# D-separation

D-Separation is a method to find from causal DAG which variables are indendent on each other given some set of conditioned variables.

Dagitty.is_d_separatedFunction
is_d_separated(dag, x, y, cond)

Checks that X variables are independent on Y variables being conditioned on third set of variables. Three sets could be given as vectors of node labels (Symbol) or as vectors of node indices in the underlying graph. Used NetworkX d_separated implementation.

Examples

julia> using Dagitty

julia> g = DAG(:A => :C, :C => :B)
DAG: {3, 2} directed simple Int64 graph with labels [:A, :B, :C])

julia> is_d_separated(g, [:A], [:B], [:C])
true

julia> is_d_separated(g, [:A], [:C], [:B])
false

julia> is_d_separated(g, [1], [2], [3])
true
Dagitty.implied_conditional_independenciesFunction
implied_conditional_independencies(dag)

From given DAG find all pair-wise conditional independencies of nodes. Returns vector of ConditionalIndependence structures.

Examples

julia> using Dagitty

julia> g = DAG(:A => :C, :C => :B)
DAG: {3, 2} directed simple Int64 graph with labels [:A, :B, :C])

julia> implied_conditional_independencies(g)
1-element Vector{ConditionalIndependence}:
ConditionalIndependence(:A, :B, [:C])

## Benchmark of D-separation

I've done simple benchmark on "asia graph" (taken from NetworkX test suite). Code is in bench/t1.{py,jl}. Results:

Python:

test1: 95.59 us
test2: 97.65 us

Julia:

test1: 10.191 μs (205 allocations: 17.78 KiB)
test2: 11.556 μs (236 allocations: 20.33 KiB)