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import numpy as np
import numpy.random as nr
def likelihood(p, cascade, node):
m = build_matrix(cascade, node)
x = m[:-1, :]
y = m[1:, node].reshape(-1)
a = 1 - np.exp(-np.dot(x, p))
return y * np.log(a) + (1 - y) * np.log(1-a)
def build_matrix(cascade, node):
try:
m = np.vstack(x for x, s in cascade if s[node])
except ValueError:
return None
return m
def simulate_cascade(g, x):
s = x ^ np.ones(g.shape[0]).astype(bool)
yield x, s
while np.any(x):
x = 1 - np.exp(-np.dot(g.T, x))
y = nr.random(x.shape[0])
x = (x >= y) & s
yield x, s
s = x ^ s
if __name__ == "__main__":
g = np.array([[0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0]])
p = 0.5
g = np.log(1. / (1 - p * g))
x = np.zeros(g.shape[0]).astype(bool)
x[0] = 1
cascade = simulate_cascade(g, x)
print likelihood(np.ones(g.shape[0]) * 0.5, cascade, 1)
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