def test_claim_4():
"""
test we can apply rule 2 forwards to rewrite pr(y|x,do(z)) as pr(y|x,z)
"""
graph = make_toy_graph()
bindings = {
'z' : set(['z']),
'x' : set(['x']),
'y' : set(['y']),
}
bind = bindings.get
root_expr = E.prob([E.v('y')], [E.v('x'), E.do(E.v('z'))])
rule = get_rule('ignore_intervention_act_forward')
sites = list(rule['site_gen'](root_expr))
assert len(sites) == 1
site, = sites
prepped_args = prepare_rule_arguments(rule['unpack_target'], site)
bound_args = bind_arguments(bind, prepped_args)
assert rule['assumption_test'](g = graph, **bound_args)
root_expr_prime = rule['apply'](site)
assert root_expr_prime == E.prob([E.v('y')], [E.v('x'), E.v('z')])
def gen_expansions(value, proof_state):
for (prob_expr, inject) in E.gen_matches(E.is_prob, proof_state.root_expr):
prob_vars = get_variable_order(prob_expr)
prob_values = [proof_state.bindings[v] for v in prob_vars]
if value in prob_values:
continue
# prob([x],[w]) -> sigma(y, product([prob([x], [y, w]), p([y], [w])]))
i = new_variable_name(proof_state.bindings)
v_i = E.v(i)
alpha_left = tuple(prob_expr[1])
alpha_right = (v_i, ) + tuple(prob_expr[2])
alpha = E.prob(alpha_left, alpha_right)
beta_left = (v_i, )
beta_right = tuple(prob_expr[2])
beta = E.prob(beta_left, beta_right)
expr_prime = E.sigma(v_i, E.product([alpha, beta]))
succ_length = proof_state.length + 1
succ_heuristic = 0
succ_bindings = dict(proof_state.bindings)
succ_bindings[i] = value
succ_root_expr = inject(expr_prime)
succ_comment = 'conditioned %s on %s' % (
pleasantly_fmt(proof_state.bindings, prob_expr),
make_canonical_variable_name(value))
succ_proof_state = ProofState(succ_length, succ_heuristic, succ_bindings, succ_root_expr,
parent=proof_state, comment=succ_comment)
yield succ_proof_state
def test_gen_matches():
root_expr = prob([v("z")], [do(v("x"))])
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 2
match_a, match_b = matches
assert match_a[0] == v("z")
assert match_b[0] == v("x")
# test substitution machinery
assert match_a[1]("banana") == prob(["banana"], [do(v("x"))])
assert match_b[1]("rambutan") == prob([v("z")], [do("rambutan")])
def test_gen_matches():
root_expr = prob([v('z')], [do(v('x'))])
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 2
match_a, match_b = matches
assert match_a[0] == v('z')
assert match_b[0] == v('x')
# test substitution machinery
assert match_a[1]('banana') == prob(['banana'], [do(v('x'))])
assert match_b[1]('rambutan') == prob([v('z')], [do('rambutan')])
def test_gen_v_sites():
root_expr = prob([v('z')], [v('w'), do(v('x')), do(v('y'))])
sites = list(gen_v_sites(root_expr))
assert len(sites) == 1
target, inject, left, vs, dos, _ = sites[0]
atom, = target
assert atom == v('w')
assert inject('banana') == prob([v('z')], ['banana', do(v('x')), do(v('y'))])
assert left == (v('z'), )
assert vs == []
assert dos == [do(v('x')), do(v('y'))]
def test_gen_v_sites():
root_expr = prob([v('z')], [v('w'), do(v('x')), do(v('y'))])
sites = list(gen_v_sites(root_expr))
assert len(sites) == 1
target, inject, left, vs, dos, _ = sites[0]
atom, = target
assert atom == v('w')
assert inject('banana') == prob(
[v('z')], ['banana', do(v('x')), do(v('y'))])
assert left == (v('z'), )
assert vs == []
assert dos == [do(v('x')), do(v('y'))]
def test_normalise_fixed_point():
root_expr = sigma(v('x'), product([prob([v('z'), v('y')], [v('b'), v('x'), do(v('a'))]),
prob([v('z'), v('y'), v('x')], [do(v('a'))])]))
bindings = {'x' : 'xxx', 'z' : 'zzz', 'y' : 'yyy', 'a' : 'aaa'}
state = ProofState(0, 0, bindings, root_expr)
normalised_state = state.normalise()
expected_result = sigma(v(0), product((prob((v(0), v(1), v(2)),(do(v(3)), )),
prob((v(1), v(2)), (do(v(3)), v(0), v(4))))))
assert normalised_state.root_expr == expected_result
def test_gen_matches_deep():
# sigma_y { p(x|y,do(z)) * p(y|do(z)) }
root_expr = sigma(v("y"), product([prob([v("x")], [v("y"), do(v("z"))]), prob([v("y")], [do(v("z"))])]))
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 6
expr, inject = matches[3]
assert expr == v("z")
root_expr_prime = inject("walrus")
assert root_expr_prime == sigma(
v("y"), product([prob([v("x")], [v("y"), do("walrus")]), prob([v("y")], [do(v("z"))])])
)
def test_full_problem():
graph = make_toy_graph()
banned_values = set([frozenset(['h'])])
heuristic = make_heuristic(banned_values, greed=10)
initial_bindings = {
'x': set(['x']),
'y': set(['y']),
}
initial_expr = E.prob([E.v('y')], [E.do(E.v('x'))])
initial_proof_state = ProofState(
length=0, # length of proof
heuristic_length=0,
bindings=initial_bindings,
root_expr=initial_expr,
).normalise()
initial_proof_state = initial_proof_state.copy(
heuristic_length=heuristic(initial_proof_state))
def goal_check(proof_state):
return proof_state.heuristic_length == 0
result = proof_search(initial_proof_state,
graph,
goal_check,
heuristic,
max_proof_length=7)
assert result['reached_goal']
def test_full_problem():
graph = make_toy_graph()
banned_values = set([frozenset(['h'])])
heuristic = make_heuristic(banned_values, greed=10)
initial_bindings = {
'x' : set(['x']),
'y' : set(['y']),
}
initial_expr = E.prob([E.v('y')], [E.do(E.v('x'))])
initial_proof_state = ProofState(
length = 0, # length of proof
heuristic_length = 0,
bindings = initial_bindings,
root_expr = initial_expr,
).normalise()
initial_proof_state = initial_proof_state.copy(heuristic_length=heuristic(initial_proof_state))
def goal_check(proof_state):
return proof_state.heuristic_length == 0
result = proof_search(initial_proof_state, graph, goal_check, heuristic, max_proof_length=7)
assert result['reached_goal']
def test_gen_matches_deep():
# sigma_y { p(x|y,do(z)) * p(y|do(z)) }
root_expr = sigma(
v('y'),
product([
prob([v('x')], [v('y'), do(v('z'))]),
prob([v('y')], [do(v('z'))])
]))
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 6
expr, inject = matches[3]
assert expr == v('z')
root_expr_prime = inject('walrus')
assert root_expr_prime == sigma(
v('y'),
product([
prob([v('x')], [v('y'), do('walrus')]),
prob([v('y')], [do(v('z'))])
]))
def main():
if len(sys.argv) != 2:
sys.stderr.write('usage: greediness (positive float...)\n')
sys.exit(1)
greed = float(sys.argv[1])
graph = make_toy_graph()
banned_values = set([frozenset(['h'])])
# dial the greed parameter up high.
# this makes the search very optimistic.
# in general this may not find the shortest proof
heuristic = make_heuristic(banned_values, greed)
initial_bindings = {
'x': frozenset(['x']),
'y': frozenset(['y']),
}
initial_expr = E.prob([E.v('y')], [E.do(E.v('x'))])
initial_proof_state = ProofState(
length=0, # length of proof
heuristic_length=0,
bindings=initial_bindings,
root_expr=initial_expr,
parent=None,
comment='initial state',
).normalise()
# this is a little silly
initial_proof_state = initial_proof_state.copy(
heuristic_length=heuristic(initial_proof_state))
def goal_check(proof_state):
return proof_state.heuristic_length == 0
result = proof_search(initial_proof_state,
graph,
goal_check,
heuristic,
max_proof_length=7)
assert result['reached_goal']
print 'success!'
display_proof_as_listing(result['path'])
out_file_name = 'proof_tree.dot'
write_proof_tree(result['path'], result['closed'], out_file_name)
def test_normalise_single_iter():
root_expr = sigma(v('x'), product([prob([v('z'), v('y')], [v('b'), v('x'), do(v('a'))]),
prob([v('z'), v('y'), v('x')], [do(v('a'))])]))
bindings = {'x' : 'xxx', 'z' : 'zzz', 'y' : 'yyy', 'a' : 'aaa'}
state = ProofState(0, 0, bindings, root_expr)
normalised_state = state.normalise(max_iters=1)
# first up: expression ordering (nb do(v()) comes before v() in sorted lists)
# sigma(x, product([prob([x y z],[do(a)]), prob([y z], [(do a) b x])]))
# so, variable order should be:
# x y z a b
# so, new variable names should be
# 0 1 2 3 4
# so, normalised state should be
# sigma(0, product([prob([0 1 2],[do(3)]), prob([1 2], [(do 3) 4 0])]))
expected_result = sigma(v(0), product((prob((v(0), v(1), v(2)),(do(v(3)), )),
prob((v(1), v(2)), (do(v(3)), v(4), v(0))))))
assert normalised_state.root_expr == expected_result
def main():
if len(sys.argv) != 2:
sys.stderr.write('usage: greediness (positive float...)\n')
sys.exit(1)
greed = float(sys.argv[1])
graph = make_toy_graph()
banned_values = set([frozenset(['h'])])
# dial the greed parameter up high.
# this makes the search very optimistic.
# in general this may not find the shortest proof
heuristic = make_heuristic(banned_values, greed)
initial_bindings = {
'x' : frozenset(['x']),
'y' : frozenset(['y']),
}
initial_expr = E.prob([E.v('y')], [E.do(E.v('x'))])
initial_proof_state = ProofState(
length = 0, # length of proof
heuristic_length = 0,
bindings = initial_bindings,
root_expr = initial_expr,
parent = None,
comment = 'initial state',
).normalise()
# this is a little silly
initial_proof_state = initial_proof_state.copy(heuristic_length=heuristic(initial_proof_state))
def goal_check(proof_state):
return proof_state.heuristic_length == 0
result = proof_search(initial_proof_state, graph, goal_check, heuristic, max_proof_length=7)
assert result['reached_goal']
print 'success!'
display_proof_as_listing(result['path'])
out_file_name = 'proof_tree.dot'
write_proof_tree(result['path'], result['closed'], out_file_name)
def inject(x=None, drop=False):
if drop:
start = ()
else:
start = (x, )
return prob(left, start + tuple(right))
def test_fmt():
root_expr = prob([v('z')], [do(v('x'))])
assert fmt(root_expr) == 'pr(z|do(x))'
def inject(x=None, drop=False):
if drop:
start = ()
else:
start = (x, )
return prob(left, start + tuple(right))
def test_fmt():
root_expr = prob([v("z")], [do(v("x"))])
assert fmt(root_expr) == "pr(z|do(x))"
