Module engine 

Variational Message Passing engine.

Implements Winn & Bishop (2005) VMP for conjugate-exponential models built on three families: Gaussian (mean-unknown / precision-known), Categorical, and Dirichlet. The engine consumes a structural description via VmpConfig and runs coordinate-ascent natural-parameter updates until the ELBO / L∞ residual converges.

The algorithm is independent of the discrete factor-potential tables carried by the FactorGraph type: VMP operates purely in continuous natural-parameter space. The user is therefore required to annotate each variable with its family and each factor with its conjugate role (see VmpFactor).

High-level flow

1. Initialise each variable’s variational distribution q(v) from its prior.
2. For each iteration:
   • For every variable v in a deterministic order:
     • Accumulate contributions from every adjacent factor (natural-parameter deltas).
     • Replace q(v)’s natural parameters by prior_nat + Σ Δ.
   • Compute the ELBO.
3. Stop when |ΔELBO| < ε or the maximum natural-parameter residual < ε.

Divergence (ELBO decreasing by more than a small tolerance) is detected and surfaced as a ConvergenceFailure error so the caller does not silently consume a broken result.

Structs

VariationalMessagePassing

The VMP coordinate-ascent engine.

VmpConfig

User-facing configuration describing a VMP problem.

VmpResult

Summary of a VMP run.

Enums

Family

Variational family assigned to a variable.

VariationalState

Variational state carried for a single variable.

VmpFactor

Conjugate relationship represented by a single factor.