def Direct_Sample(CyberNet, data, num_samples, T, s0):
"""
Returns P(data|attacker) by Monte Carlo Sampling
CyberNet : CyberNet Instance
data : list
Output of gen_data
num_samples : int
How many Monte Carlo samples
T : int
Time window
s0 : dict
Initial states of nodes
"""
net = copy.deepcopy(CyberNet)
# The states of nodes will be changing so we want to make sure
# we do not change the input network
logn_fact = gen_logn_fact(data)
#Precompute log(n!) for various n.
n = 1
nodes_to_change = [nd for nd in net.node_names if s0[nd] == 'normal' ]
nodes_no_change = [nd for nd in net.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(net, data, T, logn_fact)
numattackers = len(nodes_no_change)
prob_mod = lambda x : prob_model_given_data_times(net, data, x, T,
logn_fact, s0)
# Only input is not the infection times
probs = []
while n < num_samples:
t = 0
for nd in net.node_names:
net.node_dict[nd].state = s0[nd]
times = {nd: 0 for nd in nodes_no_change}
# Corresponds to correct order
while t<T :
infected = [nd.name for nd in net.nodes if nd.state =='infected']
at_risk = set(chain(*[net.node_dict[nd].sends_to for nd in infected])) - set(infected)
if len(at_risk) == 0:
break
at_risk_ix = [net.node_names.index(nd) for nd in at_risk]
mt_rates = np.sum(net.get_mal_trans()[:, at_risk_ix], axis=0)
#print at_risk, mt_rates, infected, n
r_rate = np.sum(mt_rates)
t += np.random.exponential(scale=1./r_rate)
# Sample time of next infection
if t<T:
next_infected = np.random.choice(list(at_risk), p = mt_rates/float(sum(mt_rates)))
# Sample node to be infected
times[next_infected] = t
net.node_dict[next_infected].state = 'infected'
#print times, n
probs.append(prob_mod(times))
n+=1
# prob_mod returns log prob so we need to exponentiate to get the mean
e_probs = np.exp(probs)
return np.log(np.mean(e_probs))
def get_likelihoods(seed, num_pos, num_neg, CyberNet, s0, T, truenet=None, directsamps=1000):
"""
seed : int
Random seed for Monte Carlo and data generation
See plot_roc_parallel for more info
"""
if truenet == None:
truenet = CyberNet
no_a_s0 = dict(zip(CyberNet.node_names, ['normal'] * len(CyberNet.nodes)))
np.random.seed(seed)
random.seed(seed)
infected_lhoods = []
# Will store the lhood w attacker and lhood difference
clean_lhoods = []
datalen = 0
for i in range(num_pos):
seed +=1
np.random.seed(seed)
random.seed(seed)
# Augment the seed by 1 to generate new sample
data = gen_data(T, truenet, s0)
if len(data[0]) > datalen:
datalen = len(data[0])
logn_fact = gen_logn_fact(data)
# Only generate these as needed
p_data_attacker = Direct_Sample(CyberNet, data, directsamps, T, s0)
p_no_attacker = prob_model_no_attacker(CyberNet, data, T, logn_fact)
infected_lhoods.append((p_data_attacker, p_no_attacker))
for j in range(num_neg):
seed += 1
np.random.seed(seed)
random.seed(seed)
# Code uses both
data = gen_data(T, truenet, no_a_s0)
if len(data[0]) > datalen:
datalen = len(data[0])
logn_fact = gen_logn_fact(data)
# Only generate these as needed
p_data_attacker = Direct_Sample(CyberNet, data, directsamps, T, s0)
p_no_attacker = prob_model_no_attacker(CyberNet, data, T, logn_fact)
clean_lhoods.append((p_data_attacker, p_no_attacker))
return np.asarray(infected_lhoods), np.asarray(clean_lhoods)
def Direct_Sample(SFTNet, data, num_samples, T, s0):
net = copy.deepcopy(SFTNet)
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in net.node_names if s0[nd] == 'normal']
nodes_no_change = [nd for nd in net.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(net, data, T)
prob_true_value = prob_model_given_data(net, data, data[-1], T, logn_fact,
s0)
numattackers = len(nodes_no_change)
prob_mod = lambda x: prob_model_given_data(net, data, x, T, logn_fact, s0)
probs = []
while n < num_samples:
t = 0
for nd in net.node_names:
net.node_dict[nd].state = s0[nd]
times = {nd: 0 for nd in nodes_no_change}
# Corresponds to correct order
while t < T:
infected = [nd.name for nd in net.nodes if nd.state == 'infected']
at_risk = set(
chain(*[net.node_dict[nd].sends_to
for nd in infected])) - set(infected)
if len(at_risk) == 0:
break
at_risk_ix = [net.node_names.index(nd) for nd in at_risk]
mt_rates = np.sum(net.get_mal_trans()[:, at_risk_ix], axis=0)
#print at_risk, mt_rates, infected, n
r_rate = np.sum(mt_rates)
t += np.random.exponential(scale=1 / r_rate)
if t < T:
next_infected = np.random.choice(list(at_risk),
p=mt_rates / sum(mt_rates))
times[next_infected] = t
net.node_dict[next_infected].state = 'infected'
#print times, n
probs.append(prob_mod(times)[1])
n += 1
e_probs = np.exp(probs)
return np.log(np.mean(e_probs)), e_probs
def Direct_Sample(SFTNet, data, num_samples, T, s0):
net = copy.deepcopy(SFTNet)
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in net.node_names if s0[nd] == 'normal' ]
nodes_no_change = [nd for nd in net.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(net, data, T)
prob_true_value = prob_model_given_data(net, data, data[-1], T, logn_fact, s0)
numattackers = len(nodes_no_change)
prob_mod = lambda x : prob_model_given_data(net, data, x, T,
logn_fact, s0)
probs = []
while n < num_samples:
t = 0
for nd in net.node_names:
net.node_dict[nd].state = s0[nd]
times = {nd: 0 for nd in nodes_no_change}
# Corresponds to correct order
while t<T :
infected = [nd.name for nd in net.nodes if nd.state =='infected']
at_risk = set(chain(*[net.node_dict[nd].sends_to for nd in infected])) - set(infected)
if len(at_risk) == 0:
break
at_risk_ix = [net.node_names.index(nd) for nd in at_risk]
mt_rates = np.sum(net.get_mal_trans()[:, at_risk_ix], axis=0)
#print at_risk, mt_rates, infected, n
r_rate = np.sum(mt_rates)
t += np.random.exponential(scale=1/r_rate)
if t<T:
next_infected = np.random.choice(list(at_risk), p = mt_rates/sum(mt_rates))
times[next_infected] = t
net.node_dict[next_infected].state = 'infected'
#print times, n
probs.append(prob_mod(times)[1])
n+=1
e_probs = np.exp(probs)
return np.log(np.mean(e_probs)), e_probs
def MCMC_MH(SFTNet, data, s0, N, T, proposal_var=100, print_jumps=False):
# TODO Need to profile this
# TODO: Need to make this more general. Not trivial
# TODO : Add sample from possible node orderings
"""
Performs MCMC integration using Metropolis Hastings. Returns
the sampled times, their associated probabilities and the
associated likelihood value. This method corresponds to David's
"half-way" approach in the 2nd version of the ASCII where we
sample (accept / reject) according to P(z | attacker) and then
take the average of P(data | z, attacker) of the accepted
values.
SFTNet : SFTNet instance
The net to do MCMC over
data : list
The data as outputted by gen_data
N : int
The number of MCMC proposals
s0 : dict
State of the net at t=0
T : int
How long the process ran for.
"""
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in SFTNet.node_names if s0[nd] == "normal"]
nodes_no_change = [nd for nd in SFTNet.node_names if s0[nd] == "infected"]
prob_no_attacker = prob_model_no_attacker(SFTNet, data, T)
prob_true_value = prob_model_given_data(SFTNet, data, data[-1], T, logn_fact)
prob_mod = lambda x: prob_model_given_data(SFTNet, data, x, T, logn_fact)
guess_times = np.sort(np.random.random(size=len(nodes_to_change)) * T)
z0 = dict(zip(nodes_to_change, guess_times))
for nd in nodes_no_change:
z0[nd] = 0
# lambda function that calls prob_model_given_data for
# specified infection times
p0 = prob_mod(z0)
# Initiial probability
# actual times
time_samples = {node.name: [] for node in SFTNet.nodes}
# container for samples
probs = []
# container for probabilities
z1 = copy.deepcopy(z0)
while n < N:
# if np.random.random() < alpha:
# order = random.sample(orderings, 1)[0]
for nd in nodes_to_change:
z1[nd] = z0[nd] + np.random.normal() * proposal_var
p1 = prob_mod(z1)
if p1[0] - p0[0] > np.log(np.random.random()):
if print_jumps:
print "A Jump at, ", n, "to ", z1, "with prob", p1, "\n"
p0 = p1
z0 = copy.deepcopy(z1)
for key, val in z0.iteritems():
time_samples[key].append(val)
probs.append(p0[:2])
n += 1
probs = np.asarray(probs)
out_ar = np.hstack((np.asarray(time_samples.values()).T, probs))
columns = copy.copy(time_samples.keys())
columns.append("P(z | attacker)")
columns.append("P(data | z, attacker)")
out = pandas.DataFrame(out_ar, columns=columns)
mcmc_results = Results(out, data[-1], prob_no_attacker, prob_true_value, data, metropolis=True)
return mcmc_results
def MCMC_MH(SFTNet, data, s0, N, T, proposal_var=100, print_jumps=False):
# TODO Need to profile this
# TODO: Need to make this more general. Not trivial
# TODO : Add sample from possible node orderings
"""
Performs MCMC integration using Metropolis Hastings. Returns
the sampled times, their associated probabilities and the
associated likelihood value. This method corresponds to David's
"half-way" approach in the 2nd version of the ASCII where we
sample (accept / reject) according to P(z | attacker) and then
take the average of P(data | z, attacker) of the accepted
values.
SFTNet : SFTNet instance
The net to do MCMC over
data : list
The data as outputted by gen_data
N : int
The number of MCMC proposals
s0 : dict
State of the net at t=0
T : int
How long the process ran for.
"""
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in SFTNet.node_names if s0[nd] == 'normal']
nodes_no_change = [nd for nd in SFTNet.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(SFTNet, data, T)
prob_true_value = prob_model_given_data(SFTNet, data, data[-1], T,
logn_fact)
prob_mod = lambda x: prob_model_given_data(SFTNet, data, x, T, logn_fact)
guess_times = np.sort(np.random.random(size=len(nodes_to_change)) * T)
z0 = dict(zip(nodes_to_change, guess_times))
for nd in nodes_no_change:
z0[nd] = 0
# lambda function that calls prob_model_given_data for
# specified infection times
p0 = prob_mod(z0)
# Initiial probability
# actual times
time_samples = {node.name: [] for node in SFTNet.nodes}
# container for samples
probs = []
# container for probabilities
z1 = copy.deepcopy(z0)
while n < N:
#if np.random.random() < alpha:
# order = random.sample(orderings, 1)[0]
for nd in nodes_to_change:
z1[nd] = z0[nd] + np.random.normal() * proposal_var
p1 = prob_mod(z1)
if (p1[0] - p0[0] > np.log(np.random.random())):
if print_jumps:
print 'A Jump at, ', n, 'to ', z1, 'with prob', p1, '\n'
p0 = p1
z0 = copy.deepcopy(z1)
for key, val in z0.iteritems():
time_samples[key].append(val)
probs.append(p0[:2])
n += 1
probs = np.asarray(probs)
out_ar = np.hstack((np.asarray(time_samples.values()).T, probs))
columns = copy.copy(time_samples.keys())
columns.append('P(z | attacker)')
columns.append('P(data | z, attacker)')
out = pandas.DataFrame(out_ar, columns=columns)
mcmc_results = Results(out,
data[-1],
prob_no_attacker,
prob_true_value,
data,
metropolis=True)
return mcmc_results
def get_roc_coords(seed,
num_pos,
num_neg,
i_net,
s0,
truenet=None,
method='Direct_Sample',
T=10000,
uni_samp_size=2000,
mcmc_steps=5000,
directsamps=1000,
burnin_rate=.25,
printsteps=False):
"""
num_pos : int
Number pf infected nets in the sample
num_neg :
Number of clean nets to generate
i_net : SFTNet
The net instance with an attacker
s0 : dict
Initial state of the net when there is an attacker
T : int
Observation Window
uni_samp_size : int
The sample size for each infection ordering in uniform sampling
"""
if truenet == None:
truenet = i_net
np.random.seed(seed)
infected_lhoods = []
# Will store the lhood w attacker and lhood difference
clean_lhoods = []
for i in range(num_pos):
if printsteps:
print 'i= ', i
data = gen_data(T, truenet, s0)
if method == 'uniform':
res = uniform_samp(i_net, s0, uni_samp_size, T, data)[0]
elif method == 'mcmc':
mh_res = MCMC_sequence(i_net,
data,
s0,
mcmc_steps,
T,
print_jumps=False)
res = mh_res.calc_log_likelihood(burnin=int(burnin_rate *
mcmc_steps))
else:
res = Direct_Sample(i_net, data, directsamps, T, s0)[0]
p_no_attacker = prob_model_no_attacker(i_net, data, T)
# infected_lhoods.append((uni_res[0], p_no_attacker))
infected_lhoods.append((res, p_no_attacker))
for j in range(num_neg):
if printsteps:
print 'j =', j
data = gen_data(
T, truenet,
dict(zip(i_net.node_names, ['normal'] * len(i_net.nodes))))
if method == 'uniform':
res = uniform_samp(i_net, s0, uni_samp_size, T, data)[0]
elif method == 'mcmc':
mh_res = MCMC_sequence(i_net,
data,
s0,
mcmc_steps,
T,
print_jumps=False)
res = mh_res.calc_log_likelihood(burnin=int(burnin_rate *
mcmc_steps))
else:
res = Direct_Sample(i_net, data, directsamps, T, s0)[0]
p_no_attacker = prob_model_no_attacker(i_net, data, T)
clean_lhoods.append((res, p_no_attacker))
return infected_lhoods, clean_lhoods
def get_roc_coords(
seed,
num_pos,
num_neg,
i_net,
s0,
truenet=None,
method="Direct_Sample",
T=10000,
uni_samp_size=2000,
mcmc_steps=5000,
directsamps=1000,
burnin_rate=0.25,
printsteps=False,
):
"""
num_pos : int
Number pf infected nets in the sample
num_neg :
Number of clean nets to generate
i_net : SFTNet
The net instance with an attacker
s0 : dict
Initial state of the net when there is an attacker
T : int
Observation Window
uni_samp_size : int
The sample size for each infection ordering in uniform sampling
"""
if truenet == None:
truenet = i_net
np.random.seed(seed)
infected_lhoods = []
# Will store the lhood w attacker and lhood difference
clean_lhoods = []
for i in range(num_pos):
if printsteps:
print "i= ", i
data = gen_data(T, truenet, s0)
if method == "uniform":
res = uniform_samp(i_net, s0, uni_samp_size, T, data)[0]
elif method == "mcmc":
mh_res = MCMC_sequence(i_net, data, s0, mcmc_steps, T, print_jumps=False)
res = mh_res.calc_log_likelihood(burnin=int(burnin_rate * mcmc_steps))
else:
res = Direct_Sample(i_net, data, directsamps, T, s0)[0]
p_no_attacker = prob_model_no_attacker(i_net, data, T)
# infected_lhoods.append((uni_res[0], p_no_attacker))
infected_lhoods.append((res, p_no_attacker))
for j in range(num_neg):
if printsteps:
print "j =", j
data = gen_data(T, truenet, dict(zip(i_net.node_names, ["normal"] * len(i_net.nodes))))
if method == "uniform":
res = uniform_samp(i_net, s0, uni_samp_size, T, data)[0]
elif method == "mcmc":
mh_res = MCMC_sequence(i_net, data, s0, mcmc_steps, T, print_jumps=False)
res = mh_res.calc_log_likelihood(burnin=int(burnin_rate * mcmc_steps))
else:
res = Direct_Sample(i_net, data, directsamps, T, s0)[0]
p_no_attacker = prob_model_no_attacker(i_net, data, T)
clean_lhoods.append((res, p_no_attacker))
return infected_lhoods, clean_lhoods
def MCMC_sequence(SFTNet, data, s0, N, T, proposal_var=100, print_jumps=False, alpha=1):
# TODO Need to profile this
# TODO: Need to make this more general. Not trivial
# TODO : Add sample from possible node orderings
"""
Performs MCMC integration using Metropolis Hastings. Returns
the sampled times, their associated probabilities and the
associated likelihood value. This method corresponds to David's
"half-way" approach in the 2nd version of the ASCII where we
sample (accept / reject) according to P(z | attacker) and then
take the average of P(data | z, attacker) of the accepted
values.
SFTNet : SFTNet instance
The net to do MCMC over
data : list
The data as outputted by gen_data
N : int
The number of MCMC proposals
s0 : dict
State of the net at t=0
T : int
How long the process ran for.
"""
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in SFTNet.node_names if s0[nd] == 'normal' ]
nodes_no_change = [nd for nd in SFTNet.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(SFTNet, data, T)
prob_true_value = prob_model_given_data(SFTNet, data, data[-1], T, logn_fact)
numattackers = len(nodes_no_change)
prob_mod = lambda x : prob_model_given_data(SFTNet, data, x, T,
logn_fact)
guess_times = np.sort(np.random.random(size=len(nodes_to_change))*T)
z0 = dict(zip(nodes_to_change, guess_times))
for nd in nodes_no_change:
z0[nd] = 0
order = sorted(z0.iterkeys(), key = lambda k: z0[k])
# lambda function that calls prob_model_given_data for
# specified infection times
p0 = prob_mod(z0)
# Initiial probability
# actual times
time_samples = {node.name : [] for node in SFTNet.nodes}
# container for samples
probs = []
# container for probabilities
z1 = copy.deepcopy(z0)
orders = gen_orderings(SFTNet, s0)
state0 = ['infected'] * numattackers + ['normal'] * len(nodes_to_change)
while n < N:
z1 = dict(zip(nodes_no_change, [0] * numattackers))
last_infect = 0
state = copy.copy(state0)
if np.random.random() < alpha:
new_order = random.choice(orders)
switch_order = True
else :
switch_order = False
new_order = order
for nd in new_order[numattackers:]:
cross_s_ix = SFTNet.cross_S.index(state)
nd_ix = SFTNet.node_names.index(nd)
incoming_rate = np.sum(SFTNet.mal_trans_mats[cross_s_ix][:, nd_ix])
last_infect = last_infect + trunc_expon(incoming_rate, T-last_infect)
z1[nd] = last_infect
state[nd_ix] = 'infected'
p1 = prob_mod(z1)
# Possible change to 2
if (p1[2] -p0[2] > np.log(np.random.random())):
if print_jumps :
print 'A Jump at, ', n, 'to ', z1, 'with prob', p1, '\n'
if switch_order:
#print ' new order ', order, ' at ', n
p0 = p1
z0 = copy.deepcopy(z1)
order = new_order
for key, val in z0.iteritems():
time_samples[key].append(val)
for nd in nodes_to_change:
if nd not in z0.keys():
time_samples[nd].append(T)
probs.append(p0[:2])
n += 1
probs = np.asarray(probs)
out_ar = np.hstack((np.asarray(time_samples.values()).T, probs))
columns = copy.copy(time_samples.keys())
columns.append('P(z | attacker)')
columns.append('P(data | z, attacker)')
out = pandas.DataFrame(out_ar, columns = columns)
mcmc_results = Results(out, data[-1], prob_no_attacker,
prob_true_value, data, metropolis = True)
return mcmc_results
def MCMC_sequence(SFTNet,
data,
s0,
N,
T,
proposal_var=100,
print_jumps=False,
alpha=1):
# TODO Need to profile this
# TODO: Need to make this more general. Not trivial
# TODO : Add sample from possible node orderings
"""
Performs MCMC integration using Metropolis Hastings. Returns
the sampled times, their associated probabilities and the
associated likelihood value. This method corresponds to David's
"half-way" approach in the 2nd version of the ASCII where we
sample (accept / reject) according to P(z | attacker) and then
take the average of P(data | z, attacker) of the accepted
values.
SFTNet : SFTNet instance
The net to do MCMC over
data : list
The data as outputted by gen_data
N : int
The number of MCMC proposals
s0 : dict
State of the net at t=0
T : int
How long the process ran for.
"""
logn_fact = gen_logn_fact(data)
n = 1
nodes_to_change = [nd for nd in SFTNet.node_names if s0[nd] == 'normal']
nodes_no_change = [nd for nd in SFTNet.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(SFTNet, data, T)
prob_true_value = prob_model_given_data(SFTNet, data, data[-1], T,
logn_fact)
numattackers = len(nodes_no_change)
prob_mod = lambda x: prob_model_given_data(SFTNet, data, x, T, logn_fact)
guess_times = np.sort(np.random.random(size=len(nodes_to_change)) * T)
z0 = dict(zip(nodes_to_change, guess_times))
for nd in nodes_no_change:
z0[nd] = 0
order = sorted(z0.iterkeys(), key=lambda k: z0[k])
# lambda function that calls prob_model_given_data for
# specified infection times
p0 = prob_mod(z0)
# Initiial probability
# actual times
time_samples = {node.name: [] for node in SFTNet.nodes}
# container for samples
probs = []
# container for probabilities
z1 = copy.deepcopy(z0)
orders = gen_orderings(SFTNet, s0)
state0 = ['infected'] * numattackers + ['normal'] * len(nodes_to_change)
while n < N:
z1 = dict(zip(nodes_no_change, [0] * numattackers))
last_infect = 0
state = copy.copy(state0)
if np.random.random() < alpha:
new_order = random.choice(orders)
switch_order = True
else:
switch_order = False
new_order = order
for nd in new_order[numattackers:]:
cross_s_ix = SFTNet.cross_S.index(state)
nd_ix = SFTNet.node_names.index(nd)
incoming_rate = np.sum(SFTNet.mal_trans_mats[cross_s_ix][:, nd_ix])
last_infect = last_infect + trunc_expon(incoming_rate,
T - last_infect)
z1[nd] = last_infect
state[nd_ix] = 'infected'
p1 = prob_mod(z1)
# Possible change to 2
if (p1[2] - p0[2] > np.log(np.random.random())):
if print_jumps:
print 'A Jump at, ', n, 'to ', z1, 'with prob', p1, '\n'
if switch_order:
#print ' new order ', order, ' at ', n
p0 = p1
z0 = copy.deepcopy(z1)
order = new_order
for key, val in z0.iteritems():
time_samples[key].append(val)
for nd in nodes_to_change:
if nd not in z0.keys():
time_samples[nd].append(T)
probs.append(p0[:2])
n += 1
probs = np.asarray(probs)
out_ar = np.hstack((np.asarray(time_samples.values()).T, probs))
columns = copy.copy(time_samples.keys())
columns.append('P(z | attacker)')
columns.append('P(data | z, attacker)')
out = pandas.DataFrame(out_ar, columns=columns)
mcmc_results = Results(out,
data[-1],
prob_no_attacker,
prob_true_value,
data,
metropolis=True)
return mcmc_results
def Direct_Sample(CyberNet, data, num_samples, T, s0):
"""
Returns P(data|attacker) by Monte Carlo Sampling
CyberNet : CyberNet Instance
data : list
Output of gen_data
num_samples : int
How many Monte Carlo samples
T : int
Time window
s0 : dict
Initial states of nodes
"""
net = copy.deepcopy(CyberNet)
# The states of nodes will be changing so we want to make sure
# we do not change the input network
logn_fact = gen_logn_fact(data)
#Precompute log(n!) for various n.
n = 1
nodes_to_change = [nd for nd in net.node_names if s0[nd] == 'normal']
nodes_no_change = [nd for nd in net.node_names if s0[nd] == 'infected']
prob_no_attacker = prob_model_no_attacker(net, data, T, logn_fact)
numattackers = len(nodes_no_change)
prob_mod = lambda x: prob_model_given_data_times(net, data, x, T,
logn_fact, s0)
# Only input is not the infection times
probs = []
while n < num_samples:
t = 0
for nd in net.node_names:
net.node_dict[nd].state = s0[nd]
times = {nd: 0 for nd in nodes_no_change}
# Corresponds to correct order
while t < T:
infected = [nd.name for nd in net.nodes if nd.state == 'infected']
at_risk = set(
chain(*[net.node_dict[nd].sends_to
for nd in infected])) - set(infected)
if len(at_risk) == 0:
break
at_risk_ix = [net.node_names.index(nd) for nd in at_risk]
mt_rates = np.sum(net.get_mal_trans()[:, at_risk_ix], axis=0)
#print at_risk, mt_rates, infected, n
r_rate = np.sum(mt_rates)
t += np.random.exponential(scale=1. / r_rate)
# Sample time of next infection
if t < T:
next_infected = np.random.choice(list(at_risk),
p=mt_rates /
float(sum(mt_rates)))
# Sample node to be infected
times[next_infected] = t
net.node_dict[next_infected].state = 'infected'
#print times, n
probs.append(prob_mod(times))
n += 1
# prob_mod returns log prob so we need to exponentiate to get the mean
e_probs = np.exp(probs)
return np.log(np.mean(e_probs))