def gen_data(filename, arsgin, save_csv=True):
"""
Generates a synthetic tablel with given properties. For full
documentation see sdg.gen_data
"""
cctypes = arsgin['cctypes']
n_rows = arsgin['num_rows']
n_cols = arsgin['num_cols']
n_views = arsgin['num_views']
n_clusters = arsgin['num_clusters']
separation = arsgin['separation']
seed = arsgin['seed']
if 'distargs' in arsgin.keys():
distargs = arsgin['distargs']
else:
distargs = None
random.seed(seed)
# need to generate cluster_weights and cols_to_views
cols_to_views = range(n_views)
for c in range(n_views, n_cols):
cols_to_views.append(random.randrange(n_views))
cluster_weights = []
for v in range(n_views):
cluster_weights.append([1./n_clusters]*n_clusters)
T, _, structure = sdg.gen_data(cctypes, n_rows, cols_to_views,
cluster_weights, separation,
seed=seed, distargs=distargs, return_structure=True)
T = numpy.array(T)
if save_csv:
header = [ 'col_'+str(col) for col in range(n_cols) ]
# write the data to a list of list
out = [header]
for row in range(n_rows):
row_out = []
for col in range(n_cols):
if cctypes[col] == 'continuous':
value = T[row][col]
elif cctypes[col] == 'multinomial':
value = int(T[row][col])
else:
raise ValueError("unsupported cctype: %s" % cctypes[col])
row_out.append(value)
out.append(row_out)
list_to_csv(filename, out)
return T, structure
def test_proper_set_up_all_continuous(self): T, M_c = sdg.gen_data(self.cctypes_all_contiuous, self.n_rows, self.cols_to_views_good, self.cluster_weights_good, self.separation_good, seed=0, distargs=None) assert(len(T) == self.n_rows) assert(len(T[0]) == len(self.cols_to_views_good))
def test_proper_set_up_mixed(self): distargs = [ None, None, dict(K=5), None, dict(K=5)] T, M_c = sdg.gen_data(self.cctypes_mixed, self.n_rows, self.cols_to_views_good, self.cluster_weights_good, self.separation_good, seed=0, distargs=distargs) assert(len(T) == self.n_rows) assert(len(T[0]) == len(self.cols_to_views_good))
def test_different_seeds_should_produce_the_different_data(self): distargs = [None]*5 T1, M_c = sdg.gen_data(self.cctypes_all_contiuous, self.n_rows, self.cols_to_views_good, self.cluster_weights_good, self.separation_good, seed=0, distargs=distargs) T2, M_c = sdg.gen_data(self.cctypes_all_contiuous, self.n_rows, self.cols_to_views_good, self.cluster_weights_good, self.separation_good, seed=12345, distargs=distargs) A1 = numpy.array(T1) A2 = numpy.array(T2) assert not numpy.all(A1==A2)
def run_experiment(argin):
num_iters = argin["num_iters"]
num_chains = argin["num_chains"]
num_rows = argin["num_rows"]
max_cols = argin["max_cols"]
rho = argin["rho"]
num_indep_queries = argin["num_indep_queries"]
independent_clusters = argin["independent_clusters"]
ct_kernel = argin["ct_kernel"]
multimodal = argin["multimodal"]
separation = argin["separation"]
all_cols = max_cols + 4 # max_cols plus number of dependent columns
seed = argin["seed"]
if seed > 0:
random.seed(seed)
numpy.random.seed(seed)
# build full data file
# generate column indices and header
col_names = [ "col_%i" % i for i in range(all_cols)]
Zv = [0,0,1,1] # our needles
Zv.extend(range(2,all_cols-2))
min_clusters = 3
max_clusters = 10
T_array = numpy.zeros( (num_rows, all_cols) )
Sigma = numpy.array( [[1.0,rho],[rho,1.0]])
mu = numpy.array([0,0])
if multimodal:
T = [[0]*num_cols]*num_rows
Zv = [0,0,1,1] # our needles
Zv.extend(range(2,num_cols-2))
random.shuffle(Zv)
num_views = max(Zv)+1
separation = [separation]*2
separation.extend([separation]*(num_views-2))
min_clusters = 4
max_clusters = 5
cluster_weights = []
# generate weights.
for v in range(num_views):
if v < 2:
num_clusters = random.randrange(min_clusters, max_clusters)
else:
num_clusters = 1
cluster_weights.append( [1.0/num_clusters]*num_clusters )
cctypes, distargs = eu.get_column_types(data_mode, num_cols, multinomial_categories)
T, _ = sdg.gen_data(cctypes, num_rows, Zv, cluster_weights, separation, distargs=distargs)
T_array = numpy.array(T)
else:
T_array[:, 0:1+1] = numpy.random.multivariate_normal(mu, Sigma, num_rows)
T_array[:, 2:3+1] = numpy.random.multivariate_normal(mu, Sigma, num_rows)
separation = .5
for col in range(4, all_cols):
num_clusters = random.randrange(min_clusters, max_clusters)+1
for row in range(num_rows):
k = random.randrange(num_clusters)
T_array[row, col] = numpy.random.randn()+k*6*separation
T = T_array.tolist()
# save file to .csv
exp_path = 'expdata/hb/'
eu.make_folder(exp_path)
filename = exp_path + "haystack_break_exp.csv"
table = "haystack_break_exp"
T.insert(0, col_names)
eu.list_to_csv(filename, T)
# done building data file
# get colum step size (powers of two)
num_steps = int( math.log(max_cols, 2) )-1
step_size = [2**t for t in range(2, num_steps+1)]
assert step_size[-1] <= max_cols
if step_size[-1] < max_cols:
step_size.append(max_cols)
assert step_size[0] == 4 and step_size[-1] == max_cols
# the needle column names
needle_a_cols = (col_names[0],col_names[1])
needle_b_cols = (col_names[2],col_names[3])
result = dict()
result['steps'] = []
for num_distractor_columns in step_size:
# create subdata
T_sub = take_T_column_subset(T, range(4+num_distractor_columns) )
subpath = exp_path+'d_'+str(num_distractor_columns)+'/'
eu.make_folder(subpath)
subfilename = subpath + "haystack_break_exp_" + str(num_distractor_columns) + ".csv"
eu.list_to_csv(subfilename, T_sub)
col_names_sub = T_sub[0]
# generate queries
queries, pairs = generate_dependence_queries(needle_a_cols, needle_b_cols,
col_names_sub, table, num_indep_queries)
num_queries = len(queries)
dependence_probs = numpy.zeros( (num_iters+1, num_queries) )
client = Client()
client('DROP BTABLE %s;' % table, yes=True)
client('CREATE BTABLE %s FROM %s;' % (table, subfilename))
init_string = 'INITIALIZE %i MODELS FOR %s;' % (num_chains, table)
print init_string
client(init_string)
client('SHOW DIAGNOSTICS FOR %s;' % table)
# do the analyses
for i in range(0,num_iters+1):
if i > 0:
if ct_kernel == 1:
client( 'ANALYZE %s FOR 1 ITERATIONS WITH MH KERNEL WAIT;' % table )
else:
client( 'ANALYZE %s FOR 1 ITERATIONS WAIT;' % table )
for q in range(num_queries):
query = queries[q]
out = client(query, pretty=False, pandas_output=False)
dependence_probs[i,q] = out[0]['data'][0][1]
subresult = dict()
# store the queries in subresult
subresult['query_col1'] = []
subresult['query_col2'] = []
subresult['dependence_probs'] = dependence_probs
for pair in pairs:
subresult['query_col1'].append(pair[0])
subresult['query_col2'].append(pair[1])
# for each query, get wether those columns were actually independent
independent = [True]*num_queries
for i in range(num_queries):
col_idx_0 = pairs[i][0]
col_idx_1 = pairs[i][1]
if Zv[col_idx_0] == Zv[col_idx_1]:
independent[i] = False
subresult['cols_independent'] = independent
subresult['distractor_cols'] = num_distractor_columns
result['steps'].append(subresult)
result['config'] = argin
result['data'] = T_array
return result
def run_experiment(argin):
num_iters = argin["num_iters"]
num_chains = argin["num_chains"]
num_rows = argin["num_rows"]
num_cols = argin["num_cols"]
with_id = argin["with_id"]
needles = argin["needles"]
mixed_types = argin["mixed_types"]
multinomial_categories = argin["multinomial_categories"]
separation = argin["separation"]
num_indep_queries = argin["num_indep_queries"]
independent_clusters = argin["independent_clusters"]
ct_kernel = argin["ct_kernel"]
seed = argin["seed"]
if seed > 0:
random.seed(seed)
# generate column indices and header
col_names = [ "col_%i" % i for i in range(num_cols)]
if mixed_types and multinomial_categories > 0:
data_mode = 'mixed'
elif multinomial_categories > 0:
data_mode = 'multinomial'
else:
data_mode = 'continuous'
if needles:
T = [[0]*num_cols]*num_rows
Zv = [0,0,1,1] # our needles
Zv.extend(range(2,num_cols-2))
# random.shuffle(Zv)
num_views = max(Zv)+1
separation = [.95]*2
separation.extend([0.0]*(num_views-2))
min_clusters = 4
max_clusters = 5
cluster_weights = []
# generate weights.
for v in range(num_views):
if v < 2:
num_clusters = random.randrange(min_clusters, max_clusters)
else:
if independent_clusters:
num_clusters = random.randrange(min_clusters, max_clusters)
else:
num_clusters = 1
cluster_weights.append( [1.0/num_clusters]*num_clusters )
cctypes, distargs = eu.get_column_types(data_mode, num_cols, multinomial_categories)
T, _ = sdg.gen_data(cctypes, num_rows, Zv, cluster_weights, separation, distargs=distargs)
else:
T, cctypes = eu.generate_noise(data_mode, num_rows, num_cols)
# # preprend the row_id
# if with_id:
# needle_a_cols = (1,2)
# needle_b_cols = (3,4)
# col_names.insert(0, 'ID')
# # TODO: ID type
# cctypes.insert(0,'continuous')
# # header = "ID,%s" % header
# if needles:
# Zv.insert(0, num_views)
# for row in range(num_rows):
# T[row].insert(0, row)
# else:
needle_a_cols = (col_names[0],col_names[1])
needle_b_cols = (col_names[2],col_names[3])
# save file to .csv
filename = "needles_exp.csv"
table = "needles_exp"
T.insert(0, col_names)
eu.list_to_csv(filename, T)
# generate queries
queries, pairs = generate_dependence_queries(needle_a_cols, needle_b_cols,
col_names, table, num_indep_queries)
num_queries = len(queries)
dependence_probs = numpy.zeros( (num_iters, num_queries) )
client = Client()
client('DROP BTABLE %s;' % table, yes=True)
client('CREATE BTABLE %s FROM %s;' % (table, filename))
init_string = 'INITIALIZE %i MODELS FOR %s;' % (num_chains, table)
print init_string
client(init_string)
client('SHOW DIAGNOSTICS FOR %s;' % table)
# do the analyses
for i in range(num_iters):
if ct_kernel == 1:
client( 'ANALYZE %s FOR 1 ITERATIONS WITH MH KERNEL WAIT;' % table )
else:
client( 'ANALYZE %s FOR 1 ITERATIONS WAIT;' % table )
for q in range(num_queries):
query = queries[q]
out = client(query, pretty=False, pandas_output=False)
dependence_probs[i,q] = out[0]['data'][0][1]
result = dict()
# store the queries in result
result['query_col1'] = []
result['query_col2'] = []
result['dependence_probs'] = dependence_probs
for pair in pairs:
result['query_col1'].append(pair[0])
result['query_col2'].append(pair[1])
# for each query, get wether those columns were actually independent
independent = [True]*num_queries
if needles:
for i in range(num_queries):
col_idx_0 = pairs[i][0]
col_idx_1 = pairs[i][1]
if Zv[col_idx_0] == Zv[col_idx_1]:
independent[i] = False
result['cols_independent'] = independent
result['config'] = argin
result['config']['data_mode'] = data_mode
client('SHOW DIAGNOSTICS FOR %s;' % table)
return result
def run_experiment(argin):
num_iters = argin["num_iters"]
num_chains = argin["num_chains"]
num_rows = argin["num_rows"]
num_cols = argin["num_cols"]
with_id = argin["with_id"]
needles = argin["needles"]
mixed_types = argin["mixed_types"]
multinomial_categories = argin["multinomial_categories"]
separation = argin["separation"]
num_indep_queries = argin["num_indep_queries"]
independent_clusters = argin["independent_clusters"]
ct_kernel = argin["ct_kernel"]
seed = argin["seed"]
if seed > 0:
random.seed(seed)
# generate column indices and header
col_names = ["col_%i" % i for i in range(num_cols)]
if mixed_types and multinomial_categories > 0:
data_mode = 'mixed'
elif multinomial_categories > 0:
data_mode = 'multinomial'
else:
data_mode = 'continuous'
if needles:
T = [[0] * num_cols] * num_rows
Zv = [0, 0, 1, 1] # our needles
Zv.extend(range(2, num_cols - 2))
# random.shuffle(Zv)
num_views = max(Zv) + 1
separation = [.95] * 2
separation.extend([0.0] * (num_views - 2))
min_clusters = 4
max_clusters = 5
cluster_weights = []
# generate weights.
for v in range(num_views):
if v < 2:
num_clusters = random.randrange(min_clusters, max_clusters)
else:
if independent_clusters:
num_clusters = random.randrange(min_clusters, max_clusters)
else:
num_clusters = 1
cluster_weights.append([1.0 / num_clusters] * num_clusters)
cctypes, distargs = eu.get_column_types(data_mode, num_cols,
multinomial_categories)
T, _ = sdg.gen_data(cctypes,
num_rows,
Zv,
cluster_weights,
separation,
distargs=distargs)
else:
T, cctypes = eu.generate_noise(data_mode, num_rows, num_cols)
# # preprend the row_id
# if with_id:
# needle_a_cols = (1,2)
# needle_b_cols = (3,4)
# col_names.insert(0, 'ID')
# # TODO: ID type
# cctypes.insert(0,'continuous')
# # header = "ID,%s" % header
# if needles:
# Zv.insert(0, num_views)
# for row in range(num_rows):
# T[row].insert(0, row)
# else:
needle_a_cols = (col_names[0], col_names[1])
needle_b_cols = (col_names[2], col_names[3])
# save file to .csv
filename = "needles_exp.csv"
table = "needles_exp"
T.insert(0, col_names)
eu.list_to_csv(filename, T)
# generate queries
queries, pairs = generate_dependence_queries(needle_a_cols, needle_b_cols,
col_names, table,
num_indep_queries)
num_queries = len(queries)
dependence_probs = numpy.zeros((num_iters, num_queries))
client = Client()
client('DROP BTABLE %s;' % table, yes=True)
client('CREATE BTABLE %s FROM %s;' % (table, filename))
init_string = 'INITIALIZE %i MODELS FOR %s;' % (num_chains, table)
print init_string
client(init_string)
client('SHOW DIAGNOSTICS FOR %s;' % table)
# do the analyses
for i in range(num_iters):
if ct_kernel == 1:
client('ANALYZE %s FOR 1 ITERATIONS WITH MH KERNEL WAIT;' % table)
else:
client('ANALYZE %s FOR 1 ITERATIONS WAIT;' % table)
for q in range(num_queries):
query = queries[q]
out = client(query, pretty=False, pandas_output=False)
dependence_probs[i, q] = out[0]['data'][0][1]
result = dict()
# store the queries in result
result['query_col1'] = []
result['query_col2'] = []
result['dependence_probs'] = dependence_probs
for pair in pairs:
result['query_col1'].append(pair[0])
result['query_col2'].append(pair[1])
# for each query, get wether those columns were actually independent
independent = [True] * num_queries
if needles:
for i in range(num_queries):
col_idx_0 = pairs[i][0]
col_idx_1 = pairs[i][1]
if Zv[col_idx_0] == Zv[col_idx_1]:
independent[i] = False
result['cols_independent'] = independent
result['config'] = argin
result['config']['data_mode'] = data_mode
client('SHOW DIAGNOSTICS FOR %s;' % table)
return result
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
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(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(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