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A guide program is a probabilistic program whose generated probability distribution approximates a model's posterior distribution. Its adjustable parameters are fitted by variational inference. The guide must assign probability only where the target allows it when minimizing $D_{\mathrm{KL}}(q\Vert p)$, but a tractable guide can still miss important target regions.

A probabilistic program maps elementary random choices to outputs and observation weights. Its mathematical meaning can be specified by the pushforward measure on outputs, normalized after conditioning when the observation has finite positive mass. Different random-choice spaces can implement the same output law.