do-calculus-backdoor-finder

do-calculus-backdoor-finder.py

"""
Copyright 2021 stormouse
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
"""

# A practice on finding and blocking backdoor path in Pearlian do-calculus.
# Reference: https://www.bradyneal.com/causal-inference-course
# Note: the code is not production ready, non-performant and might even be INCORRECT.

from functools import reduce
import itertools

graph = {
    "nodes": ['U', 'V', 'W', 'X', 'Z', 'Y'],
    "edges": [
        ('U', 'V'),
        ('U', 'X'),
        ('W', 'V'),
        ('W', 'Y'),
        ('V', 'X'),
        ('V', 'Y'),
        ('X', 'Z'),
        ('Z', 'Y'),
    ]
}

def list_paths(t, y, edges):
    adj_list = {}
    for a, b in edges:
        adj_list.setdefault(a, {})
        adj_list.setdefault(b, {})
        adj_list[a][b] = 1
        adj_list[b][a] = -1
    
    results = []
    def traverse(cur, path):
        if cur == y:
            results.append(path.copy())
        else:
            for next in adj_list[cur]:
                if next not in path:
                    path.append(next)
                    traverse(next, path)
                    del path[-1]
    
    init_path = [t]
    traverse(t, init_path)
    return results


def list_backdoor_paths(t, y, edges):
    all_paths = list_paths(t, y, edges)

    def is_backdoor(path):
        return len(path) > 1 and path[0] == t and (path[1], path[0]) in edges

    return filter(is_backdoor, all_paths)


def list_unblocked_backdoor_paths(t, y, edges, conditioned):
    def has_descendent(conditioned):
        descendents = set(t)
        while True:
            n = len(descendents)
            descendents |= set(edge[1] for edge in edges if edge[0] in descendents)
            if len(descendents) == n:
                break
        return any([node in descendents for node in conditioned if node != t])

    def is_blocked(path):
        if len(path) < 3:
            return False
        for i in range(len(path) - 2):
            a, b, c = path[i], path[i + 1], path[i + 2]
            if (b, a) in edges and b in conditioned:
                return True
            elif (a, b) in edges and (c, b) in edges and b not in conditioned:
                return True
        return False

    return list(filter(lambda p: not is_blocked(p), list_backdoor_paths(t, y, edges)))

def suggest_backdoor_closer(t, y, edges, unblocked_paths):
    if len(unblocked_paths) == 0:
        return []
    
    candidates = [set(i) for i in itertools.product(*[path[1:-1] for path in unblocked_paths])]
    valid_candidates = list(filter(lambda x: len(list_unblocked_backdoor_paths(t, y, edges, x)) == 0, candidates))
    return None if len(valid_candidates) == 0 else valid_candidates

def print_path(path):
    return '  ' + ' -> '.join([str(x) for x in path])

print("Unblocked backdoor paths:")
print('\n'.join(print_path(p) for p in list_unblocked_backdoor_paths('X', 'Y', graph['edges'], set())))

print("\nPossible variable sets to condition on to close backdoors:")
print(suggest_backdoor_closer('X', 'Y', graph['edges'], list_unblocked_backdoor_paths('X', 'Y', graph['edges'], set())))

print("\nUnblocked backdoor paths conditioning on {{'U', 'V'}}:")
print(list_unblocked_backdoor_paths('X', 'Y', graph['edges'], set(['U', 'V'])))