Edward2

Per-target obligations of Transpilation correctness for \(\mathsf{T} = \mathrm{Edward2}\).

Semantics

Edward2's denotational semantics is the trace semantics of Tran, Hoffman, Saurous, Brevdo, Murphy, and Blei (2018) instantiated on top of TensorFlow Probability's tfp.distributions hierarchy. A program is a Python function whose edward2.<Family>(...) calls register RandomVariable sites in an ed.tape context; the log-density probe is

with ed.tape() as t:
    model(...)
log_p = sum(rv.distribution.log_prob(rv.value) for rv in t.values())

returning the joint log-density of the trace.

Unconstrained-space change of variables

Identity at the renderer level. TFP handles bijector-based reparametrizations at inference time; \(\Psi_{\mathsf{Edward2}} = \mathrm{id}\) for the model-side denotation.

Family parameterizations

Edward2 families are TFP Distribution classes exported via edward2. The QVR ↔ Edward2 arg mapping is identity for every family that has a corresponding TFP class. \(\pi_{F, \mathsf{Edward2}} = \mathrm{id}\) and \(c_{F, \mathsf{Edward2}} = 0\).

Per-construct emit

Sample / observe. <name> = edward2.<Family>(<args>, sample_shape=[B0, B1, ...], name="<name>") for latents and observed variables. The sample_shape argument carries the batch-axis shape.

Plate. Captured via sample_shape=[B]. By TFP's documented broadcasting semantics, sample_shape=[B] produces a \(B\)-fold i.i.d. product (TFP user guide on "Shapes and Broadcasting").

Marginalize. Explicit-latent rewrite (head the marginalization discussion).

Score / let / return. Edward2 has no native factor primitive; the renderer raises UnsupportedConstruct(["construct:ScoreStep"]) if a score step is encountered. Deterministic let-bindings emit as Python assignments. The function returns the named random variables.

Acceptance

  • Tier 1 pipeline composition. Structural checks cover the emitted model function and the renderer pipeline.
  • Tier 2 external syntax. Python's AST parser accepts the generated modules in the external-validation matrix.
  • Tier 3 numeric equivalence. For selected fixtures, the ed.tape-based probe is compared with the QVR reference on the shared finite grid and tolerance described in the test contract.

References

  • Dustin Tran, Matthew Hoffman, Rif A. Saurous, Eugene Brevdo, Kevin Murphy, and David M. Blei. 2018. Simple, distributed, and accelerated probabilistic programming. In Neural Information Processing Systems, 7598-7609. https://arxiv.org/abs/1810.03958