def test_reconstruction(s=3,
n=200,
p=50,
snr=7,
rho=0.1,
split_frac=0.8,
lam_frac=0.7,
ndraw=100,
burnin=200,
bootstrap=True,
solve_args={
'min_its': 50,
'tol': 1.e-10
},
reference_known=False):
X, y, beta, _ = logistic_instance(n=n, p=p, s=s, rho=rho, snr=snr)
m = int(split_frac * n)
nonzero = np.where(beta)[0]
loss = rr.glm.logistic(X, y)
epsilon = 1. / np.sqrt(n)
lam = lam_frac * np.mean(
np.fabs(np.dot(X.T, np.random.binomial(1, 1. / 2, (n, 2000)))).max(0))
W = np.ones(p) * lam
W[0] = 0 # use at least some unpenalized
penalty = rr.group_lasso(np.arange(p),
weights=dict(zip(np.arange(p), W)),
lagrange=1.)
M_est = split_glm_group_lasso(loss, epsilon, m, penalty)
mv = multiple_queries([M_est])
mv.solve()
M_est.selection_variable['variables'] = M_est.selection_variable[
'variables']
nactive = np.sum(M_est.selection_variable['variables'])
if nactive == 0:
return None
if set(nonzero).issubset(
np.nonzero(M_est.selection_variable['variables'])[0]):
active_set = np.nonzero(M_est.selection_variable['variables'])[0]
target_sampler, target_observed = glm_target(
loss, M_est.selection_variable['variables'], mv)
target_sample = target_sampler.sample(ndraw=ndraw,
burnin=burnin,
keep_opt=True)
reconstruction = target_sampler.reconstruction_map(target_sample)
logdens = target_sampler.log_randomization_density(target_sample)
return logdens.shape
def test_multiple_queries_individual_coeff_small(ndraw=10000,
burnin=2000,
bootstrap=True):
s, n, p = 3, 100, 20
randomizer = randomization.laplace((p,), scale=1)
X, y, beta, _ = logistic_instance(n=n, p=p, s=s, rho=0, snr=20.)
nonzero = np.where(beta)[0]
lam_frac = 3.
loss = rr.glm.logistic(X, y)
epsilon = 1.
lam = lam_frac * np.mean(np.fabs(np.dot(X.T, np.random.binomial(1, 1. / 2, (n, 10000)))).max(0))
W = np.ones(p)*lam
W[0] = 0 # use at least some unpenalized
penalty = rr.group_lasso(np.arange(p),
weights=dict(zip(np.arange(p), W)), lagrange=1.)
# randomization
M_est = glm_group_lasso(loss, epsilon, penalty, randomizer)
mv = multiple_queries([M_est])
mv.solve()
active_vars = M_est.selection_variable['variables']
nactive = np.sum(active_vars)
active_set = np.nonzero(active_vars)[0]
pvalues = []
true_beta = beta[active_vars]
print(nonzero, active_set)
if set(nonzero).issubset(active_set):
for j in range(nactive):
print(j)
subset = np.zeros(p, np.bool)
subset[active_set[j]] = True
target_sampler, target_observed = glm_target(loss,
active_vars,
mv,
subset=subset,
bootstrap=bootstrap,
reference=np.zeros((1,)))
test_stat = lambda x: x
pval = target_sampler.hypothesis_test(test_stat,
target_observed,
alternative='twosided',
ndraw=ndraw,
burnin=burnin)
pvalues.append(pval)
return pvalues, [active_set[j] in nonzero for j in range(nactive)]