def _shrink(adj, X, lamb, **kwargs):
# Initialize CMI cache matrix
n, d = X.shape
cmis = np.zeros([d, d])
cmis[np.eye(d, dtype=bool)] = np.inf
for i in range(d):
x = X[:, i]
for j in adj[i].nonzero()[0]:
other_adj_i = adj[i] & (np.arange(d) != j)
y = X[:, j]
z = X[:, other_adj_i]
cmis[i, j] = conditional_mutual_information(x, y, z, **kwargs)
while np.count_nonzero(adj) > 0:
scores = cmis + cmis.T
imin, jmin = np.unravel_index(np.argmin(scores), scores.shape)
if scores[imin, jmin] > lamb:
return adj
adj[imin, jmin] = adj[jmin, imin] = 0
cmis[imin, jmin] = cmis[jmin, imin] = np.inf
# Re-compute CMIs
for i in range(d):
x = X[:, i]
for j in adj[i].nonzero()[0]:
other_adj_i = adj[i] & (np.arange(d) != j)
y = X[:, j]
z = X[:, other_adj_i]
cmis[i, j] = conditional_mutual_information(x, y, z, **kwargs)
return adj
def _grow(adj, X, lamb, **kwargs):
# Initialize CMI cache matrix
n, d = X.shape
cmis = np.zeros([d, d])
cmis[np.eye(d, dtype=bool)] = -np.inf
for i in range(d):
x = X[:, i]
for j in range(i):
y = X[:, j]
cmis[i, j] = cmis[j, i] = mutual_information(x, y, **kwargs)
while np.count_nonzero(adj) < d**2 - d:
scores = cmis + cmis.T
imax, jmax = np.unravel_index(np.argmax(scores), scores.shape)
if scores[imax, jmax] <= lamb:
return adj
adj[imax, jmax] = adj[jmax, imax] = 1
cmis[imax, jmax] = cmis[jmax, imax] = -np.inf
# Re-compute CMIs
for i in (imax, jmax):
x = X[:, i]
z = X[:, adj[i]]
non_adj = ~adj[i] & (np.arange(d) != i)
for j in non_adj.nonzero()[0]:
y = X[:, j]
cmis[i, j] = conditional_mutual_information(x, y, z, **kwargs)
return adj
def _shrink(selected, X, y, lamb, k, **kwargs):
while True:
min_cmi = np.inf
for i in selected:
x = X[:, i]
z = X[:, list(set(selected) - {i})]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if min_cmi > cmi:
min_cmi = cmi
min_idx = i
if min_cmi >= lamb or len(selected) == k:
return selected
selected.remove(min_idx)
def _shrink(adj, i, X, lamb, **kwargs):
n, d = X.shape
x = X[:, i]
for j in adj[i].nonzero()[0]:
other_adj = adj[i] & (np.arange(d) != j)
y = X[:, j]
z = X[:, other_adj]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if cmi <= lamb:
adj[i, j] = adj[j, i] = 0
if np.count_nonzero(adj[i]) == 0:
break
return adj
def _grow(selected, X, y, lamb, k, **kwargs):
n, d = X.shape
while True:
max_cmi = -np.inf
not_selected = set(range(d)) - set(selected)
z = X[:, selected]
for i in not_selected:
x = X[:, i]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if max_cmi < cmi:
max_cmi = cmi
max_idx = i
if max_cmi <= lamb or len(selected) == k:
return selected
selected.append(max_idx)
def _shrink(adj, i, X, lamb, **kwargs):
n, d = X.shape
x = X[:, i]
updated = True
while updated:
updated = False
for j in adj[i].nonzero()[0]:
other_adj = adj[i] & (np.arange(d) != j)
y = X[:, j]
z = X[:, other_adj]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if cmi <= lamb:
adj[i, j] = adj[j, i] = 0
updated = True
break
return adj
def _grow(adj, i, X, lamb, **kwargs):
n, d = X.shape
x = X[:, i]
updated = True
while updated:
updated = False
non_adj = ~adj[i] & (np.arange(d) != i)
for j in non_adj.nonzero()[0]:
y = X[:, j]
z = X[:, adj[i]]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if cmi > lamb:
adj[i, j] = adj[j, i] = 1
updated = True
break
return adj
def _grow(adj, i, X, lamb, **kwargs):
n, d = X.shape
x = X[:, i]
updated = True
while updated:
updated = False
vmax = -np.inf
z = X[:, adj[i]]
non_adj = ~adj[i] & (np.arange(d) != i)
for j in non_adj.nonzero()[0]:
y = X[:, j]
cmi = conditional_mutual_information(x, y, z, **kwargs)
if vmax < cmi:
vmax = cmi
imax, jmax = i, j
if vmax >= lamb:
adj[imax, jmax] = adj[jmax, imax] = 1
updated = True
return adj