def laplace_approx(G, delta, D, as_log_prob=True, diag=False):
"""
Log of Laplace approximation of G-Wishart normalization constant
Log of the Laplace approximation of the normalization constant of the G-Wishart
distribution outlined by Lenkoski and Dobra (2011, doi:10.1198/jcgs.2010.08181)
"""
from utils.Graph import Graph
G = Graph(len(G), G)
G = igraph.Graph.Adjacency(G.GetAdjM().tolist(), mode=1)
df = delta
rate = D
if rate is None:
# If the rate matrix is the identity matrix (I_p), then the mode of the
# G-Wishart distribution is (df - 2) * I_p such that the Laplace approximation simplifies.
p = G.vcount()
n_e = G.ecount()
return 0.5 * (
(p*(df - 1.0) + n_e)*np.log(df - 2.0) - p*(df - 2.0) \
+ p*np.log(4.0 * np.pi) + n_e*np.log(2.0 * np.pi)
)
return log_gwish_norm_laplace_cpp(G.__graph_as_capsule(), df, rate, diag)
def test_constrained_cov_0():
n = 10
for _ in range(10):
g = Graph(n)
g.SetRandom()
a = g.GetAdjM()[np.triu_indices(n, 1)]
T = np.random.random((n,n))
C = T.transpose() @ T
C_star = constrained_cov(g.GetDOL(), C, np.eye(n))
K = np.linalg.inv(C_star)
b = (abs(K[np.triu_indices(n, 1)]) > 1e-10).astype(int)
assert((a == b).all())
def test_generate_data():
np.random.seed(123)
for _ in range(10):
n = 10
m = 10000
g = Graph(n)
g.SetRandom()
X = generate_data(n, m, g, threshold=1e-6)
a = g.GetAdjM()[np.triu_indices(n, 1)]
b = (np.abs(np.linalg.inv((X.transpose() @ X) / (m-1))[np.triu_indices(n, 1)]) > 0.1).astype(int)
threshold = n
assert(np.sum(a != b) < threshold)
# Larger matrices require very large number of samples for it to converge to the correct graph
