Examples

Basic Graph Operations

d-Separation

using CausalDynamics, Graphs, DAGMakie, CairoMakie

# Create a graph: Z → X → Y, Z → Y
g = DiGraph(3)
add_edge!(g, 1, 2)  # Z → X
add_edge!(g, 1, 3)  # Z → Y
add_edge!(g, 2, 3)  # X → Y

# X and Y are d-separated by Z
d_separated(g, 2, 3, [1])  # true

false

Ancestors and Descendants

# Get ancestors of a node
ancestors = get_ancestors(g, 3)  # {1, 2}

# Get descendants of a node
descendants = get_descendants(g, 1)  # {2, 3}

Set{Int64} with 2 elements:
  2
  3

Identification

Backdoor Criterion

# Find backdoor adjustment set
adj_set = backdoor_adjustment_set(g, 2, 3)  # Set([1])

# Check if backdoor adjustment is possible
is_backdoor_adjustable(g, 2, 3)  # true

fig = plot_backdoor_paths(g, 2, 3; node_labels = ["Z", "X", "Y"])
fig

Frontdoor Criterion

using CausalDynamics, Graphs, DAGMakie, CairoMakie

# Frontdoor example: U → X → M → Y, U → Y
g_frontdoor = DiGraph(4)
add_edge!(g_frontdoor, 1, 2)  # U → X
add_edge!(g_frontdoor, 1, 4)  # U → Y
add_edge!(g_frontdoor, 2, 3)  # X → M
add_edge!(g_frontdoor, 3, 4)  # M → Y

# Find frontdoor mediator sets (each set is a valid Z)
mediator_sets = find_frontdoor_mediators(g_frontdoor, 2, 4)  # [Set([3])]
mediator_nodes = reduce(union, mediator_sets; init = Set{Int}())

fig = plot_causal_graph(
    g_frontdoor;
    node_labels = ["U", "X", "M", "Y"],
    highlight_nodes = mediator_nodes,
)
fig

SCM Framework

GraphSCM

using CausalDynamics, Graphs

# Create a GraphSCM
g = DiGraph(2)
add_edge!(g, 1, 2)

equations = Dict(
    1 => (u) -> u,
    2 => (x, u) -> x + u
)

exogenous = Set([1])

scm = GraphSCM(g, equations, exogenous)

GraphSCM(SimpleDiGraph{Int64}(1, [[2], Int64[]], [Int64[], [1]]), Dict{Int64, Function}(2 => Main.var"Main".var"#5#6"(), 1 => Main.var"Main".var"#3#4"()), Set([1]))

Discrete-time CDM

using CausalDynamics, Random

cdm = DiscreteTimeCDM(
    [:a, :y];
    initialise = (rng) -> (a = 0.0, y = 0.0),
    sample_noise = (rng, state, t) -> (u_a = randn(rng), u_y = randn(rng)),
    step = (state, t, noise, intervention) -> begin
        a = intervention_value(intervention, :a, t, 0.5 * state.a + noise.u_a)
        y = 2a + noise.u_y
        (a = a, y = y)
    end,
)

T = 30
factual = simulate(cdm, T; rng = Random.Xoshiro(1))
cf = counterfactual(cdm, factual.noise; intervention = do_sequence(:a, fill(1.0, T)))
(factual.T, length(factual.series[:y]), length(cf.series[:y]))

(30, 30, 30)

The CDCS book Chapter 28 works the confounded protein / treatment example with this API.

For more examples, see the package's examples/ directory. For DAG layout and theming beyond these façades, see DAGMakie.jl.