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import mleNode as mn
import numpy as np
from numpy.linalg import norm
import numpy.random as nr
from scipy.optimize import minimize
import matplotlib.pyplot as plt
import seaborn
from random import random, randint
seaborn.set_style("white")
def simulate_cascade(x, graph):
"""
Simulate an IC cascade given a graph and initial state.
For each time step we yield:
- susc: the nodes susceptible at the beginning of this time step
- x: the subset of susc who became infected
"""
susc = np.ones(graph.shape[0], dtype=bool) # t=0, everyone is susceptible
yield x, susc
while np.any(x):
susc = susc ^ x # nodes infected at previous step are now inactive
if not np.any(susc):
break
x = 1 - np.exp(-np.dot(graph.T, x))
y = nr.random(x.shape[0])
x = (x >= y) & susc
yield x, susc
def uniform_source(graph, *args, **kwargs):
x0 = np.zeros(graph.shape[0], dtype=bool)
x0[nr.randint(0, graph.shape[0])] = True
return x0
def simulate_cascades(n, graph, source=uniform_source):
for t in xrange(n):
x0 = source(graph, t)
yield simulate_cascade(x0, graph)
def build_cascade_list(cascades, collapse=False):
x, s = [], []
for cascade in cascades:
xlist, slist = zip(*cascade)
x.append(np.vstack(xlist))
s.append(np.vstack(slist))
if not collapse:
return x, s
else:
return np.vstack(x), np.vstack(s)
def cascadeLkl(graph, infect, sus):
# There is a problem with the current implementation
# Note that you need to take into account the time diff between the label
# and the values being conditioned. Note also that the matrix if stacked as
# such will require to keep track of the state 0 of each cascade.
a = np.dot(infect, graph)
return np.log(1. - np.exp(-a[(infect[1:])*sus[1:]])).sum() \
- a[(~infect[1:])*sus].sum()
if __name__ == "__main__":
# g = np.array([[0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0]])
g = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
p = 0.5
g = np.log(1. / (1 - p * g))
# error = []
def source(graph, t):
x0 = np.zeros(graph.shape[0], dtype=bool)
a = randint(0, 1)
x0[a] = True
if random() > t:
x0[1-a] = True
return x0
thresh = np.arange(0., 1.1, step=0.2)
sizes = np.arange(10, 100, step=10)
nsimul = 10
r = np.zeros(len(sizes), len(thresh))
for t in thresh:
for i in nsimul:
cascades = simulate_cascades(np.max(sizes), g,
source=lambda graph: source(graph, t))
e = np.zeros(g.shape[0])
for j, s in enumerate(sizes):
x, y = mn.build_matrix(cascades, 2)
e += mn.infer(x[:s], y[:s])
for i, t in enumerate(thresh):
plt.plot(sizes, e[:, i], label=str(t))
plt.legend()
plt.show()
# conf = mn.bootstrap(x, y, n_iter=100)
# estimand = np.linalg.norm(np.delete(conf - g[0], 0, axis=1), axis=1)
# error.append(mn.confidence_interval(*np.histogram(estimand, bins=50)))
# plt.semilogx(sizes, error)
# plt.show()
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