def mcmc_chain(G, D, sig_prob=None, sampler=sample_sigma_uniformly):
sig_prob = sig_prob if sig_prob is not None else dict()
calculate_probability = lambda sigma: sum(
state_probabilities(G, sigma, O)[1] for O in D)
sample = sampler(n=G.shape[0])
prob = calculate_probability(sample)
sig_prob[tuple(sample)] = prob
while True:
new_sample = sampler(sample)
try:
new_prob = sig_prob[tuple(new_sample)]
except KeyError:
new_prob = calculate_probability(new_sample)
sig_prob[tuple(new_sample)] = new_prob
alpha = math.exp(new_prob - prob)
r = min(1, alpha)
u = random.random()
if u < r:
sample = new_sample
prob = new_prob
yield sample
def calculate_sigma(G, O):
probabilities = collections.defaultdict(int)
normalizer = -math.inf
print("Calculating sigma...")
for sigma in itertools.product((1, 2), repeat=G.shape[0]):
sigma_arr = numpy.array(sigma)
_, O_prob = state_probabilities.state_probabilities(G, sigma_arr, O)
probabilities[sigma] = O_prob
normalizer = numpy.logaddexp(normalizer, O_prob)
for sigma, prob in probabilities.items():
probabilities[sigma] = math.exp(prob - normalizer)
print("Calculated sigma.")
return probabilities
def calculate_sigma(G, O):
probabilities = collections.defaultdict(int)
normalizer = -math.inf
print("Calculating sigma...")
for sigma in itertools.product((1, 2), repeat=G.shape[0]):
sigma_arr = numpy.array(sigma)
_, O_prob = state_probabilities.state_probabilities(G, sigma_arr, O)
probabilities[sigma] = O_prob
normalizer = numpy.logaddexp(normalizer, O_prob)
for sigma, prob in probabilities.items():
probabilities[sigma] = math.exp(prob - normalizer)
print("Calculated sigma.")
return probabilities
def calculate_final_distribution(G, O):
sigmas, sig_ind_prob, samples = mcmc.sig_mcmc_2(G, [O], 10000, 100)
bar1 = sig_ind_prob/samples;
bar2 = numpy.ones(G.shape[0]) - bar1;
ind = numpy.arange(G.shape[0]);
p1 = plot.bar(ind, bar1, 0.35, color='r');
p2 = plot.bar(ind, bar2, 0.35, color='b', bottom=bar1);
plot.ylabel('L/R')
plot.title('Switch index')
plot.legend((p1[0], p2[0]), ('L', 'R'))
plot.show();
bar = numpy.zeros(len(sigmas));
label = numpy.zeros(len(sigmas));
ind = numpy.arange(len(sigmas));
i = 0;
for sigma, n in sigmas.items():
bar[i] = n/float(samples);
label[i] = mcmc.sigma_hash(sigmas);
i += 1;
p1 = plot.bar(ind, bar, 0.1, color='black');
#plot.xticks(ind+0.1/2., tuple(label));
plot.ylabel('Probability of sigma')
plot.xlabel('Sigma index')
plot.title('Joint probability of sigma')
plot.show();
s = numpy.zeros(G.shape)
for sigma, n in sigmas.items():
sigma = numpy.array(sigma)
# s2 is already normalized, i.e. it is
# p(s, O | G, sigma)/p(O | G, sigma) = p(s | G, O, sigma)
s2, _ = state_probabilities.state_probabilities(G, sigma, O)
# multiply s2 by p(sigma | G, O)
s2 *= n / samples
# sum over all sigmas
s += s2
return s
def calculate_final_distribution(G, O):
sigmas, sig_ind_prob, samples = mcmc.sig_mcmc_2(G, [O], 10000, 100)
bar1 = sig_ind_prob / samples
bar2 = numpy.ones(G.shape[0]) - bar1
ind = numpy.arange(G.shape[0])
p1 = plot.bar(ind, bar1, 0.35, color='r')
p2 = plot.bar(ind, bar2, 0.35, color='b', bottom=bar1)
plot.ylabel('L/R')
plot.title('Switch index')
plot.legend((p1[0], p2[0]), ('L', 'R'))
plot.show()
bar = numpy.zeros(len(sigmas))
label = numpy.zeros(len(sigmas))
ind = numpy.arange(len(sigmas))
i = 0
for sigma, n in sigmas.items():
bar[i] = n / float(samples)
label[i] = mcmc.sigma_hash(sigmas)
i += 1
p1 = plot.bar(ind, bar, 0.1, color='black')
#plot.xticks(ind+0.1/2., tuple(label));
plot.ylabel('Probability of sigma')
plot.xlabel('Sigma index')
plot.title('Joint probability of sigma')
plot.show()
s = numpy.zeros(G.shape)
for sigma, n in sigmas.items():
sigma = numpy.array(sigma)
# s2 is already normalized, i.e. it is
# p(s, O | G, sigma)/p(O | G, sigma) = p(s | G, O, sigma)
s2, _ = state_probabilities.state_probabilities(G, sigma, O)
# multiply s2 by p(sigma | G, O)
s2 *= n / samples
# sum over all sigmas
s += s2
return s
def observations_needed(max_nodes=100, runs=50):
"""Calculates the number of observations needed
to get a good estimate of the stop position."""
failure_probabilities = []
with open("observations_needed.dat", 'w') as obs_file:
for nodes in range(6, max_nodes + 1, 2):
total_observations_needed = 0
failed_runs = 0
i = 0
while True:
G, sigma = generate_g.generate_graph_and_settings(nodes)
O, actual_path = generate_g.simulate_train(G, sigma, 200)
for observations in range(1, len(O)):
s, _ = state_probabilities.state_probabilities(
G, sigma, O[:observations])
if s.max() > 0.90:
break
else:
print(s.max())
failed_runs += 1
continue
total_observations_needed += observations
i += 1
if i >= runs:
break
obs_file.write("{}\t{}\n".format(nodes,
total_observations_needed / runs))
print(nodes, total_observations_needed / runs)
failure_probability = failed_runs / (runs + failed_runs)
print("Failure probability: {}".format(failure_probability))
failure_probabilities.append(failure_probability)
print("Average failure probability: {}".format(
sum(failure_probabilities) / len(failure_probabilities)))
def observations_needed(max_nodes=100, runs=50):
"""Calculates the number of observations needed
to get a good estimate of the stop position."""
failure_probabilities = []
with open("observations_needed.dat", 'w') as obs_file:
for nodes in range(6, max_nodes + 1, 2):
total_observations_needed = 0
failed_runs = 0
i = 0
while True:
G, sigma = generate_g.generate_graph_and_settings(nodes)
O, actual_path = generate_g.simulate_train(G, sigma, 200)
for observations in range(1, len(O)):
s, _ = state_probabilities.state_probabilities(
G, sigma, O[:observations])
if s.max() > 0.90:
break
else:
print(s.max())
failed_runs += 1
continue
total_observations_needed += observations
i += 1
if i >= runs:
break
obs_file.write("{}\t{}\n".format(nodes, total_observations_needed / runs))
print(nodes, total_observations_needed / runs)
failure_probability = failed_runs / (runs + failed_runs)
print("Failure probability: {}".format(failure_probability))
failure_probabilities.append(failure_probability)
print("Average failure probability: {}".format(sum(failure_probabilities) / len(failure_probabilities)))
def mcmc_chain_2(G, D, init=100, sig_prob=None, sig_ind_prob=None):
sig_prob = sig_prob if sig_prob is not None else dict()
sig_ind_prob = sig_ind_prob if sig_ind_prob is not None else np.ones(G.shape[0]);
sig_ind_prob *= init/2;
t = init;
calculate_probability = lambda sigma: sum(
state_probabilities(G, sigma, O)[1] for O in D)
sample = sample_sigma_uniformly(n=G.shape[0])
prob = calculate_probability(sample)
sig_prob[tuple(sample)] = prob
while True:
new_sample = sample_posterior_sigma(sig_ind_prob, t)
try:
new_prob = sig_prob[tuple(new_sample)]
except KeyError:
new_prob = calculate_probability(new_sample)
sig_prob[tuple(new_sample)] = new_prob
alpha = math.exp(new_prob - prob)
alpha *= switch_probability_posterior(new_sample, sig_ind_prob, t)
alpha /= switch_probability_posterior(sample, sig_ind_prob, t)
r = min(1, alpha)
u = random.random()
if u < r:
sample = new_sample
prob = new_prob
sig_ind_prob += sample - np.ones(G.shape[0]);
t += 1;
yield sample
if prob < 5:
print('Some wrong observation made')
wrongObs = obs
while wrongObs == obs:
wrongObs = random.randrange(1, 5)
obs = wrongObs
O.append(obs)
s_old = s
s = G[s, ext]
for a in range(0, 3):
if G[s, a] == s_old:
orientation = a
break
actual_path.append(s)
return O, actual_path
if __name__ == '__main__':
G, sigma = generate_graph_and_settings(6)
O, path = simulate_train(G, sigma, 20)
print("Actual path:", path)
print("Observations:", O)
import state_probabilities
s, O_prob = state_probabilities.state_probabilities(G, sigma, O)
predicted_node, predicted_label = np.unravel_index(s.argmax(), s.shape)
print("Last observation was generated after exiting " \
"node {} at label {} with probability {}".format(
predicted_node, "0LR"[predicted_label], s.max()))
if prob < 5:
print('Some wrong observation made')
wrongObs = obs
while wrongObs == obs:
wrongObs = random.randrange(1, 5)
obs = wrongObs
O.append(obs)
s_old = s
s = G[s, ext]
for a in range(0, 3):
if G[s, a] == s_old:
orientation = a
break
actual_path.append(s)
return O, actual_path
if __name__ == '__main__':
G, sigma = generate_graph_and_settings(6)
O, path = simulate_train(G, sigma, 20)
print("Actual path:", path)
print("Observations:", O)
import state_probabilities
s, O_prob = state_probabilities.state_probabilities(G, sigma, O)
predicted_node, predicted_label = np.unravel_index(s.argmax(), s.shape)
print("Last observation was generated after exiting " \
"node {} at label {} with probability {}".format(
predicted_node, "0LR"[predicted_label], s.max()))
