def plot_mix(i):
plt.clf()
plt.title('Proposal density - iteration %i' %i)
plot_mixture(vb.make_mixture(), 1, 2, visualize_weights=True, cmap='jet')
plt.colorbar()
plt.xlabel('$x_2$')
plt.ylabel('$x_3$')
plt.xlim(-30,10)
plt.ylim(-30,30)
plt.draw()
return i
short_patches = pypmc.tools.patch_data(stacked_data, L=100)
# run hierarchical clustering
hc = pypmc.mix_adapt.hierarchical.Hierarchical(short_patches, long_patches, verbose=True)
hc.run()
hcmix = hc.g
# run variational bayes with mixture --> use the long patches as initial guess
merge = pypmc.mix_adapt.variational.VBMerge(short_patches, len(stacked_data), initial_guess=long_patches)
merge.run(1000, abs_tol=1e-5, rel_tol=1e-10, prune=.5*len(vb.data)/vb.K, verbose=True)
# Note: ``prune`` should be ``vb.N/vb.K`` but ``.5*len(vb.data)/vb.K`` is smaller (due to taking every 50th sample only)
# and still merge tends to prune too much --> overall message remains valid
mergemix = merge.make_mixture()
# plot the mixtures from these algorithms
plt.figure(); plt.title('Hierarchical'); plot_mixture(hc.g)
plt.figure(); plt.title('VB samples'); plot_mixture(vbmix)
plt.figure(); plt.title('VB mixtures'); plot_mixture(mergemix)
plt.draw()
# define an importance sampler for each proposal and run 10**5 steps
hc_sampler = pypmc.sampler.importance_sampling.DeterministicIS(log_target, hcmix, std_weights=True)
vb_sampler = pypmc.sampler.importance_sampling.DeterministicIS(log_target, vbmix, std_weights=True)
merge_sampler = pypmc.sampler.importance_sampling.DeterministicIS(log_target, mergemix, std_weights=True)
hc_sampler.run(10**5)
vb_sampler.run(10**5)
merge_sampler.run(10**5)
# plot importance samples
plt.figure(); plt.title('Hierarchical')
plt.hist2d(hc_sampler.history[:][:,1], hc_sampler.history[:][:,2], weights=hc_sampler.history[:][:,0], cmap='gray_r', bins=100)
# data points
N = 500
data = np.random.normal(size=2 * N).reshape(N, 2)
# maximum number of components in mixture
K = 6
vb = GaussianInference(data,
components=K,
alpha=10 * np.ones(K),
nu=3 * np.ones(K))
# plot data and initial guess
plt.subplot(1, 2, 1)
plt.scatter(data[:, 0], data[:, 1], color='gray')
initial_mix = vb.make_mixture()
plot_mixture(initial_mix, cmap='gist_rainbow')
x_range = (-4, 4)
y_range = x_range
plt.xlim(x_range)
plt.ylim(y_range)
plt.gca().set_aspect('equal')
plt.title('Initial')
# compute variational Bayes posterior
vb.run(prune=0.5 * len(data) / K, verbose=True)
# obtain most probable mixture and plot it
mix = vb.make_mixture()
plt.subplot(1, 2, 2)
plt.scatter(data[:, 0], data[:, 1], color='gray')
plt.xlim(x_range)
# form the "long_patches"
long_patches = pypmc.mix_adapt.r_value.make_r_gaussmix(mcmc_data)
# form first proposal with PMC
print 'running PMC'
pmcmix = pypmc.mix_adapt.pmc.gaussian_pmc(stacked_data[::100], long_patches, copy=True)
pmcmix.prune(.5/len(long_patches))
for i in range(1000-1):
print i
pypmc.mix_adapt.pmc.gaussian_pmc(stacked_data[::100], pmcmix, copy=False)
pmcmix.prune(.5/len(long_patches))
plt.figure()
plot_mixture(pmcmix)
plt.xlim(-6,6)
plt.ylim(-6,6)
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.savefig('first_prop_pmc_7500.pdf')
print 'PMC done'
# form first proposal with Variational Bayes
# run variational bayes with samples --> use the long patches as initial guess
vb = pypmc.mix_adapt.variational.GaussianInference(stacked_data[::100], initial_guess=long_patches)
print 'running VB...'
vb.run(1000, abs_tol=1e-5, rel_tol=1e-10, prune=.5*len(vb.data)/vb.K, verbose=True)
print 'VB done'
plt.title('Markov Chain 2')
plt.hexbin(mcmc_data[1][:,1], mcmc_data[1][:,2], cmap='gray_r', extent=(-30,10,-30,30))
plt.xlabel('$x_2$')
plt.ylabel('$x_3$')
plt.draw()
# form the "long_patches"
long_patches = pypmc.mix_adapt.r_value.make_r_gaussmix(mcmc_data)
# run variational bayes with samples --> use the long patches as initial guess
vb = pypmc.mix_adapt.variational.GaussianInference(stacked_data[::50], initial_guess=long_patches)
vb.run(1000, abs_tol=1e-5, rel_tol=1e-10, prune=.5*len(vb.data)/vb.K, verbose=True)
vbmix = vb.make_mixture()
plt.figure()
plt.title('Proposal density')
plot_mixture(vbmix, 1, 2)
plt.xlabel('$x_2$')
plt.ylabel('$x_3$')
plt.xlim(-30,10)
plt.ylim(-30,30)
plt.draw()
# define an importance sampler for each proposal and run 10**5 steps
vb_sampler = pypmc.sampler.importance_sampling.DeterministicIS(log_target, vbmix, std_weights=True)
vb_sampler.run(10**5)
# plot importance samples
plt.figure()
plt.title('Importance Samples')
plt.hist2d(vb_sampler.history[:][:,2], vb_sampler.history[:][:,3], weights=vb_sampler.std_weights[:][:,0], cmap='gray_r', bins=100)
plt.xlabel('$x_2$')
mcmcmix_components.append(pypmc.density.gauss.Gauss(mean, cov))
except np.linalg.LinAlgError:
print "Could not create component:"
print 'mean:', mean
print 'cov:', cov
statusfile.write("Could not create component:\n")
statusfile.write("mean: %s\n" %mean)
statusfile.write("cov: %s\n" %cov)
# delete components with negative det
if mcmcmix_components[-1].det_sigma <= 0.:
mcmcmix_components.pop()
mcmcmix = pypmc.density.mixture.MixtureDensity(mcmcmix_components)
plt.figure()
plt.title('from chains')
plot_mixture(mcmcmix, 0,1)
plotfile.savefig()
# --------------------------- end of markov chain ---------------------------------------
# --------------------------- chain grouping --------------------------------------------
chain_groups = pypmc.mix_adapt.r_value.r_group([np.mean(mc.history[:], axis=0) for mc in mcs],
[np.cov(mc.history[:], rowvar=0) for mc in mcs],
len(val), critical_r)
statusfile.write('found %i chain grous\n' %len(chain_groups) )
long_patches_means = []
long_patches_covs = []
for group in chain_groups:
