def main():
run_data = {}
run_id = 0
scale = 0.5
emissions_normal = { 1: Normal(0, 2.0 * scale),
2: Normal(3.5, 3.0 * scale),
3: Normal(6.5, 1.0 * scale) }
emissions_laplace = { 1: Laplace(0, 2.0 * scale),
2: Laplace(3.5, 3.0 * scale),
3: Laplace(6.5, 1.0 * scale) }
emission_spec = emissions_normal
dists = [Normal(max_sigma = 6.0) for n in range(3)]
num_state_reps = 50
num_emission_reps = 4
num_gamma_init_reps = 4
num_blocks = [1, 2, 5, 10, 20, 50]
verbose = False
graphics_on = False
total_work = (num_state_reps * num_emission_reps *
2 * num_gamma_init_reps * len(num_blocks))
work = 0
for state_rep in range(num_state_reps):
print 'State repetition %d' % state_rep
# Generate HMM states
while True:
model = HMM([('Start', (1,), (1.0,)),
(1, (1,2,3), (0.98, 0.02, 0.0)),
(2, (1,2,3), (0.02, 0.95, 0.03)),
(3, (1,2,3,'End'), (0.03, 0.03, 0.93, 0.01))],
emission_spec)
model.simulate()
num_data = len(model.state_vec)
if num_data < 5000 and num_data > 100: break
counts = {}
for state in model.state_vec:
if not state in counts:
counts[state] = 0
counts[state] += 1
if verbose: print 'Counts: %s' % str(counts)
# Generate shuffled indices for repeatable shuffling
shuffling = np.arange(num_data)
np.random.shuffle(shuffling)
for emission_rep in range(num_emission_reps):
if verbose: print 'Emission repetition %d' % emission_rep
model.emit()
for shuffled in [False, True]:
if verbose: print 'Shuffling HMM run: %s' % str(shuffled)
states = np.array(model.state_vec)
emissions = np.array(model.emission_vec)
if shuffled:
states = states[shuffling]
emissions = emissions[shuffling]
for num_block in num_blocks:
if verbose: print 'Blocks: %d' % num_block
blocks = np.array_split(np.arange(num_data), num_block)
for gamma_rep in range(num_gamma_init_reps):
if verbose: print 'Initial gamma seed: %d' % gamma_rep
init_gamma = np.array(states) - 1
run_id += 1
this_run = {}
this_run['num data'] = num_data
this_run['state rep'] = state_rep
this_run['emission rep'] = emission_rep
this_run['shuffled'] = shuffled
this_run['blocks'] = num_block
this_run['gamma init rep'] = gamma_rep
start_time = time.clock()
results = em(emissions,
dists,
blocks = blocks,
gamma_seed = gamma_rep,
init_gamma = init_gamma,
count_restart = 0.0)
pi = results['pi']
dists = results['dists']
reps = results['reps']
conv = results['converged']
run_time = time.clock() - start_time
this_run['run time'] = run_time
this_run['reps'] = reps
conv_status = conv and 'converged' or 'not converged'
this_run['convergence'] = conv_status
print 'Reps: %d (%s)' % (reps, conv_status)
print 'Time elapsed: %.2f' % run_time
if verbose: print_mixture(pi, dists)
if graphics_on:
display_densities(emissions, dists)
display_hist(emissions, dists)
act = emission_spec.values()
this_run['err mean max'] = max_error_mean(dists, act)
this_run['err mean mean'] = mean_error_mean(dists, act)
like = np.zeros(num_data)
pi_overall = np.mean(pi, 0)
for p, dist in zip(pi_overall, dists):
like += p * dist.density(states)
this_run['log likelihood'] = np.sum(np.log(like))
like = np.zeros(num_data)
for i, block in enumerate(blocks):
for p, dist in zip(pi[i], dists):
comp = p * dist.density(states[block])
like[block] += comp
this_run['log likelihood local'] = np.sum(np.log(like))
run_data[run_id] = this_run
work += 1
print 'Finished run %d/%d' % (work, total_work)
# Output data to CSV
cols = set()
for id in run_data:
for k in run_data[id]:
cols.add(k)
with open('outfile.csv', 'wb') as f:
writer = csv.writer(f)
writer.writerow(list(cols))
writer.writerows([[run_data[id][c] for c in cols] for id in run_data])
# Do EM
results = em(noisy_emissions,
[NormalFixedMean(m, max_sigma=max_sigma) for m in range(256)],
count_restart=count_restart,
blocks=blocks)
dists = results['dists']
pi = results['pi']
print 'Iterations: %(reps)d' % results
gamma = np.transpose(results['gamma'])
means = np.array([d.mean() for d in dists])
sds = np.array([d.sd() for d in dists])
# Display summary figures
display_densities(real_emissions, dists)
# Reconstruct with argmax
im_argmax = Image.new('L', (width, height))
reconstruct_argmax = means[np.argmax(gamma, axis=1)]
im_argmax.putdata(reconstruct_argmax)
summary.paste(im_argmax, (10, 40 + height))
# Reconstruct with weighted average
im_avg = Image.new('L', (width, height))
reconstruct_avg = [np.average(means, weights=g, axis=0) for g in gamma]
im_avg.putdata(reconstruct_avg)
summary.paste(im_avg, (30 + width, 40 + height))
# Show summary image
summary.show()
model,
count_restart = count_restart,
blocks = blocks,
init_gamma = init_gamma,
pi_max = pi_max)
print 'Iterations: %d (%s)' % (results['reps'], block_strategy)
dists = results['dists']
pi = results['pi']
# Display results
if show_each:
for p, d in zip(np.transpose(pi), dists):
print '%s: %s' % (p, d.display())
print
if graphics:
display_densities(data.reshape((dim*dim,)), dists)
display_hist(data.reshape((dim*dim,)), dists)
# Compute errors
errors[mu][block_strategy].append(rmse(dists, mu))
# Summarize runs
errs, confs = {}, {}
for block_strategy in block_strategies:
errs[block_strategy], confs[block_strategy] = [], []
for mu in mus:
print 'mu = %.2f' % mu
for block_strategy in block_strategies:
error = np.array(errors[mu][block_strategy])
err, conf = np.mean(error), 2.0 * np.std(error) / np.sqrt(reps)
errs[block_strategy].append(err)
init_reps = em_steps,
max_reps = em_steps,
pi_max = pi_max,
trace = True)
if show_each:
print 'Iterations: %(reps)d' % results
dists, dists_trace = results['dists'], results['dists_trace']
pi, pi_trace = results['pi'], results['pi_trace']
# Display results
if show_each:
for p, d in zip(np.transpose(pi), dists):
print '%s: %s' % (p, d.display())
print
if graphics:
display_densities(data, dists)
display_hist(data, dists)
if plot_trace:
pi_trace = np.array(pi_trace)
v = np.transpose(pi_trace[:,:,0])
u = np.empty((em_steps+1))
w = np.empty((num_blocks, (em_steps+1)))
m = np.empty((2, em_steps+1))
for t in range((em_steps+1)):
d = dists_trace[t]
m1, m2 = d[0].mean(), d[1].mean()
u[t] = m1 - m2
m[0,t] = m1
m[1,t] = m2
for b in range(num_blocks):
model,
count_restart=count_restart,
blocks=blocks,
init_gamma=init_gamma,
pi_max=pi_max)
print 'Iterations: %d (%s)' % (results['reps'], block_strategy)
dists = results['dists']
pi = results['pi']
# Display results
if show_each:
for p, d in zip(np.transpose(pi), dists):
print '%s: %s' % (p, d.display())
print
if graphics:
display_densities(data.reshape((dim * dim, )), dists)
display_hist(data.reshape((dim * dim, )), dists)
# Compute errors
errors[mu][block_strategy].append(rmse(dists, mu))
# Summarize runs
errs, confs = {}, {}
for block_strategy in block_strategies:
errs[block_strategy], confs[block_strategy] = [], []
for mu in mus:
print 'mu = %.2f' % mu
for block_strategy in block_strategies:
error = np.array(errors[mu][block_strategy])
err, conf = np.mean(error), 2.0 * np.std(error) / np.sqrt(reps)
errs[block_strategy].append(err)
# Do EM
results = em(noisy_emissions,
[NormalFixedMean(m, max_sigma = max_sigma) for m in range(256)],
count_restart = count_restart,
blocks = blocks)
dists = results['dists']
pi = results['pi']
print 'Iterations: %(reps)d' % results
gamma = np.transpose(results['gamma'])
means = np.array([d.mean() for d in dists])
sds = np.array([d.sd() for d in dists])
# Display summary figures
display_densities(real_emissions, dists)
# Reconstruct with argmax
im_argmax = Image.new('L', (width, height))
reconstruct_argmax = means[np.argmax(gamma, axis=1)]
im_argmax.putdata(reconstruct_argmax)
summary.paste(im_argmax, (10, 40 + height))
# Reconstruct with weighted average
im_avg = Image.new('L', (width, height))
reconstruct_avg = [np.average(means, weights=g, axis=0) for g in gamma]
im_avg.putdata(reconstruct_avg)
summary.paste(im_avg, (30 + width, 40 + height))
# Show summary image
summary.show()
init_reps=em_steps,
max_reps=em_steps,
pi_max=pi_max,
trace=True)
if show_each:
print 'Iterations: %(reps)d' % results
dists, dists_trace = results['dists'], results['dists_trace']
pi, pi_trace = results['pi'], results['pi_trace']
# Display results
if show_each:
for p, d in zip(np.transpose(pi), dists):
print '%s: %s' % (p, d.display())
print
if graphics:
display_densities(data, dists)
display_hist(data, dists)
if plot_trace:
pi_trace = np.array(pi_trace)
v = np.transpose(pi_trace[:, :, 0])
u = np.empty((em_steps + 1))
w = np.empty((num_blocks, (em_steps + 1)))
m = np.empty((2, em_steps + 1))
for t in range((em_steps + 1)):
d = dists_trace[t]
m1, m2 = d[0].mean(), d[1].mean()
u[t] = m1 - m2
m[0, t] = m1
m[1, t] = m2
for b in range(num_blocks):
