RxInfer and GraphPPL integration

CausalDynamics.jl handles identification (backdoor adjustment sets, prepare_for_rxinfer). GraphPPL.jl specifies the observational generative head; RxInfer.jl runs variational message-passing inference.

Nonlinear bistable state-space inference

The extension also provides infer_bistable_state_space, an explicit nonlinear state-space model for the CDCS bistable benchmark. Its transition is represented as a GraphPPL Delta factor:

μ[t] ~ bistable_transition(x[t], a[t], c[t], r[t], Δt) where {
    algorithm = Linearization()
}

This is the RxInfer 6 notation. The extension selects the same linearisation through meta on RxInfer 4 and 5, so callers use the same package API across these versions. See the RxInfer migration guide.

RxInfer therefore performs Gaussian variational message passing with local linearisation of the cubic drift; this is a nonlinear factor rather than a pre-filtered observed proxy. The result exposes posterior state means and variances through state_means and state_variances.

result = infer_bistable_state_space(y, a, c, r; iterations = 20)
result.state_means
result.state_variances

The method estimates latent states conditional on declared transition and noise parameters. It does not by itself identify interventions, learn regime mechanisms, or establish causal validity. Compare its posterior predictive and interventional rollouts with the particle-filter reference before making policy claims.

Choosing an inference backend

Use the RxInfer backend when the transition and observation factors admit a smooth local linearisation and fast repeated posterior updates matter. Use the Laplace or assumed-density filter for a lightweight baseline, particle filtering when the posterior is strongly non-Gaussian or multimodal, and Turing/NUTS when joint parameter uncertainty or a richer likelihood is the primary target. The certificate returned by infer_bistable_state_space records the backend, factor type, linearisation method and numerical settings so these choices remain auditable.

Load the extension:

using CausalDynamics
using RxInfer   # activates CausalDynamicsRxInfer

Workflow

Build a DAG and attach tabular data (DataFrame or NamedTuple).
prepare_for_rxinfer(g, X, Y; node_names=...) — confounders + identifiability flag.
infer_backdoor_effect(g, data, X, Y; ...) — Frisch–Waugh partialing in Julia, then a conjugate GraphPPL head and VI for τ.

Confounders in the identified adjustment set are partialled out of outcome and treatment (residualise_backdoor) so the RxInfer head is a single conjugate slope τ on residualised (y, x). A full multi-coefficient GraphPPL regression with latent β vectors is reserved for a later release (non-conjugate without custom initialisation).

Hierarchical Bayesian heads (random intercepts / partial pooling on residualised ATE) belong in application GraphPPL models or optional demos — not in CausalDynamics core and not as a substitute for identify or CausalTargeted MSM / LMTP. Generative nesting uses RandomEffectSpec / simulate_hierarchical_intercept_ate; see Hierarchical / nested units.

using CausalDynamics, RxInfer, Graphs, DataFrames, Random

g = DiGraph(3)
add_edge!(g, 1, 2)
add_edge!(g, 1, 3)
add_edge!(g, 2, 3)
names = Dict(1 => :Z, 2 => :X, 3 => :Y)
data = DataFrame(Z=randn(100), X=randn(100), Y=randn(100))

result = infer_backdoor_effect(g, data, 2, 3; node_names=names)
result.τ_mean   # posterior mean; do not use Statistics.mean(result.τ_posterior)

See examples/rxinfer_backdoor.jl in the package root.

API

Function	Role
`has_rxinfer()`	Extension loaded?
`prepare_for_rxinfer`	Identification bridge (always available)
`residualise_backdoor`	Frisch–Waugh partialing of `(y, x)` on confounders
`backdoor_graphppl_model`	GraphPPL `@model` generator (`backdoor_gaussian_ate`)
`ppl_data_from_spec`	Tabular → residualised RxInfer data tuple
`infer_backdoor_effect`	Full identify + partial + infer pipeline
`posterior_mean_τ`	Scalar mean from `τ_posterior` marginals

Naming

Identification and RxInfer façades stay in Pearl / SciML vocabulary. Temporal identity may use the closed lexicon on Terminology. Whitehead glossary terms used in the CDCS book belong in the book’s Concept Reference, not this page.

Dependencies

Optional weak dependencies: GraphPPL, RxInfer. They are not required for core CausalDynamics.

On Julia 1.13, CausalTargeted + CausalDynamics resolve with RxInfer 4, 5, and 6 under the package compat bounds; the CDCS book environment has resolved and tested RxInfer 6. Julia 1.12 remains supported by the package compat bounds. PrettyTables enters only transitively (via DataFrames / MLJ) at 2.x, matching RxInfer’s weak PrettyTablesExt. Neither owned package pins PrettyTables.

The CDCS book environment lists RxInfer explicitly and is the reference unified stack for stress notebooks (CausalTargeted stress validation).

If Pkg.resolve() still fails in an older or heavily pinned application env, check for stale Manifest pins (PrettyTables 1.x) or cap Graphs at 1.13 when RxInfer 5.x clashes with DataStructures 0.19. See AgeSCM docs/RXINFER_DEPS.md for a resolved stack example.