Add Dor & Tasi PDAG completion algorithm (#112)

* Add Dor & Tasi

* Update src/pdag.jl

* Make it non-breaking

Author: mschauer

docs/src/library.md

@@ -31,6 +31,8 @@ CausalInference.meek_rule2
 CausalInference.meek_rule3
 CausalInference.meek_rule4
 pdag2dag!
+pdag_to_dag_dortasi!
+pdag_to_dag_meek!
 ```
 
 ## PC algorithm

src/CausalInference.jl

@@ -25,7 +25,7 @@ export plot_pc_graph_recipes, plot_fci_graph_recipes # if GraphRecipes is loaded
 export plot_pc_graph_tikz, plot_fci_graph_tikz # if TikzGraphs is loaded
 export orient_unshielded, orientable_unshielded, apply_pc_rules
 export ges
-export pdag2dag!
+export pdag2dag!, pdag_to_dag_meek!, pdag_to_dag_dortasi!
 
 #include("pinv.jl")
 include("graphs.jl")

src/meek.jl

@@ -108,11 +108,11 @@ function meek_rule4(dg, v, w)
 end
 
 """
-    pdag2dag!(g, rule4=false)
+    pdag_to_dag_meek!(g, rule4=false)
 
 Complete PDAG to DAG using meek_rules.
 """
-function pdag2dag!(g, rule4=false)
+function pdag_to_dag_meek!(g, rule4=false)
     while true
         # find unoriented edge
         for e in edges(g) # go through edges (bad to start in the beginning?)
@@ -127,4 +127,9 @@ function pdag2dag!(g, rule4=false)
         @label orient
         meek_rules!(g; rule4)
     end
+    g
 end
+"""
+Deprecated alias for `pdag_to_dag_meek!`.
+"""
+const pdag2dag! = pdag_to_dag_meek!

src/pdag.jl

@@ -147,3 +147,40 @@ Children of x in g are vertices y such that there is a directed edge y <-- x.
 Returns sorted array.
 """
 children(g, x) = setdiff(outneighbors(g, x), inneighbors(g, x))
+
+"""
+    pdag_to_dag_dortasi!!(g)
+
+Complete PDAG to DAG using Dor & Tasi (1992).
+"""
+function pdag_to_dag_dortasi!(g)
+    removed = falses(nv(g)) # Mark vertices removed from (sub-)graph A. Efficient if degree small?
+    while !all(removed)
+        touched = false
+        for x in vertices(g)
+            removed[x] && continue
+            for y in outneighbors(g, x)
+                removed[y] && continue
+                has_edge(g, y, x) || @goto skip # not a sink
+            end
+            for y in neighbors_undirected(g, x)
+                removed[y] && continue
+                for z in inneighbors(g, x) # contains all adjacents by assumption
+                    removed[z] && continue
+                    y==z || isadjacent(g, y, z) || @goto skip
+                end
+            end
+            for y in copy(outneighbors(g, x))
+                removed[y] && continue
+                rem_edge!(g, x, y)
+            end
+            touched = true
+            removed[x] = true
+            @label skip
+        end
+        if !touched
+            error("PDAG has no consistent extension to a DAG")
+        end
+    end
+    return g
+end

test/cpdag.jl

@@ -57,6 +57,16 @@ for stable in (true, false)
 
             h1 = pc_oracle(g; stable)
             h2 = cpdag(g)
+           
+            g2 = pdag_to_dag_dortasi!(copy(h2))
+            @test !is_cyclic(g2)
+            @test h2 == cpdag(g2)
+     
+            g2 = pdag_to_dag_meek!(copy(h2))
+            @test !is_cyclic(g2)
+            @test h2 == cpdag(g2)
+        
+
             h1 == h2 || println(vpairs(g))
             @test vpairs(h1) ⊆ vpairs(h2)
             @test vpairs(h2) ⊆ vpairs(h1)