def test_behavior_X_list(self): X = [0, 1, 2, 3] counts = qtu.bincount(X) assert counts == [1, 1, 1, 1] X = [1, 2, 2, 4, 6] counts = qtu.bincount(X) assert counts == [1, 2, 0, 1, 0, 1] bins = range(7) counts = qtu.bincount(X,bins) assert counts == [0, 1, 2, 0, 1, 0, 1] bins = [1,2,4,6] counts = qtu.bincount(X,bins) assert counts == [1, 2, 1, 1]
def test_behavior_X_array(self): X = numpy.array([0, 1, 2, 3]) counts = qtu.bincount(X) assert counts == [1, 1, 1, 1] X = numpy.array([1, 2, 2, 4, 6]) counts = qtu.bincount(X) assert counts == [1, 2, 0, 1, 0, 1] bins = range(7) counts = qtu.bincount(X,bins) assert counts == [0, 1, 2, 0, 1, 0, 1] bins = [1,2,4,6] counts = qtu.bincount(X,bins) assert counts == [1, 2, 1, 1]
def test_behavior_X_array(self):
X = numpy.array([0, 1, 2, 3])
counts = qtu.bincount(X)
assert counts == [1, 1, 1, 1]
X = numpy.array([1, 2, 2, 4, 6])
counts = qtu.bincount(X)
assert counts == [1, 2, 0, 1, 0, 1]
bins = range(7)
counts = qtu.bincount(X, bins)
assert counts == [0, 1, 2, 0, 1, 0, 1]
bins = [1, 2, 4, 6]
counts = qtu.bincount(X, bins)
assert counts == [1, 2, 1, 1]
def test_behavior_X_list(self):
X = [0, 1, 2, 3]
counts = qtu.bincount(X)
assert counts == [1, 1, 1, 1]
X = [1, 2, 2, 4, 6]
counts = qtu.bincount(X)
assert counts == [1, 2, 0, 1, 0, 1]
bins = range(7)
counts = qtu.bincount(X, bins)
assert counts == [0, 1, 2, 0, 1, 0, 1]
bins = [1, 2, 4, 6]
counts = qtu.bincount(X, bins)
assert counts == [1, 2, 1, 1]
def test_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=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(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(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_one_feature_mixture(component_model_type, num_clusters=3, show_plot=False, seed=None):
"""
"""
random.seed(seed)
N = 1000
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 = numpy.array(T)
T_list = T
# create a crosscat state
M_c = du.gen_M_c_from_T(T_list, cctypes=[cctype])
state = State.p_State(M_c, T_list)
# 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)
# Get support over all component models
discrete_support = qtu.get_mixture_support(cctype, component_model_type,
structure['component_params'][0], nbins=500)
# calculate simple predictive probability for each point
Q = [(N,0,x) for x in discrete_support]
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.
if is_discrete[component_model_type.model_type]:
bins = 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(20,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:
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)
pylab.show()
return p
def test_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 = 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
