def test_continuous_support_should_return_proper_number_of_bins(self):
X = qtu.get_mixture_support('continuous',
ccmext.p_ContinuousComponentModel,
self.params_list_normal, nbins=500)
assert len(X) == 500
X = qtu.get_mixture_support('continuous',
ccmext.p_ContinuousComponentModel,
self.params_list_normal, nbins=522)
assert len(X) == 522
def test_multinomial_support_should_return_proper_number_of_bins(self):
# support should be range(len(weights))
X = qtu.get_mixture_support('multinomial',
mcmext.p_MultinomialComponentModel,
self.params_list_multinomial)
assert len(X) == len(self.params_list_multinomial[0]['weights'])
def check_predictive_sample_improvement(component_model_type, seed=0, show_plot=True):
""" Shows the error of predictive sample over iterations.
"""
num_transitions = 100
num_samples = 10
num_clusters = 2
separation = .9 # cluster separation
N = 150
random.seed(seed)
get_next_seed = lambda : random.randrange(2147483647)
# generate a single column of data from the component_model
cctype = component_model_type.cctype
T, M_c, struc = sdg.gen_data([cctype], N, [0], [[.5,.5]], [separation],
seed=get_next_seed(), distargs=[distargs[cctype]],
return_structure=True)
T_array = numpy.array(T)
X = numpy.zeros((N,num_transitions))
KL = numpy.zeros((num_samples, num_transitions))
support = qtu.get_mixture_support(cctype, component_model_type,
struc['component_params'][0], nbins=1000, support=.995)
true_log_pdf = qtu.get_mixture_pdf(support, component_model_type,
struc['component_params'][0],[.5,.5])
for s in range(num_samples):
# generate the state
state = State.p_State(M_c, T, SEED=get_next_seed())
for i in range(num_transitions):
# transition
state.transition()
# get partitions and generate a predictive column
X_L = state.get_X_L()
X_D = state.get_X_D()
T_inf = sdg.predictive_columns(M_c, X_L, X_D, [0],
seed=get_next_seed())
if cctype == 'multinomial':
K = distargs[cctype]['K']
weights = numpy.zeros(numpy.array(K))
for params in struc['component_params'][0]:
weights += numpy.array(params['weights'])*(1.0/num_clusters)
weights *= float(N)
inf_hist = qtu.bincount(T_inf, bins=list(range(K)))
err, _ = stats.power_divergence(inf_hist, weights, lambda_='pearson')
err = numpy.ones(N)*err
else:
err = (T_array-T_inf)**2.0
KL[s,i] = qtu.KL_divergence(component_model_type,
struc['component_params'][0], [.5,.5], M_c, X_L, X_D,
true_log_pdf=true_log_pdf, support=support)
for j in range(N):
X[j,i] += err[j]
X /= num_samples
# mean and standard error
X_mean = numpy.mean(X,axis=0)
X_err = numpy.std(X,axis=0)/float(num_samples)**.5
KL_mean = numpy.mean(KL, axis=0)
KL_err = numpy.std(KL, axis=0)/float(num_samples)**.5
if show_plot:
pylab.subplot(1,2,1)
pylab.errorbar(list(range(num_transitions)), X_mean, yerr=X_err)
pylab.xlabel('iteration')
pylab.ylabel('error across each data point')
pylab.title('error of predictive sample over iterations, N=%i' % N)
pylab.subplot(1,2,2)
pylab.errorbar(list(range(num_transitions)), KL_mean, yerr=KL_err)
pylab.xlabel('iteration')
pylab.ylabel('KL divergence')
pylab.title('KL divergence, N=%i' % N)
pylab.show()
# error should decrease over time
return X_mean[0] > X_mean[-1] and KL_mean[0] > KL_mean[-1]
def test_kl_divergence_as_a_function_of_N_and_transitions():
n_clusters = 3
n_chains = 8
do_times = 4
# N_list = [25, 50, 100, 250, 500, 1000, 2000]
N_list = [25, 50, 100, 175, 250, 400, 500]
# max_transitions = 500
max_transitions = 500
transition_interval = 50
t_iterations = max_transitions / transition_interval
cctype = "continuous"
cluster_weights = [1.0 / float(n_clusters)] * n_clusters
separation = 0.5
get_next_seed = lambda: random.randrange(2147483647)
# data grid
KLD = numpy.zeros((len(N_list), t_iterations + 1))
for _ in range(do_times):
for n in range(len(N_list)):
N = N_list[n]
T, M_c, struc = sdg.gen_data(
[cctype],
N,
[0],
[cluster_weights],
[separation],
seed=get_next_seed(),
distargs=[None],
return_structure=True,
)
M_r = du.gen_M_r_from_T(T)
# precompute the support and pdf to speed up calculation of KL divergence
support = qtu.get_mixture_support(
cctype, ccmext.p_ContinuousComponentModel, struc["component_params"][0], nbins=1000, support=0.995
)
true_log_pdf = qtu.get_mixture_pdf(
support, ccmext.p_ContinuousComponentModel, struc["component_params"][0], cluster_weights
)
# intialize a multiprocessing engine
mstate = mpe.MultiprocessingEngine(cpu_count=8)
X_L_list, X_D_list = mstate.initialize(M_c, M_r, T, n_chains=n_chains)
# kl_divergences
klds = numpy.zeros(len(X_L_list))
for i in range(len(X_L_list)):
X_L = X_L_list[i]
X_D = X_D_list[i]
KLD[n, 0] += qtu.KL_divergence(
ccmext.p_ContinuousComponentModel,
struc["component_params"][0],
cluster_weights,
M_c,
X_L,
X_D,
n_samples=1000,
support=support,
true_log_pdf=true_log_pdf,
)
# run transition_interval then take a reading. Rinse and repeat.
for t in range(t_iterations):
X_L_list, X_D_list = mstate.analyze(M_c, T, X_L_list, X_D_list, n_steps=transition_interval)
for i in range(len(X_L_list)):
X_L = X_L_list[i]
X_D = X_D_list[i]
KLD[n, t + 1] += qtu.KL_divergence(
ccmext.p_ContinuousComponentModel,
struc["component_params"][0],
cluster_weights,
M_c,
X_L,
X_D,
n_samples=1000,
support=support,
true_log_pdf=true_log_pdf,
)
KLD /= float(n_chains * do_times)
pylab.subplot(1, 3, 1)
pylab.contourf(list(range(0, max_transitions + 1, transition_interval)), N_list, KLD)
pylab.title("KL divergence")
pylab.ylabel("N")
pylab.xlabel("# transitions")
pylab.subplot(1, 3, 2)
m_N = numpy.mean(KLD, axis=1)
e_N = numpy.std(KLD, axis=1) / float(KLD.shape[1]) ** -0.5
pylab.errorbar(N_list, m_N, yerr=e_N)
pylab.title("KL divergence by N")
pylab.xlabel("N")
pylab.ylabel("KL divergence")
pylab.subplot(1, 3, 3)
m_t = numpy.mean(KLD, axis=0)
e_t = numpy.std(KLD, axis=0) / float(KLD.shape[0]) ** -0.5
pylab.errorbar(list(range(0, max_transitions + 1, transition_interval)), m_t, yerr=e_t)
pylab.title("KL divergence by transitions")
pylab.xlabel("trasition")
pylab.ylabel("KL divergence")
pylab.show()
return KLD
def test_kl_divergence_as_a_function_of_N_and_transitions():
n_clusters = 3
n_chains = 8
do_times = 4
# N_list = [25, 50, 100, 250, 500, 1000, 2000]
N_list = [25, 50, 100, 175, 250, 400, 500]
# max_transitions = 500
max_transitions = 500
transition_interval = 50
t_iterations = max_transitions/transition_interval
cctype = 'continuous'
cluster_weights = [1.0/float(n_clusters)]*n_clusters
separation = .5
get_next_seed = lambda : random.randrange(2147483647)
# data grid
KLD = numpy.zeros((len(N_list), t_iterations+1))
for _ in range(do_times):
for n in range(len(N_list)):
N = N_list[n]
T, M_c, struc = sdg.gen_data([cctype], N, [0], [cluster_weights],
[separation], seed=get_next_seed(), distargs=[None],
return_structure=True)
M_r = du.gen_M_r_from_T(T)
# precompute the support and pdf to speed up calculation of KL divergence
support = qtu.get_mixture_support(cctype,
ccmext.p_ContinuousComponentModel,
struc['component_params'][0], nbins=1000, support=.995)
true_log_pdf = qtu.get_mixture_pdf(support,
ccmext.p_ContinuousComponentModel,
struc['component_params'][0],cluster_weights)
# intialize a multiprocessing engine
mstate = mpe.MultiprocessingEngine(cpu_count=8)
X_L_list, X_D_list = mstate.initialize(M_c, M_r, T, n_chains=n_chains)
# kl_divergences
klds = numpy.zeros(len(X_L_list))
for i in range(len(X_L_list)):
X_L = X_L_list[i]
X_D = X_D_list[i]
KLD[n,0] += qtu.KL_divergence(ccmext.p_ContinuousComponentModel,
struc['component_params'][0], cluster_weights, M_c,
X_L, X_D, n_samples=1000, support=support,
true_log_pdf=true_log_pdf)
# run transition_interval then take a reading. Rinse and repeat.
for t in range( t_iterations ):
X_L_list, X_D_list = mstate.analyze(M_c, T, X_L_list, X_D_list,
n_steps=transition_interval)
for i in range(len(X_L_list)):
X_L = X_L_list[i]
X_D = X_D_list[i]
KLD[n,t+1] += qtu.KL_divergence(ccmext.p_ContinuousComponentModel,
struc['component_params'][0], cluster_weights, M_c,
X_L, X_D, n_samples=1000, support=support,
true_log_pdf=true_log_pdf)
KLD /= float(n_chains*do_times)
pylab.subplot(1,3,1)
pylab.contourf(list(range(0,max_transitions+1,transition_interval), N_list, KLD))
pylab.title('KL divergence')
pylab.ylabel('N')
pylab.xlabel('# transitions')
pylab.subplot(1,3,2)
m_N = numpy.mean(KLD,axis=1)
e_N = numpy.std(KLD,axis=1)/float(KLD.shape[1])**-.5
pylab.errorbar(N_list, m_N, yerr=e_N)
pylab.title('KL divergence by N')
pylab.xlabel('N')
pylab.ylabel('KL divergence')
pylab.subplot(1,3,3)
m_t = numpy.mean(KLD,axis=0)
e_t = numpy.std(KLD,axis=0)/float(KLD.shape[0])**-.5
pylab.errorbar(list(range(0,max_transitions+1,transition_interval), m_t, yerr=e_t))
pylab.title('KL divergence by transitions')
pylab.xlabel('trasition')
pylab.ylabel('KL divergence')
pylab.show()
return KLD
def check_one_feature_mixture(component_model_type, num_clusters=3, show_plot=False, seed=None):
"""
"""
random.seed(seed)
N = 300
separation = .9
get_next_seed = lambda : random.randrange(2147483647)
cluster_weights = [[1.0/float(num_clusters)]*num_clusters]
cctype = component_model_type.cctype
T, M_c, structure = sdg.gen_data([cctype], N, [0], cluster_weights,
[separation], seed=get_next_seed(),
distargs=[distargs[cctype]],
return_structure=True)
T_list = list(T)
T = numpy.array(T)
# pdb.set_trace()
# create a crosscat state
M_c = du.gen_M_c_from_T(T_list, cctypes=[cctype])
state = State.p_State(M_c, T_list)
# Get support over all component models
discrete_support = qtu.get_mixture_support(cctype, component_model_type,
structure['component_params'][0], nbins=250)
# calculate simple predictive probability for each point
Q = [(N,0,x) for x in discrete_support]
# transitions
state.transition(n_steps=200)
# get the sample
X_L = state.get_X_L()
X_D = state.get_X_D()
# generate samples
# kstest has doesn't compute the same answer with row and column vectors
# so we flatten this column vector into a row vector.
predictive_samples = sdg.predictive_columns(M_c, X_L, X_D, [0],
seed=get_next_seed()).flatten(1)
probabilities = su.simple_predictive_probability(M_c, X_L, X_D, []*len(Q), Q)
# get histogram. Different behavior for discrete and continuous types. For some reason
# the normed property isn't normalizing the multinomial histogram to 1.
# T = T[:,0]
if is_discrete[component_model_type.model_type]:
bins = list(range(len(discrete_support)))
T_hist = numpy.array(qtu.bincount(T, bins=bins))
S_hist = numpy.array(qtu.bincount(predictive_samples, bins=bins))
T_hist = T_hist/float(numpy.sum(T_hist))
S_hist = S_hist/float(numpy.sum(S_hist))
edges = numpy.array(discrete_support,dtype=float)
else:
T_hist, edges = numpy.histogram(T, bins=min(50,len(discrete_support)), normed=True)
S_hist, _ = numpy.histogram(predictive_samples, bins=edges, normed=True)
edges = edges[0:-1]
# Goodness-of-fit-tests
if not is_discrete[component_model_type.model_type]:
# do a KS tests if the distribution in continuous
# cdf = lambda x: component_model_type.cdf(x, model_parameters)
# stat, p = stats.kstest(predictive_samples, cdf) # 1-sample test
stat, p = stats.ks_2samp(predictive_samples, T[:,0]) # 2-sample test
test_str = "KS"
else:
# Cressie-Read power divergence statistic and goodness of fit test.
# This function gives a lot of flexibility in the method <lambda_> used.
freq_obs = S_hist*N
freq_exp = numpy.exp(probabilities)*N
stat, p = stats.power_divergence(freq_obs, freq_exp, lambda_='pearson')
test_str = "Chi-square"
if show_plot:
pylab.clf()
lpdf = qtu.get_mixture_pdf(discrete_support, component_model_type,
structure['component_params'][0], [1.0/num_clusters]*num_clusters)
pylab.axes([0.1, 0.1, .8, .7])
# bin widths
width = (numpy.max(edges)-numpy.min(edges))/len(edges)
pylab.bar(edges, T_hist, color='blue', alpha=.5, width=width, label='Original data', zorder=1)
pylab.bar(edges, S_hist, color='red', alpha=.5, width=width, label='Predictive samples', zorder=2)
# plot actual pdf of support given data params
pylab.scatter(discrete_support,
numpy.exp(lpdf),
c="blue",
edgecolor="none",
s=100,
label="true pdf",
alpha=1,
zorder=3)
# plot predictive probability of support points
pylab.scatter(discrete_support,
numpy.exp(probabilities),
c="red",
edgecolor="none",
s=100,
label="predictive probability",
alpha=1,
zorder=4)
pylab.legend()
ylimits = pylab.gca().get_ylim()
pylab.ylim([0,ylimits[1]])
title_string = "%i samples drawn from %i %s components: \ninference after 200 crosscat transitions\n%s test: p = %f" \
% (N, num_clusters, component_model_type.cctype, test_str, round(p,4))
pylab.title(title_string, fontsize=12)
filename = component_model_type.model_type + "_mixtrue.png"
pylab.savefig(filename)
pylab.close()
return p
def check_one_feature_mixture(component_model_type,
num_clusters=3,
show_plot=False,
seed=None):
"""
"""
random.seed(seed)
N = 300
separation = .9
get_next_seed = lambda: random.randrange(2147483647)
cluster_weights = [[1.0 / float(num_clusters)] * num_clusters]
cctype = component_model_type.cctype
T, M_c, structure = sdg.gen_data([cctype],
N, [0],
cluster_weights, [separation],
seed=get_next_seed(),
distargs=[distargs[cctype]],
return_structure=True)
T_list = list(T)
T = numpy.array(T)
# pdb.set_trace()
# create a crosscat state
M_c = du.gen_M_c_from_T(T_list, cctypes=[cctype])
state = State.p_State(M_c, T_list)
# Get support over all component models
discrete_support = qtu.get_mixture_support(
cctype,
component_model_type,
structure['component_params'][0],
nbins=250)
# calculate simple predictive probability for each point
Q = [(N, 0, x) for x in discrete_support]
# transitions
state.transition(n_steps=200)
# get the sample
X_L = state.get_X_L()
X_D = state.get_X_D()
# generate samples
# kstest has doesn't compute the same answer with row and column vectors
# so we flatten this column vector into a row vector.
predictive_samples = sdg.predictive_columns(
M_c, X_L, X_D, [0], seed=get_next_seed()).flatten(1)
probabilities = su.simple_predictive_probability(M_c, X_L, X_D,
[] * len(Q), Q)
# get histogram. Different behavior for discrete and continuous types. For some reason
# the normed property isn't normalizing the multinomial histogram to 1.
# T = T[:,0]
if is_discrete[component_model_type.model_type]:
bins = list(range(len(discrete_support)))
T_hist = numpy.array(qtu.bincount(T, bins=bins))
S_hist = numpy.array(qtu.bincount(predictive_samples, bins=bins))
T_hist = T_hist / float(numpy.sum(T_hist))
S_hist = S_hist / float(numpy.sum(S_hist))
edges = numpy.array(discrete_support, dtype=float)
else:
T_hist, edges = numpy.histogram(T,
bins=min(50, len(discrete_support)),
normed=True)
S_hist, _ = numpy.histogram(predictive_samples,
bins=edges,
normed=True)
edges = edges[0:-1]
# Goodness-of-fit-tests
if not is_discrete[component_model_type.model_type]:
# do a KS tests if the distribution in continuous
# cdf = lambda x: component_model_type.cdf(x, model_parameters)
# stat, p = stats.kstest(predictive_samples, cdf) # 1-sample test
stat, p = stats.ks_2samp(predictive_samples, T[:, 0]) # 2-sample test
test_str = "KS"
else:
# Cressie-Read power divergence statistic and goodness of fit test.
# This function gives a lot of flexibility in the method <lambda_> used.
freq_obs = S_hist * N
freq_exp = numpy.exp(probabilities) * N
stat, p = stats.power_divergence(freq_obs, freq_exp, lambda_='pearson')
test_str = "Chi-square"
if show_plot:
pylab.clf()
lpdf = qtu.get_mixture_pdf(discrete_support, component_model_type,
structure['component_params'][0],
[1.0 / num_clusters] * num_clusters)
pylab.axes([0.1, 0.1, .8, .7])
# bin widths
width = (numpy.max(edges) - numpy.min(edges)) / len(edges)
pylab.bar(edges,
T_hist,
color='blue',
alpha=.5,
width=width,
label='Original data',
zorder=1)
pylab.bar(edges,
S_hist,
color='red',
alpha=.5,
width=width,
label='Predictive samples',
zorder=2)
# plot actual pdf of support given data params
pylab.scatter(discrete_support,
numpy.exp(lpdf),
c="blue",
edgecolor="none",
s=100,
label="true pdf",
alpha=1,
zorder=3)
# plot predictive probability of support points
pylab.scatter(discrete_support,
numpy.exp(probabilities),
c="red",
edgecolor="none",
s=100,
label="predictive probability",
alpha=1,
zorder=4)
pylab.legend()
ylimits = pylab.gca().get_ylim()
pylab.ylim([0, ylimits[1]])
title_string = "%i samples drawn from %i %s components: \ninference after 200 crosscat transitions\n%s test: p = %f" \
% (N, num_clusters, component_model_type.cctype, test_str, round(p,4))
pylab.title(title_string, fontsize=12)
filename = component_model_type.model_type + "_mixtrue.png"
pylab.savefig(filename)
pylab.close()
return p