Identification algorithms

src/CausalInference.jl

@@ -4,9 +4,10 @@ using Graphs.SimpleGraphs
 using Combinatorics
 using Base.Iterators
 
+export ancestors, descendants, alt_test_dsep, test_covariate_adjustment, alt_test_backdoor, find_dsep, find_min_dsep, find_covariate_adjustment, find_backdoor_adjustment, find_min_covariate_adjustment, find_frontdoor_adjustment, list_dseps, list_covariate_adjustment, list_backdoor_adjustment, list_frontdoor_adjustment
 export dsep, skeleton, gausscitest, dseporacle, partialcor
 export unshielded, pcalg, vskel
-export cpdag
+export cpdag, alt_cpdag
 export digraph, vpairs, skel_oracle, pc_oracle, randdag
 export cmitest, kl_entropy, kl_renyi, kl_mutual_information
 export kl_cond_mi, kl_perm_mi_test, kl_perm_cond_mi_test
@@ -30,6 +31,7 @@ include("fci.jl")
 include("misc.jl")
 include("recantingwitness.jl")
 include("backdoor.jl")
+include("gensearch.jl")
 
 # Compatibility with the new "Package Extensions" (https://github.com/JuliaLang/julia/pull/47695)
 const EXTENSIONS_SUPPORTED = isdefined(Base, :get_extension)

src/backdoor.jl

@@ -1,6 +1,11 @@
 export backdoor_criterion
 export backdoors
 
+# TODOs
+# - start with implementing a general Bayes-Ball type graph search
+# - then implement efficient algorithms for finding backdoor adjustment sets
+
+
 function backdoors(g::AbstractGraph{T}, U::Vector) where {T}
     seen = zeros(Bool, nv(g))
     bd = zeros(Bool, nv(g))

src/cpdag.jl

@@ -1,5 +1,54 @@
 import Base: iterate, length
 
+"""
+    alt_cpdag(g::DiGraph)
+
+Computes CPDAG from a DAG using a simpler adaption of Chickering's conversion algorithm without ordering all edges
+(equivalent to the PC algorithm with `d`-seperation as independence test, see `pc_oracle`.)
+
+Reference: M. Chickering: Learning equivalence classes of Bayesian
+network structures. Journal of Machine Learning Research 2 (2002).
+M. Chickering: A Transformational Characterization of Equivalent Bayesian Network Structures. (1995).
+"""
+function alt_cpdag(g)
+    compelled = SimpleDiGraph(nv(g))
+    reversible = SimpleDiGraph(nv(g))
+    to = topological_sort_by_dfs(g)
+    invto = invperm(to)
+    iscompelled = falses(nv(g))
+    for y in to
+        indegree(g, y) == 0 && continue
+        x = argmax(x -> invto[x], inneighbors(g, y))
+        iscompelled[inneighbors(g, y)] .= false
+        for w in inneighbors(compelled, x)
+            if !has_edge(g, w, y)
+                iscompelled[inneighbors(g, y)] .= true
+                @goto add_edges
+            else
+                iscompelled[w] = true
+            end
+        end
+        for z in inneighbors(g, y)
+            z == x && continue
+            if !has_edge(g, z, x)
+                iscompelled[inneighbors(g, y)] .= true
+                @goto add_edges
+            end
+        end
+        @label add_edges
+        for v in inneighbors(g, y)
+            if iscompelled[v]
+                add_edge!(compelled, v, y) 
+            else
+                add_edge!(reversible, v, y)
+                add_edge!(reversible, y, v)
+            end
+        end
+    end
+    return union(compelled, reversible)
+end
+
+
 """
     ordered_edges(dag)