Stochastic VI Chain

Use this skill when a recovery or implementation needs deterministic evidence for the paper's view of stochastic VI optimization as a Markov chain. Do not use it to claim full probabilistic-programming VI training unless the gradient oracle is connected to a real model.

Inputs

• chains: positive number of independent optimization runs.
• iterations: positive number of stochastic update steps.
• dimensions: positive variational parameter dimension.
• learning_rate, noise_scale, seed, and optional optimum vector.

Outputs

• JSON containing iterates, gradients, initial_parameters, optimum, and run metadata.
• Chain-major arrays: chains x iterations x dimensions.

Workflow

1. Choose or supply a known optimum.
2. Initialize chains away from the optimum with deterministic seed control.
3. At each step, evaluate a negative-quadratic gradient plus zero-mean Gaussian noise.
4. Apply a constant-step stochastic gradient update and record the trace.
5. Use the trace for downstream Rhat, ESS, MCSE, and iterate-averaging checks.

Validation

Run:

python3 scripts/simulate_chains.py --chains 4 --iterations 120 --dimensions 5 --output /tmp/stochastic_vi_chains.json
python3 tests/test_simulate_chains.py

Limitations

The bundled simulator is a reduced proxy for optimizer dynamics. It preserves stochastic iterate behavior and trainable-parameter updates but does not replace a full model-specific ELBO gradient.