Associations.jl integration (discovery → identification)

CausalDynamics.jl does not implement causal discovery. Associations.jl (formerly CausalityTools.jl) supplies association measures, independence tests, PC, and OCE graph inference. This package bridges discovered structure to identification APIs.

Load the extension:

using CausalDynamics
using Associations
using DataFrames  # required together with Associations

Pattern: tabular PC → backdoor

using CausalDynamics, Associations, DataFrames, Random, StableRNGs

rng = StableRNG(1)
n = 2000
z = randn(rng, n)
x = 0.8 * z .+ 0.3 * randn(rng, n)
y = 0.7 * x .+ 0.5 * z .+ 0.3 * randn(rng, n)
df = DataFrame(z = z, x = x, y = y)

ĝ = infer_pc_graph(df, [:z, :x, :y]; verbose = false)
confounders, ok = prepare_from_discovery(ĝ, :x, :y; complete = true)
# confounders == [:z], ok == true

PC returns a CPDAG (partially directed graph). Pass complete=true to cpdag_to_dag when a fully oriented DAG is required before backdoor adjustment.

Pattern: OCE → temporal identification

# Bivariate VAR-like series (vectors, one per variable)
ts = [x₁, x₂]
spec = infer_oce_temporal_spec(ts, [:x₁, :x₂]; verbose = false)
u = unroll_temporal_dag(spec, T = 5)
adj = temporal_backdoor_adjustment_nodes(u, :x₁, 1, :x₂, 2)

OCE embedding lags in parents_τs map to TemporalDAGSpec lags via oce_parents_to_temporal_spec (lag = abs(τ)).

One-shot helper

confounders, ok = discover_and_prepare(
    df, :x, :y;
    method = :pc,
    names = [:z, :x, :y],
    complete = true,
)

What stays in Associations

Independence / association estimators (association, independence, …)
PC, OCE, CCM, transfer entropy, and related tests
FCI, GES, PCMCI (use other tools or future Associations releases)

IEE (Associations-backed; reference port retained)

Interventional Embedding Entropy [@shi2026interventional] ranks IntDC edges from observational series. With Associations loaded, mi = :auto uses KSG1; use mi = :reference for the MATLAB-faithful port:

using CausalDynamics, Associations, DataFrames

scores = iee_score_matrix([x, y]; p = 2, k = 2)  # mi=:auto
spec = iee_to_temporal_spec(scores, [:x, :y]; threshold = 0.05, lag = 1)
u = unroll_temporal_dag(spec, 5)

See Methods adoption for ODE parent ranking and sensitivity.

What stays in CausalDynamics

backdoor_adjustment_set, d_separated, frontdoor, IV
DiscreteTimeCDM, counterfactual, g_computation
TMLE / RxInfer estimation bridges after identification

Executable recipe: examples/discovery_to_identification.jl.

See the CDCS book — Causal Discovery for narrative context.