def ci_cons(X, v, alpha_level, L, theta_l, theta_u, K, test="lr", corrected=True, verbose=False):
arr = array_from_data(X, [v])
fit_model = StationaryLogistic()
fit_model.beta["x_0"] = None
fit_model.confidence_cons(arr, "x_0", alpha_level, K, L, theta_l, theta_u, test, verbose)
method = "conservative-%s" % test
return fit_model.conf["x_0"][method]
def ci_cons(X, v, alpha_level, L, theta_l, theta_u,
K, test = 'lr', corrected = True, verbose = False):
arr = array_from_data(X, [v])
fit_model = StationaryLogistic()
fit_model.beta['x_0'] = None
fit_model.confidence_cons(arr, 'x_0', alpha_level, K,
L, theta_l, theta_u, test, verbose)
method = 'conservative-%s' % test
return fit_model.conf['x_0'][method]
def ci_cons(X, v, alpha_level, L, theta_l, theta_u,
K, test = 'lr', corrected = True, verbose = False):
arr = array_from_data(X, [v])
fit_model = StationaryLogistic()
fit_model.beta['x_0'] = None
fit_model.confidence_cons(arr, 'x_0', alpha_level, K,
L, theta_l, theta_u, test, corrected,
verbose)
method = 'conservative-%s' % test
return fit_model.conf['x_0'][method]
def ci_cmle_wald(X, v, alpha_level):
arr = array_from_data(X, [v])
A = arr.as_dense()
r = A.sum(1)
c = A.sum(0)
s_model = StationaryLogistic()
s_model.beta["x_0"] = None
fit_model = FixedMargins(s_model)
arr.new_row_covariate("r", np.int)[:] = r
arr.new_col_covariate("c", np.int)[:] = c
fit_model.fit = fit_model.base_model.fit_conditional
fit_model.confidence_wald(arr, alpha_level=alpha_level)
return safe_ci(fit_model, "x_0", "wald")
def ci_cmle_boot(X, v, alpha_level):
arr = array_from_data(X, [v])
A = arr.as_dense()
r = A.sum(1)
c = A.sum(0)
s_model = StationaryLogistic()
s_model.beta['x_0'] = None
fit_model = FixedMargins(s_model)
arr.new_row_covariate('r', np.int)[:] = r
arr.new_col_covariate('c', np.int)[:] = c
fit_model.fit = fit_model.base_model.fit_conditional
fit_model.confidence_boot(arr, alpha_level = alpha_level)
return fit_model.conf['x_0']['pivotal']
def generate_data(case, theta, seed):
# Advance random seed for parameter and covariate construction
seed.next()
case = params['case']
alpha = beta = kappa = offset = 0
conditional_sample = False
if 'fixed_example' in case:
# Load parameters and covariates
with open(case['fixed_example'], 'r') as example_file:
example = json.load(example_file)
v = np.array(example['nu'])
M, N = v.shape
if 'alpha' in example:
alpha = np.array(example['alpha']).reshape((M,1))
if 'beta' in example:
beta = np.array(example['beta']).reshape((1,N))
if 'kappa' in example:
kappa = example['kappa']
if 'offset' in example:
offset = example['offset']
if ('r' in example) and ('c' in example):
conditional_sample = True
r = example['r']
c = example['c']
else:
# Generate parameters and covariates
M, N = case['M'], case['N']
if 'alpha_min' in case:
alpha = np.random.uniform(size = (M,1)) + case['alpha_min']
if 'beta_min' in case:
beta = np.random.uniform(size = (1,N)) + case['beta_min']
if 'kappa' in case:
kappa = case['kappa']
if case['v_discrete']:
v = np.sign(np.random.random(size = (M,N)) - 0.5)
elif case['v_uniform']:
v = np.random.uniform(size = (M,N))
elif case['v_normal']:
v = np.random.normal(size = (M,N))
if 'v_scale' in case:
v *= case['v_scale']
if 'v_loc' in case:
v += case['v_loc']
if ('r' in case) and ('c' in case):
conditional_sample = True
r = case['r']
c = case['c']
# Generate Bernoulli probabilities from logistic regression model
logit_P = np.zeros((M,N)) + kappa
logit_P += alpha
logit_P += beta
logit_P += theta * v
logit_P += offset
if conditional_sample:
arr = Array(M, N)
arr.new_edge_covariate('x_0')[:] = logit_P
arr.new_row_covariate('r', dtype = np.int)[:] = r
arr.new_col_covariate('c', dtype = np.int)[:] = c
base_model = StationaryLogistic()
base_model.beta['x_0'] = 1.0
data_model = FixedMargins(base_model)
while True:
# Advance random seed for data generation
seed.next()
# Generate data for this trial
if conditional_sample:
X = data_model.generate(arr, coverage = 100.0)
else:
P = 1.0 / (1.0 + np.exp(-logit_P))
X = np.random.random((M,N)) < P
yield X, v
def fit_and_summarize(name, fit_model, use_covs):
print name
if use_covs:
for cov_name in cov_names:
fit_model.beta[cov_name] = None
fit_model.fit(net, verbose=params['verbose'])
print 'NLL: %.2f' % fit_model.nll(net)
print 'kappa: %.2f' % fit_model.kappa
if use_covs:
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, fit_model.beta[cov_name])
print '\n'
fit_and_summarize('Stationary', Stationary(), False)
fit_and_summarize('Stationary', StationaryLogistic(), True)
if params['offset_extremes']:
print 'Detecting subnetworks associated with infinite parameter estimates.\n'
net.offset_extremes()
if params['plot']: net.show_offset('pub_date')
fit_and_summarize('Nonstationary', NonstationaryLogistic(), False)
fit_and_summarize('Nonstationary', NonstationaryLogistic(), True)
# Redisplay heatmap, ordered by estimated alphas from last fit, i.e.,
# NonstationaryLogistic with publication date difference covariates
# XX: Following plots are broken
#if params['plot']:
# net.show_heatmap('alpha_out')
# net.show_heatmap('alpha_in')
outfile = open('scratch.json', 'w')
'plot_mse_beta': True
}
# Set random seed for reproducible output
np.random.seed(137)
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Initialize full network
net = Network(params['N'])
# Generate covariates and associated coefficients
data_base_model = StationaryLogistic()
covariates = []
for b in range(params['B']):
name = 'x_%d' % b
covariates.append(name)
data_base_model.beta[name] = np.random.normal(0, params['beta_sd'])
x_node = np.random.normal(0, 1, params['N'])
def f_x(i_1, i_2):
return abs(x_node[i_1] - x_node[i_2]) < params['x_diff_cutoff']
net.new_edge_covariate(name).from_binary_function_ind(f_x)
data_model = FixedMargins(data_base_model)
net.new_node_covariate_int('r')
def f_x(i_1, i_2):
return np.random.uniform(-np.sqrt(3), np.sqrt(3))
arr.new_edge_covariate(name).from_binary_function_ind(f_x)
data_model.match_kappa(arr, params['kappa_target'])
# Specify parameter of interest that the confidence interval will try
# to capture
for c in params['covariates_of_interest']:
theta_true = data_model.beta[c]
print '%s theta_true: %.2f' % (c, theta_true)
# Setup fit model
if params['fit_method'] == 'conditional':
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
fit_model.generate = fit_model.generate_margins
fit_model.fit = fit_model.fit_conditional
else:
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
else:
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Test coverage
methods = []
if params['do_wald']:
# contour expects x, y, z generated by meshgrid...
CS = plt.contour(x, y, np.transpose(z), colors='k')
plt.plot(theta_star_1, theta_star_2, 'b*', markersize=12)
plt.plot(theta_opt_1, theta_opt_2, 'ro', markersize=12)
# plt.clabel(CS, inline = 1, fontsize = 10, fmt = '%1.1f')
plt.xlabel(r'$\theta_2$', fontsize=14)
plt.ylabel(r'$\theta_1$', fontsize=14)
return theta_opt_1, theta_opt_2
# Grid search for stationary and non-stationary fits
plt.subplot(142)
plt.title('Stationary')
grid_fit(StationaryLogistic(), lambda n, m: m.nll(n), profile=True)
plt.subplot(143)
plt.title('Nonstationary')
grid_fit(NonstationaryLogistic(),
lambda n, m: m.nll(n),
profile=True,
pre_offset=True)
# Grid search for conditional fit
plt.subplot(144)
plt.title('Conditional')
def f_nll(n, m):
P = m.edge_probabilities(n)
w = P / (1.0 - P)
# Set random seed for reproducible output
np.random.seed(137)
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Initialize political blogs network from file. The "value" covariate
# is the ground truth membership to the left-leaning (0) or
# right-leaning (1) class.
net = network_from_file_gml('data/polblogs/polblogs.gml', ['value'])
net.new_node_covariate_int('truth')[:] = net.node_covariates['value'][:]
# Initialize fitting model
fit_base_model = StationaryLogistic()
fit_model = Blockmodel(fit_base_model, params['fit_K'])
if params['fit_nonstationary']:
n_fit_base_model = NonstationaryLogistic()
n_fit_model = Blockmodel(n_fit_base_model, params['fit_K'])
net.new_node_covariate_int('z')
if params['blockmodel_fit_method'] == 'kl':
fit_model.fit = fit_model.fit_kl
n_fit_model.fit = n_fit_model.fit_kl
# Set up recording of results from experiment
s_results = Results(params['sub_sizes'], params['sub_sizes'],
params['num_reps'], 'Stationary fit')
add_array_stats(s_results)
def class_mismatch(n):
truth = n.node_covariates['truth'][:]
def display_cis(model):
procedures = set()
for par in model.conf:
for procedure in model.conf[par]:
procedures.add(procedure)
for procedure in procedures:
print '%s:' % procedure
for par in model.conf:
if not procedure in model.conf[par]: continue
ci = model.conf[par][procedure]
print ' %s: (%.2f, %.2f)' % (par, ci[0], ci[1])
print
print 'Fitting stationary model'
s_model = StationaryLogistic()
for cov_name in cov_names:
s_model.beta[cov_name] = None
s_model.fit(net)
print 'NLL: %.2f' % s_model.nll(net)
print 'kappa: %.2f' % s_model.kappa
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, s_model.beta[cov_name])
print
for rep in range(params['n_samples']):
s_samples[rep,:,:] = s_model.generate(net)
s_model.confidence_boot(net, n_bootstrap = params['n_bootstrap'])
s_model.confidence_wald(net)
display_cis(s_model)
print 'Fitting conditional model'
def do_experiment(params):
if params['dump_fits'] and params['load_fits']:
print 'Warning: simultaneously dumping and loading is a bad idea.'
if params['dump_fits']:
fits = []
if params['load_fits']:
with open(params['load_fits'], 'r') as fits_file:
loaded_params_pick, loaded_fits = json.load(fits_file)
loaded_params = dict([(k, unpick(v)) for (k, v) in loaded_params_pick])
# Compare on parameters that control data generation and inference
run_params = [
'N', 'B', 'theta_sd', 'theta_fixed', 'alpha_unif_sd',
'alpha_norm_sd', 'alpha_gamma_sd', 'cov_unif_sd', 'cov_norm_sd',
'cov_disc_sd', 'kappa_target', 'pre_offset', 'post_fit',
'fit_nonstationary', 'fit_method', 'num_reps', 'is_T', 'sampling',
'sub_sizes_r', 'sub_sizes_c', 'random_seed'
]
for p in run_params:
if not np.all(loaded_params[p] == params[p]):
print 'Warning: load mismatch on', p
# Set random seed for reproducible output
seed = Seed(params['random_seed'])
# Initialize full network
arr = Network(params['N'])
# Generate node-level propensities to extend and receive edges
if params['alpha_norm_sd'] > 0.0:
alpha_norm(arr, params['alpha_norm_sd'])
elif params['alpha_unif_sd'] > 0.0:
alpha_unif(arr, params['alpha_unif_sd'])
elif params['alpha_gamma_sd'] > 0.0:
# Choosing location somewhat arbitrarily to give unit skewness
alpha_gamma(arr, 4.0, params['alpha_gamma_sd'])
else:
alpha_zero(arr)
# Generate covariates and associated coefficients
data_model = NonstationaryLogistic()
covariates = []
for b in range(params['B']):
name = 'x_%d' % b
covariates.append(name)
if name in params['theta_fixed']:
data_model.beta[name] = params['theta_fixed'][name]
else:
data_model.beta[name] = np.random.normal(0, params['theta_sd'])
if params['cov_unif_sd'] > 0.0:
c = np.sqrt(12) / 2
def f_x(i_1, i_2):
return np.random.uniform(-c * params['cov_unif_sd'],
c * params['cov_unif_sd'])
elif params['cov_norm_sd'] > 0.0:
def f_x(i_1, i_2):
return np.random.normal(0, params['cov_norm_sd'])
elif params['cov_disc_sd'] > 0.0:
def f_x(i_1, i_2):
return (params['cov_disc_sd'] *
(np.sign(np.random.random() - 0.5)))
else:
print 'Error: no covariate distribution specified.'
sys.exit()
arr.new_edge_covariate(name).from_binary_function_ind(f_x)
# Generate large network, if necessary
if not params['sampling'] == 'new':
data_model.match_kappa(arr, params['kappa_target'])
arr.generate(data_model)
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
else:
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Set up recording of results from experiment
results = Results(params['sub_sizes_r'],
params['sub_sizes_c'],
params['num_reps'],
interactive=params['interactive'])
add_array_stats(results)
if params['plot_sig']:
from scipy.stats import chi2
crit = lambda dof: -0.5 * chi2.ppf(0.95, dof)
umle_f = lambda n, f: f.nll(n, ignore_offset=True)
umle_d = lambda n, d: d.nll(n, ignore_offset=True)
umle_n = lambda n: NonstationaryLogistic().nll(n, ignore_offset=True)
results.new('UMLE F-N', 'nm', lambda n, d, f: umle_f(n, f) - umle_n(n))
results.new('UMLE F-D', 'nm',
lambda n, d, f: umle_f(n, f) - umle_d(n, d))
cmle_a_f = lambda n, f: acnll(n.as_dense(),
np.exp(f.edge_probabilities(n)))
cmle_a_d = lambda n, d: acnll(n.as_dense(),
np.exp(d.edge_probabilities(n)))
cmle_a_n = lambda n: acnll(n.as_dense(), np.ones_like(n.as_dense()))
results.new('CMLE-A F-N', 'nm',
lambda n, d, f: cmle_a_f(n, f) - cmle_a_n(n))
results.new('CMLE-A F-D', 'nm',
lambda n, d, f: cmle_a_f(n, f) - cmle_a_d(n, d))
cmle_is_f = lambda n, f: f.fit_conditional(n, evaluate=True, T=50)
cmle_is_d = lambda n, d: d.fit_conditional(n, evaluate=True, T=50)
cmle_is_n = lambda n: NonstationaryLogistic().fit_conditional(
n, evaluate=True, T=50)
results.new('CMLE-IS F-N', 'nm',
lambda n, d, f: cmle_is_f(n, f) - cmle_is_n(n))
results.new('CMLE-IS F-D', 'nm',
lambda n, d, f: cmle_is_f(n, f) - cmle_is_d(n, d))
c_cmle_f = lambda n, f: f.fit_c_conditional(n, evaluate=True)
c_cmle_d = lambda n, d: d.fit_c_conditional(n, evaluate=True)
c_cmle_n = lambda n: NonstationaryLogistic().fit_c_conditional(
n, evaluate=True)
results.new('C-CMLE F-N', 'nm',
lambda n, d, f: c_cmle_f(n, f) - c_cmle_n(n))
results.new('C-CMLE F-D', 'nm',
lambda n, d, f: c_cmle_f(n, f) - c_cmle_d(n, d))
results.new('UMLE sig.', 'dof', lambda M, N, B: crit((M - 1) +
(N - 1) + 1 + B))
results.new('CMLE sig.', 'dof', lambda M, N, B: crit(B))
results.new('C-CMLE sig.', 'dof', lambda M, N, B: crit((M - 1) + B))
if params['sampling'] == 'new':
results.new('Subnetwork kappa', 'm', lambda d, f: d.kappa)
def true_est_theta_c(c):
return (lambda d, f: d.beta[c]), (lambda d, f: f.beta[c])
for c in covariates:
# Need to do this hackily to avoid for-loop/lambda-binding weirdness.
f_true, f_est = true_est_theta_c(c)
results.new('True theta_{%s}' % c, 'm', f_true)
results.new('Est. theta_{%s}' % c, 'm', f_est)
if params['pre_offset'] or params['post_fit']:
results.new('# Active', 'n',
lambda n: np.isfinite(n.offset.matrix()).sum())
else:
results.new('# Active', 'n', lambda n: n.M * n.N)
if params['fisher_information']:
def info_theta_c(c):
def f_info_theta_c(d, f):
return d.I_inv['theta_{%s}' % c]
return f_info_theta_c
for c in covariates:
results.new('Info theta_{%s}' % c, 'm', info_theta_c(c))
if params['baseline']:
def rel_mse_p_ij(n, d, f):
P = d.edge_probabilities(n)
return rel_mse(f.edge_probabilities(n), f.baseline(n), P)
results.new('Rel. MSE(P_ij)', 'nm', rel_mse_p_ij)
if not (params['pre_offset'] or params['post_fit']):
def rel_mse_logit_p_ij(n, d, f):
logit_P = d.edge_probabilities(n, logit=True)
logit_Q = f.baseline_logit(n)
return rel_mse(f.edge_probabilities(n, logit=True), logit_Q,
logit_P)
results.new('Rel. MSE(logit P_ij)', 'nm', rel_mse_logit_p_ij)
if params['fit_method'] in [
'convex_opt', 'conditional', 'c_conditional', 'irls',
'conditional_is'
]:
results.new('Wall time (sec.)', 'm',
lambda d, f: f.fit_info['wall_time'])
if params['fit_method'] in ['convex_opt', 'conditional', 'conditional_is']:
def work(f):
w = 0
for work_type in ['nll_evals', 'grad_nll_evals', 'cnll_evals']:
if work_type in f.fit_info:
w += f.fit_info[work_type]
return w
results.new('Work', 'm', lambda d, f: work(f))
results.new('||ET_final - T||_2', 'm',
lambda d, f: l2(f.fit_info['grad_nll_final']))
for sub_size in zip(results.M_sizes, results.N_sizes):
print 'subnetwork size =', sub_size
if params['sampling'] == 'new':
gen = RandomSubnetworks(arr, sub_size)
else:
gen = RandomSubnetworks(arr, sub_size, method=params['sampling'])
for rep in range(params['num_reps']):
seed.next()
sub = gen.sample()
if params['fisher_information']:
data_model.fisher_information(sub)
if params['sampling'] == 'new':
data_model.match_kappa(sub, params['kappa_target'])
sub.generate(data_model)
if params['load_fits']:
fit, loaded_fits = loaded_fits[0], loaded_fits[1:]
fit_model.beta = unpick(fit['theta'])
if params['fix_broken_cmle_is']:
for b_n in fit_model.beta:
fit_model.beta[b_n] += 0.1474
if 'alpha' in fit:
sub.row_covariates['alpha_out'] = unpick(fit['alpha'])
if 'beta' in fit:
sub.col_covariates['alpha_in'] = unpick(fit['beta'])
if 'kappa' in fit:
fit_model.kappa = fit['kappa']
if 'offset' in fit:
sub.offset = unpick(fit['offset'])
if 'fit_info' in fit:
fit_model.fit_info = unpick(fit['fit_info'])
else:
if params['pre_offset']:
sub.offset_extremes()
if params['fit_method'] == 'convex_opt':
fit_model.fit_convex_opt(sub, verbose=params['verbose'])
elif params['fit_method'] == 'irls':
fit_model.fit_irls(sub, verbose=params['verbose'])
elif params['fit_method'] == 'logistic':
fit_model.fit_logistic(sub)
elif params['fit_method'] == 'logistic_l2':
fit_model.fit_logistic_l2(sub, prior_precision=1.0)
elif params['fit_method'] == 'conditional':
fit_model.fit_conditional(sub, verbose=params['verbose'])
elif params['fit_method'] == 'conditional_is':
fit_model.fit_conditional(sub,
T=params['is_T'],
verbose=params['verbose'])
elif params['fit_method'] == 'c_conditional':
fit_model.fit_c_conditional(sub, verbose=params['verbose'])
elif params['fit_method'] == 'composite':
fit_model.fit_composite(sub,
T=100,
verbose=params['verbose'])
elif params['fit_method'] == 'brazzale':
fit_model.fit_brazzale(sub)
elif params['fit_method'] == 'saddlepoint':
fit_model.fit_saddlepoint(sub)
elif params['fit_method'] == 'none':
pass
if params['post_fit']:
sub.offset_extremes()
fit_model.fit_convex_opt(sub, fix_beta=True)
if params['dump_fits']:
fit = {}
fit['theta'] = pick(fit_model.beta)
if 'alpha_out' in sub.row_covariates:
fit['alpha'] = pick(sub.row_covariates['alpha_out'])
if 'alpha_in' in sub.row_covariates:
fit['beta'] = pick(sub.col_covariates['alpha_in'])
if not fit_model.kappa is None:
fit['kappa'] = fit_model.kappa
if not sub.offset is None:
sub.offset.dirty()
fit['offset'] = pick(sub.offset)
if not fit_model.fit_info is None:
fit['fit_info'] = pick(fit_model.fit_info)
fits.append(fit)
if params['find_good'] > 0:
abs_err = abs(fit_model.beta['x_0'] - data_model.beta['x_0'])
if abs_err < params['find_good']:
print abs_err
sub.offset = None
fit_model.fit_conditional(sub, T=1000, verbose=True)
print fit_model.beta['x_0']
print fit_model.fit_info
f = file('goodmat.mat', 'wb')
import scipy.io
Y = np.array(sub.as_dense(), dtype=np.float)
X = sub.edge_covariates['x_0'].matrix()
scipy.io.savemat(f, {'Y': Y, 'X': X})
sys.exit()
if params['find_bad'] > 0:
abs_err = abs(fit_model.beta['x_0'] - data_model.beta['x_0'])
if abs_err > params['find_bad']:
print abs_err
sub.offset = None
fit_model.fit_conditional(sub, T=1000, verbose=True)
print fit_model.beta['x_0']
print fit_model.fit_info
f = file('badmat.mat', 'wb')
import scipy.io
Y = np.array(sub.as_dense(), dtype=np.float)
X = sub.edge_covariates['x_0'].matrix()
scipy.io.savemat(f, {'Y': Y, 'X': X})
sys.exit()
results.record(sub_size, rep, sub, data_model, fit_model)
if params['verbose']:
print
if params['dump_fits']:
with open(params['dump_fits'], 'w') as outfile:
json.dump(([(p, pick(params[p])) for p in params], fits), outfile)
# Compute beta MSEs
covariate_naming = []
for c in covariates:
mse_name = 'MSE(theta_{%s})' % c
true_name = 'True theta_{%s}' % c
est_name = 'Est. theta_{%s}' % c
results.estimate_mse(mse_name, true_name, est_name)
covariate_naming.append((c, mse_name, true_name, est_name))
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Should not vary between runs with the same seed and same number
# of arrays tested
seed.final()
results.summary()
return results, covariate_naming
heatmap(A)
plt.subplot(332)
plt.title('Network')
graph = nx.DiGraph()
for n1, n2 in edges:
graph.add_edge(n1, n2)
pos = nx.graphviz_layout(graph, prog='neato')
nx.draw(graph, pos, node_size=10, with_labels=False)
# Store sampled typical networks from fit models
s_samples = np.empty((params['n_samples'], net.N, net.N))
ns_samples = np.empty((params['n_samples'], net.N, net.N))
c_samples = np.empty((params['n_samples'], net.N, net.N))
print 'Fitting stationary model'
s_model = StationaryLogistic()
for cov_name in cov_names:
s_model.beta[cov_name] = None
s_model.fit(net)
print 'NLL: %.2f' % s_model.nll(net)
print 'kappa: %.2f' % s_model.kappa
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, s_model.beta[cov_name])
print
for rep in range(params['n_samples']):
s_samples[rep, :, :] = s_model.generate(net)
s_model.confidence(net, n_bootstrap=params['n_bootstrap'])
print 'Pivotal:'
for cov_name in cov_names:
ci = s_model.conf[cov_name]['pivotal']
print ' %s: (%.2f, %.2f)' % (cov_name, ci[0], ci[1])
data_model.beta[name] = np.random.normal(0, params['beta_sd'])
def f_x(i_1, i_2):
return np.random.uniform(-np.sqrt(3), np.sqrt(3))
arr.new_edge_covariate(name).from_binary_function_ind(f_x)
data_model.match_kappa(arr, params['kappa_target'])
# Specify parameter of interest that the confidence interval will try
# to capture
for c in params['covariates_of_interest']:
theta_true = data_model.beta[c]
print '%s theta_true: %.2f' % (c, theta_true)
# Setup fit model
if params['fit_method'] == 'conditional':
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
fit_model.generate = fit_model.generate_margins
fit_model.fit = fit_model.fit_conditional
else:
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
else:
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Test coverage
methods = []
if params['do_wald']:
# Initialize the data model; generate covariates and associated coefficients
data_model = NonstationaryLogistic()
data_model.kappa = -7.0
covariates = ['x_1', 'x_2', 'x_3', 'x_4', 'x_5']
for covariate in covariates:
data_model.beta[covariate] = np.random.normal(0, 1.0)
x_node = np.random.normal(0, 1.0, N)
def f_x(i_1, i_2):
return abs(x_node[i_1] - x_node[i_2]) < 0.3
net.new_edge_covariate(covariate).from_binary_function_ind(f_x)
net.generate(data_model)
print 'True beta_1: %.2f' % data_model.beta['x_1']
# Initialize the fit model; specify which covariates it should have terms for
fit_model = StationaryLogistic()
for covariate in covariates:
fit_model.beta[covariate] = None
# Set up plotting
f = plt.figure()
ax = f.add_subplot(1, 1, 1, aspect = 'equal')
ax.set_title('95% confidence regions')
ax.set_xlim(data_model.beta['x_1'] - 2.0, data_model.beta['x_1'] + 2.0)
ax.set_ylim(data_model.beta['x_2'] - 2.0, data_model.beta['x_2'] + 2.0)
ax.set_xlabel('beta_1')
ax.set_ylabel('beta_2')
# Set up random subnetwork generator, and run fitting experiments
gen = RandomSubnetworks(net, (sub_N, sub_N))
for rep in range(10):
med_degree = np.median(degree)
net.new_node_covariate('low_degree').from_pairs(net.names,
degree < med_degree)
for v_1, v_2, name in [(0, 0, 'high_to_high'),
(1, 1, 'low_to_low'),
(0, 1, 'high_to_low')]:
covariates.append(name)
def f_x(i_1, i_2):
return ((net.node_covariates['low_degree'][i_1] == v_1) and
(net.node_covariates['low_degree'][i_2] == v_2))
net.new_edge_covariate(name).from_binary_function_ind(f_x)
# Initialize fitting model
fit_model = StationaryLogistic()
n_fit_model = NonstationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
n_fit_model.beta[c] = None
# Set up recording of results from experiment
results = Results(params['sub_sizes'], params['num_reps'], 'Stationary fit')
add_network_stats(results)
def est_theta_c(c):
return lambda d, f: f.beta[c]
for c in covariates:
f_est = est_theta_c(c)
results.new('%s' % c, 'm', f_est)
all_results = {}
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Initialize full network
net = Network(params['N'])
# Generate underlying edge probabilities as offsets
P_alpha, P_beta = params['P_beta_params']
P = np.random.beta(P_alpha, P_beta, (params['N'],params['N']))
net.initialize_offset()[:,:] = logit(P)
# Generate covariates and associated coefficients
data_model = StationaryLogistic()
covariates = []
data_model.beta = {}
for b in range(params['B']):
name = 'x_%d' % b
covariates.append(name)
data_model.beta[name] = np.random.normal(0, params['beta_sd'])
x_node = np.random.normal(0, 1, params['N'])
def f_x(i_1, i_2):
return abs(x_node[i_1] - x_node[i_2]) < params['x_diff_cutoff']
net.new_edge_covariate(name).from_binary_function_ind(f_x)
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
class_probs = np.random.dirichlet(np.repeat(params['class_conc'], params['K']))
z = np.where(np.random.multinomial(1, class_probs, params['N']) == 1)[1]
net.new_node_covariate_int('z_true')[:] = z
data_model = Blockmodel(data_base_model, params['K'], 'z_true')
Theta = np.random.normal(params['Theta_mean'], params['Theta_sd'],
(params['K'],params['K']))
Theta += params['Theta_diag'] * np.identity(params['K'])
Theta -= np.mean(Theta)
data_model.Theta = Theta
net.generate(data_model)
if params['plot_network']:
net.show_heatmap('z_true')
# Initialize fitting model
fit_base_model = StationaryLogistic()
for c in covariates:
fit_base_model.beta[c] = None
fit_model = Blockmodel(fit_base_model, params['fit_K'])
if params['fit_nonstationary']:
n_fit_base_model = NonstationaryLogistic()
for c in covariates:
n_fit_base_model.beta[c] = None
n_fit_model = Blockmodel(n_fit_base_model, params['fit_K'])
net.new_node_covariate_int('z')
# Set up recording of results from experiment
s_results = Results(params['sub_sizes'], params['num_reps'], 'Stationary fit')
add_network_stats(s_results)
s_results.new('Subnetwork kappa', 'm', lambda d, f: d.base_model.kappa)
def f_c(c):
def display_cis(model):
procedures = set()
for par in model.conf:
for procedure in model.conf[par]:
procedures.add(procedure)
for procedure in procedures:
print '%s:' % procedure
for par in model.conf:
if not procedure in model.conf[par]: continue
ci = model.conf[par][procedure]
print ' %s: (%.2f, %.2f)' % (par, ci[0], ci[1])
print
print 'Fitting stationary model'
s_model = StationaryLogistic()
for cov_name in cov_names:
s_model.beta[cov_name] = None
s_model.fit(net)
print 'NLL: %.2f' % s_model.nll(net)
print 'kappa: %.2f' % s_model.kappa
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, s_model.beta[cov_name])
print
for rep in range(params['n_samples']):
s_samples[rep, :, :] = s_model.generate(net)
s_model.confidence_boot(net, n_bootstrap=params['n_bootstrap'])
s_model.confidence_wald(net)
display_cis(s_model)
print 'Fitting conditional model'
def generate_data(case, theta, seed):
# Advance random seed for parameter and covariate construction
seed.next()
case = params["case"]
alpha = beta = kappa = offset = 0
conditional_sample = False
if "fixed_example" in case:
# Load parameters and covariates
with open(case["fixed_example"], "r") as example_file:
example = json.load(example_file)
v = np.array(example["nu"])
M, N = v.shape
if "alpha" in example:
alpha = np.array(example["alpha"]).reshape((M, 1))
if "beta" in example:
beta = np.array(example["beta"]).reshape((1, N))
if "kappa" in example:
kappa = example["kappa"]
if "offset" in example:
offset = example["offset"]
if ("r" in example) and ("c" in example):
conditional_sample = True
r = example["r"]
c = example["c"]
else:
# Generate parameters and covariates
M, N = case["M"], case["N"]
if "alpha_min" in case:
alpha = np.random.uniform(size=(M, 1)) + case["alpha_min"]
if "beta_min" in case:
beta = np.random.uniform(size=(1, N)) + case["beta_min"]
if "kappa" in case:
kappa = case["kappa"]
if case["v_discrete"]:
v = np.random.random(size=(M, N)) < 0.5
else:
v = np.random.uniform(size=(M, N))
if "v_min" in case:
v += case["v_min"]
if ("r" in case) and ("c" in case):
conditional_sample = True
r = case["r"]
c = case["c"]
# Generate Bernoulli probabilities from logistic regression model
logit_P = np.zeros((M, N)) + kappa
logit_P += alpha
logit_P += beta
logit_P += theta * v
logit_P += offset
if conditional_sample:
arr = Array(M, N)
arr.new_edge_covariate("x_0")[:] = logit_P
arr.new_row_covariate("r", dtype=np.int)[:] = r
arr.new_col_covariate("c", dtype=np.int)[:] = c
base_model = StationaryLogistic()
base_model.beta["x_0"] = 1.0
data_model = FixedMargins(base_model)
while True:
# Advance random seed for data generation
seed.next()
# Generate data for this trial
if conditional_sample:
X = data_model.generate(arr, coverage=2.0)
else:
P = 1.0 / (1.0 + np.exp(-logit_P))
X = np.random.random((M, N)) < P
yield X, v
else:
data_model.beta[name] = np.random.normal(0, params['beta_sd'])
def f_x(i_1, i_2):
return np.random.uniform(-np.sqrt(3), np.sqrt(3))
arr.new_edge_covariate(name).from_binary_function_ind(f_x)
data_model.match_kappa(arr, params['kappa_target'])
# Specify parameter of interest that the confidence interval will try to capture
for c in params['covariates_of_interest']:
theta_true = data_model.beta[c]
print '%s theta_true: %.2f' % (c, theta_true)
# Setup fit model
if params['fit_method'] == 'conditional':
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
fit_model.generate = fit_model.generate_margins
fit_model.fit = fit_model.fit_conditional
else:
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
else:
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Test coverage
methods = []
if params['do_large_sample']:
'sub_sizes': np.arange(10, 70, 10, dtype=np.int),
'plot_mse_beta': True }
# Set random seed for reproducible output
np.random.seed(137)
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Initialize full network
net = Network(params['N'])
# Generate covariates and associated coefficients
data_base_model = StationaryLogistic()
covariates = []
for b in range(params['B']):
name = 'x_%d' % b
covariates.append(name)
data_base_model.beta[name] = np.random.normal(0, params['beta_sd'])
x_node = np.random.normal(0, 1, params['N'])
def f_x(i_1, i_2):
return abs(x_node[i_1] - x_node[i_2]) < params['x_diff_cutoff']
net.new_edge_covariate(name).from_binary_function_ind(f_x)
data_model = FixedMargins(data_base_model)
net.new_node_covariate_int('r')
net.new_node_covariate_int('c')
plt.title('Covariates')
covariate_levels = np.zeros((net.N, net.N))
num_covariates = len(cov_names)
for i, val in enumerate(np.linspace(1.0, 0.4, num_covariates)):
covariate_levels[net.edge_covariates[cov_names[i]].matrix() == True] = val
heatmap(covariate_levels, 'Blues')
plt.subplot(333)
plt.title('Network')
graph = nx.DiGraph()
for n1, n2 in edges:
graph.add_edge(n1, n2)
pos = nx.nx_pydot.graphviz_layout(graph, prog = 'neato')
nx.draw(graph, pos, node_size = 10, with_labels = False)
print 'Fitting stationary model'
s_model = StationaryLogistic()
for cov_name in cov_names:
s_model.beta[cov_name] = None
s_model.fit(net, verbose = True)
print 'NLL: %.2f' % s_model.nll(net)
print 'kappa: %.2f' % s_model.kappa
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, s_model.beta[cov_name])
print
print 'Fitting nonstationary model'
alpha_zero(net)
ns_model = NonstationaryLogistic()
for cov_name in cov_names:
ns_model.beta[cov_name] = None
ns_model.fit(net, verbose = True)
n_rep = 100
n_boot = 10
alpha_level = 0.05
net = Network(N)
alpha_norm(net, alpha_sd)
for d in range(D):
net.new_edge_covariate('x_%d' % d)[:,:] = np.random.normal(0, 1, (N, N))
data_model = NonstationaryLogistic()
for d in range(D):
data_model.beta['x_%d' % d] = np.random.normal(0, 1)
data_model.beta['x_0'] = theta
data_model.match_kappa(net, kappa_target)
s_fit = StationaryLogistic()
ns_fit = NonstationaryLogistic()
for d in range(D):
s_fit.beta['x_%d' % d] = None
ns_fit.beta['x_%d' % d] = None
def safe_ci(model, name, method):
if name in model.conf:
if method in model.conf[name]:
return model.conf[name][method]
else:
return (0.0, 0.0)
braz_covered = 0
ws_covered = 0
wn_covered = 0
(np.sign(np.random.random() - 0.5)))
else:
print 'Error: no covariate distribution specified.'
sys.exit()
net.new_edge_covariate(name).from_binary_function_ind(f_x)
# Specify data model as generation of permuation networks
net.new_node_covariate_int('r')[:] = 1
net.new_node_covariate_int('c')[:] = 1
data_model = FixedMargins(data_model, 'r', 'c', coverage = 2.0)
if params['fit_nonstationary']:
fit_model = NonstationaryLogistic()
else:
fit_model = StationaryLogistic()
for b in data_model.base_model.beta:
fit_model.beta[b] = 0.0
# Set up recording of results from experiment
results = Results(params['sub_sizes'], params['sub_sizes'], params['num_reps'])
add_array_stats(results)
def true_est_theta_b(b):
return (lambda d, f: d.base_model.beta[b]), (lambda d, f: f.beta[b])
for b in fit_model.beta:
# Need to do this hackily to avoid for-loop/lambda-binding weirdness.
f_true, f_est = true_est_theta_b(b)
results.new('True theta_{%s}' % b, 'm', f_true)
results.new('Est. theta_{%s}' % b, 'm', f_est)
results.new('# Active', 'n', lambda n: n.N ** 2)
results.new('Separated', 'm', lambda d, f: f.fit_info['separated'])
# Report parameters for the run
print 'Parameters:'
for field in params:
print '%s: %s' % (field, str(params[field]))
# Initialize full network
net = Network(params['N'])
# Generate underlying edge probabilities as offsets
P_alpha, P_beta = params['P_beta_params']
P = np.random.beta(P_alpha, P_beta, (params['N'], params['N']))
net.initialize_offset()[:, :] = logit(P)
# Generate covariates and associated coefficients
data_model = StationaryLogistic()
covariates = []
data_model.beta = {}
for b in range(params['B']):
name = 'x_%d' % b
covariates.append(name)
data_model.beta[name] = np.random.normal(0, params['beta_sd'])
x_node = np.random.normal(0, 1, params['N'])
def f_x(i_1, i_2):
return abs(x_node[i_1] - x_node[i_2]) < params['x_diff_cutoff']
net.new_edge_covariate(name).from_binary_function_ind(f_x)
plt.title('Covariates')
covariate_levels = np.zeros((net.N, net.N))
num_covariates = len(cov_names)
for i, val in enumerate(np.linspace(1.0, 0.4, num_covariates)):
covariate_levels[net.edge_covariates[cov_names[i]].matrix() == True] = val
heatmap(covariate_levels, 'Blues')
plt.subplot(333)
plt.title('Network')
graph = nx.DiGraph()
for n1, n2 in edges:
graph.add_edge(n1, n2)
pos = nx.graphviz_layout(graph, prog='neato')
nx.draw(graph, pos, node_size=10, with_labels=False)
print 'Fitting stationary model'
s_model = StationaryLogistic()
for cov_name in cov_names:
s_model.beta[cov_name] = None
s_model.fit(net, verbose=True)
print 'NLL: %.2f' % s_model.nll(net)
print 'kappa: %.2f' % s_model.kappa
for cov_name in cov_names:
print '%s: %.2f' % (cov_name, s_model.beta[cov_name])
print
print 'Fitting nonstationary model'
alpha_zero(net)
ns_model = NonstationaryLogistic()
for cov_name in cov_names:
ns_model.beta[cov_name] = None
ns_model.fit(net, verbose=True)
c = case['c']
# Generate Bernoulli probabilities from logistic regression model
logit_P = np.zeros((M,N)) + kappa
logit_P += alpha
logit_P += beta
logit_P += theta * v
logit_P += offset
if conditional_sample:
arr = Array(M, N)
arr.new_edge_covariate('x_0')[:] = logit_P
arr.new_row_covariate('r', dtype = np.int)[:] = r
arr.new_col_covariate('c', dtype = np.int)[:] = c
base_model = StationaryLogistic()
base_model.beta['x_0'] = 1.0
data_model = FixedMargins(base_model)
while True:
# Advance random seed for data generation
seed.next()
# Generate data for this trial
if conditional_sample:
X = data_model.generate(arr, coverage = 100.0)
else:
P = 1.0 / (1.0 + np.exp(-logit_P))
X = np.random.random((M,N)) < P
yield X, v
class_probs = np.random.dirichlet(np.repeat(params['class_conc'], params['K']))
z = np.where(np.random.multinomial(1, class_probs, params['N']) == 1)[1]
net.new_node_covariate_int('z_true')[:] = z
data_model = Blockmodel(data_base_model, params['K'], 'z_true')
Theta = np.random.normal(params['Theta_mean'], params['Theta_sd'],
(params['K'], params['K']))
Theta += params['Theta_diag'] * np.identity(params['K'])
Theta -= np.mean(Theta)
data_model.Theta = Theta
net.generate(data_model)
if params['plot_network']:
net.show_heatmap('z_true')
# Initialize fitting model
fit_base_model = StationaryLogistic()
for c in covariates:
fit_base_model.beta[c] = None
fit_model = Blockmodel(fit_base_model, params['fit_K'])
if params['fit_nonstationary']:
n_fit_base_model = NonstationaryLogistic()
for c in covariates:
n_fit_base_model.beta[c] = None
n_fit_model = Blockmodel(n_fit_base_model, params['fit_K'])
net.new_node_covariate_int('z')
# Set up recording of results from experiment
s_results = Results(params['sub_sizes'], params['num_reps'], 'Stationary fit')
add_network_stats(s_results)
s_results.new('Subnetwork kappa', 'm', lambda d, f: d.base_model.kappa)
degree = r + c
med_degree = np.median(degree)
net.new_node_covariate('low_degree').from_pairs(net.names,
degree < med_degree)
for v_1, v_2, name in [(0, 0, 'high_to_high'), (1, 1, 'low_to_low'),
(0, 1, 'high_to_low')]:
covariates.append(name)
def f_x(i_1, i_2):
return ((net.node_covariates['low_degree'][i_1] == v_1)
and (net.node_covariates['low_degree'][i_2] == v_2))
net.new_edge_covariate(name).from_binary_function_ind(f_x)
# Initialize fitting model
fit_model = StationaryLogistic()
n_fit_model = NonstationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
n_fit_model.beta[c] = None
# Set up recording of results from experiment
results = Results(params['sub_sizes'], params['num_reps'], 'Stationary fit')
add_network_stats(results)
def est_theta_c(c):
return lambda d, f: f.beta[c]
for c in covariates: