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):
return ((lambda d, f: d.base_model.beta[c]),
(lambda d, f: f.base_model.beta[c]))
for c in covariates:
# Need to do this hackily to avoid for-loop/lambda-binding weirdness.
f_true, f_estimated = f_c(c)
s_results.new('True beta_{%s}' % c, 'm', f_true)
s_results.new('Estimated beta_{%s}' % c, 'm', f_estimated)
s_results.new('Class mismatch', 'n',
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'])
if params['fisher_information']:
def info_theta_b(b):
def f_info_theta_b(d, f):
return d.base_model.I_inv['theta_{%s}' % b]
return f_info_theta_b
# Initialize full network
blocks = params['N'] / params['D']
edges = []
for block in range(blocks):
for i in range(params['D']):
v_1 = 'n_%d' % (block * params['D'] + i)
for j in range(params['D']):
v_2 = 'n_%d' % (((block + 1) * params['D'] + j) % params['N'])
edges.append((v_1, v_2))
net = network_from_edges(edges)
# Set up recording of results from experiment
results_by_method = { }
for method_name in params['sampling_methods']:
results = Results(params['sub_sizes'], params['sub_sizes'],
params['num_reps'], title = method_name)
add_array_stats(results, network = True)
results.new('# Active', 'n',
lambda n: np.isfinite(n.offset.matrix()).sum())
results_by_method[method_name] = results
for sub_size in params['sub_sizes']:
size = (sub_size, sub_size)
print 'subnetwork size = %s' % str(size)
generators = \
{ 'random_node': RandomSubnetworks(net, size, method = 'node'),
'random_edge': RandomSubnetworks(net, size, method = 'edge'),
'link_trace': RandomSubnetworks(net, size, method = 'link'),
'link_trace_f': RandomSubnetworks(net, size, method = 'link_f') }
for generator in generators:
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
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'][:]
estimated = n.node_covariates['z'][:]
return minimum_disagreement(truth, estimated, normalized = False)
s_results.new('Class mismatch', 'n', class_mismatch)
all_results = { 's': s_results }
if params['fit_nonstationary']:
n_results = s_results.copy()
n_results.title = 'Nonstationary fit'
all_results['n'] = n_results
if params['fit_conditional']:
c_results = s_results.copy()
c_results.title = 'Conditional fit'
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')
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Set up recording of results from experiment
gibbs_results = {}
for gibbs_cover in params['gibbs_covers']:
results = Results(params['sub_sizes'], params['sub_sizes'],
params['num_reps'],
'Gibbs cover: %.2f' % gibbs_cover)
def f_c(c):
return (lambda d, f: d.base_model.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_estimated = f_c(c)
results.new('True beta_{%s}' % c, 'm', f_true)
results.new('Est. beta_{%s}' % c, 'm', f_estimated)
gibbs_results[gibbs_cover] = results
for sub_size in params['sub_sizes']:
size = (sub_size, sub_size)
print 'Subnetwork size = %s' % str(size)
gen = RandomSubnetworks(net, size)
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()
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'], params['sub_sizes'], params['num_reps'])
add_array_stats(results)
def f_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_estimated = f_c(c)
results.new('True beta_{%s}' % c, 'm', f_true)
results.new('Estimated beta_{%s}' % c, 'm', f_estimated)
results.new('MSE(P_{ij})', 'nm',
lambda n, d, f: np.mean((d.edge_probabilities(n) - \
f.edge_probabilities(n))**2))
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()
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'], params['sub_sizes'],
params['num_reps'])
add_array_stats(results)
def f_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_estimated = f_c(c)
results.new('True beta_{%s}' % c, 'm', f_true)
results.new('Estimated beta_{%s}' % c, 'm', f_estimated)
results.new('MSE(P_{ij})', 'nm',
lambda n, d, f: np.mean((d.edge_probabilities(n) - \
f.edge_probabilities(n))**2))
results.new('MSE(logit_P_{ij})', 'nm',
lambda n, d, f: np.mean((d.edge_probabilities(n, logit = True) - \
f.edge_probabilities(n, logit = True))**2))
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 = {}
if params['fit_stationary']:
s_results = results.copy()
s_results.title = 'Stationary fit'
all_results['s'] = s_results
if params['fit_nonstationary']:
n_results = results.copy()
n_results.title = 'Nonstationary fit'
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):
return ((lambda d, f: d.base_model.beta[c]),
(lambda d, f: f.base_model.beta[c]))
for c in covariates:
# Need to do this hackily to avoid for-loop/lambda-binding weirdness.
f_true, f_estimated = f_c(c)
s_results.new('True beta_{%s}' % c, 'm', f_true)
s_results.new('Estimated beta_{%s}' % c, 'm', f_estimated)
s_results.new('Class mismatch', 'n',
lambda n: minimum_disagreement(n.node_covariates['z_true'][:], \
n.node_covariates['z'][:]))
def rel_mse_p_ij(n, d, f):
P = d.edge_probabilities(n)
# Initialize full network
blocks = params['N'] / params['D']
edges = []
for block in range(blocks):
for i in range(params['D']):
v_1 = 'n_%d' % (block * params['D'] + i)
for j in range(params['D']):
v_2 = 'n_%d' % (((block + 1) * params['D'] + j) % params['N'])
edges.append((v_1, v_2))
net = network_from_edges(edges)
# Set up recording of results from experiment
results_by_method = {}
for method_name in params['sampling_methods']:
results = Results(params['sub_sizes'],
params['sub_sizes'],
params['num_reps'],
title=method_name)
add_array_stats(results, network=True)
results.new('# Active', 'n',
lambda n: np.isfinite(n.offset.matrix()).sum())
results_by_method[method_name] = results
for sub_size in params['sub_sizes']:
size = (sub_size, sub_size)
print 'subnetwork size = %s' % str(size)
generators = \
{ 'random_node': RandomSubnetworks(net, size, method = 'node'),
'random_edge': RandomSubnetworks(net, size, method = 'edge'),
'link_trace': RandomSubnetworks(net, size, method = 'link'),
'link_trace_f': RandomSubnetworks(net, size, method = 'link_f') }
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')
fit_model = StationaryLogistic()
for c in covariates:
fit_model.beta[c] = None
# Set up recording of results from experiment
gibbs_results = {}
for gibbs_cover in params['gibbs_covers']:
results = Results(params['sub_sizes'], params['sub_sizes'],
params['num_reps'], 'Gibbs cover: %.2f' % gibbs_cover)
def f_c(c):
return (lambda d, f: d.base_model.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_estimated = f_c(c)
results.new('True beta_{%s}' % c, 'm', f_true)
results.new('Est. beta_{%s}' % c, 'm', f_estimated)
gibbs_results[gibbs_cover] = results
for sub_size in params['sub_sizes']:
size = (sub_size, sub_size)
print 'Subnetwork size = %s' % str(size)
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
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 = {}
if params['fit_stationary']:
s_results = results.copy()
s_results.title = 'Stationary fit'