samples to estimate the ELBO gradient.

Validation

Run:

python tests/test_score_gradient.py

Limitations

This skill does not reduce estimator variance and does not know model structure. Use a variance-reduction skill for Rao-Blackwellization and control variates.