1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
|
import numpy as np
import numpy.random as nr
def likelihood(p, cascades, node):
x, y = build_matrix(cascades, node)
a = 1 - np.exp(-np.dot(x, p))
return np.inner(y, np.log(a)) + np.inner((1 - y), np.log(1-a))
def build_matrix(cascades, node):
def aux(cascade, node):
try:
m = np.vstack(x for x, s in cascade if s[node])
except ValueError:
return None
x = m[:-1, :]
y = m[1:, node]
return x, y
pairs = (aux(cascade, node) for cascade in cascades)
xs, ys = zip(*(pair for pair in pairs if pair))
x = np.vstack(xs)
y = np.concatenate(ys)
return x, y
def simulate_cascade(x, graph):
susc = x ^ np.ones(graph.shape[0]).astype(bool)
yield x, susc
while np.any(x):
x = 1 - np.exp(-np.dot(graph.T, x))
y = nr.random(x.shape[0])
x = (x >= y) & susc
yield x, susc
susc ^= x
def simulate_cascades(n, graph):
for _ in xrange(n):
x = np.zeros(g.shape[0]).astype(bool)
x[nr.random()] = True
yield simulate_cascade(x, graph)
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))
cascades = simulate_cascades(10, g)
print likelihood(p * np.ones(g.shape[0]), cascades, 3)
|
