def to_gauss_dag(self, perm):
"""
Return a GaussDAG with the same mean and covariance as this GGM, and is a minimal IMAP of this GGM
consistent with the node ordering `perm`.
Parameters
----------
perm:
The desired permutation, or total order, of the nodes in the result.
Returns
-------
Examples
--------
TODO
"""
from causaldag import DAG, GaussDAG
d = DAG(nodes=self.nodes)
ixs = list(
itr.chain.from_iterable(
((f, s) for f in range(s)) for s in range(len(perm))))
for i, j in ixs:
pi_i, pi_j = perm[i], perm[j]
if not np.isclose(
self.partial_correlation(pi_i, pi_j,
d.markov_blanket(pi_i)), 0):
d.add_arc(pi_i, pi_j, unsafe=True)
arcs = dict()
means = []
Sigma = self.covariance
variances = []
for i in perm:
ps = list(d.parents_of(i))
# === LINEAR REGRESSION TO FIND EDGE WEIGHTS
S_xx = Sigma[np.ix_(ps, ps)]
S_xy = Sigma[ps, i]
coeffs = inv(S_xx) @ S_xy
# === COMPUTE MEAN AND VARIANCE
mean = self.means[i] - self.means[ps] @ coeffs.T
variance = Sigma[i, i] - Sigma[i, ps] @ coeffs
for p, coeff in zip(ps, coeffs):
print(p, i)
arcs[(p, i)] = coeff
means.append(mean)
variances.append(variance)
return GaussDAG(list(range(self.num_nodes)),
arcs,
means=means,
variances=variances)
def perm2dag(perm,
ci_tester: CI_Tester,
verbose=False,
fixed_adjacencies=set(),
fixed_gaps=set(),
node2nbrs=None,
older=False):
"""
TODO
Parameters
----------
perm
ci_tester
verbose
fixed_adjacencies
fixed_gaps
node2nbrs
older
Examples
--------
TODO
"""
d = DAG(nodes=set(perm))
ixs = list(
itr.chain.from_iterable(
((f, s) for f in range(s)) for s in range(len(perm))))
for i, j in ixs:
pi_i, pi_j = perm[i], perm[j]
# === IF FIXED, DON'T TEST
if (pi_i, pi_j) in fixed_adjacencies or (pi_j,
pi_i) in fixed_adjacencies:
d.add_arc(pi_i, pi_j)
continue
if (pi_i, pi_j) in fixed_gaps or (pi_j, pi_i) in fixed_gaps:
continue
# === TEST MARKOV BLANKET
mb = d.markov_blanket(pi_i) if node2nbrs is None else (
set(perm[:j]) - {pi_i}) & (node2nbrs[pi_i] | node2nbrs[pi_j])
mb = mb if not older else set(perm[:j]) - {pi_i}
is_ci = ci_tester.is_ci(pi_i, pi_j, mb)
if not is_ci:
d.add_arc(pi_i, pi_j, unsafe=True)
if verbose:
print("%s indep of %s given %s: %s" % (pi_i, pi_j, mb, is_ci))
return d
def perm2dag(perm: list,
ci_tester: CI_Tester,
verbose=False,
fixed_adjacencies: Set[UndirectedEdge] = set(),
fixed_gaps: Set[UndirectedEdge] = set(),
node2nbrs=None,
older=False,
progress=False):
"""
Given a permutation, find the minimal IMAP consistent with that permutation and the results of conditional independence
tests from ci_tester.
Parameters
----------
perm:
list of nodes representing the permutation.
ci_tester:
object for testing conditional independence.
verbose:
if True, log each CI test.
fixed_adjacencies:
set of nodes known to be adjacent.
fixed_gaps:
set of nodes known not to be adjacent.
node2nbrs:
TODO
older:
TODO
Examples
--------
>>> from causaldag.utils.ci_tests import MemoizedCI_Tester, gauss_ci_test, gauss_ci_suffstat
>>> perm = [0,1,2]
>>> suffstat = gauss_ci_suffstat(samples)
>>> ci_tester = MemoizedCI_Tester(gauss_ci_test, suffstat)
>>> perm2dag(perm, ci_tester, fixed_gaps={frozenset({1, 2})})
"""
if fixed_adjacencies:
adj = next(iter(fixed_adjacencies))
if not isinstance(adj, frozenset):
raise ValueError('fixed_adjacencies should contain frozensets')
if fixed_gaps:
adj = next(iter(fixed_gaps))
if not isinstance(adj, frozenset):
raise ValueError('fixed_gaps should contain frozensets')
d = DAG(nodes=set(perm))
ixs = list(
itr.chain.from_iterable(
((f, s) for f in range(s)) for s in range(len(perm))))
ixs = ixs if not progress else tqdm(ixs)
for i, j in ixs:
pi_i, pi_j = perm[i], perm[j]
# === IF FIXED, DON'T TEST
if frozenset({pi_i, pi_j}) in fixed_adjacencies:
d.add_arc(pi_i, pi_j)
continue
if frozenset({pi_i, pi_j}) in fixed_gaps:
continue
# === TEST MARKOV BLANKET
mb = d.markov_blanket(pi_i) if node2nbrs is None else (
set(perm[:j]) - {pi_i}) & (node2nbrs[pi_i] | node2nbrs[pi_j])
mb = mb if not older else set(perm[:j]) - {pi_i}
is_ci = ci_tester.is_ci(pi_i, pi_j, mb)
if not is_ci:
d.add_arc(pi_i, pi_j, unsafe=True)
if verbose:
print(f"{pi_i} is independent of {pi_j} given {mb}: {is_ci}")
return d
