def test_logistic(n=200,
p=30,
burnin=2000,
ndraw=8000,
compute_interval=False,
sandwich=True,
selected=False,
s=6,
snr=10,
nsim=None):
X, y, beta, lasso_active = logistic_instance(n=n,
p=p,
snr=snr,
s=s,
scale=False,
center=False,
rho=0.1)
n, p = X.shape
lam = 0.6 * np.mean(
np.fabs(np.dot(X.T, np.random.standard_normal((n, 10000)))).max(0))
L = randomized_logistic(
y,
X,
lam, (True, 0.4 * np.diag(np.sqrt(np.diag(np.dot(X.T, X))))),
sandwich=sandwich,
selected=selected)
L.fit()
if (set(range(s)).issubset(L.active) and L.active.shape[0] > s):
L.unbiased_estimate[:] = np.zeros(p)
L.constraints.mean[:p] = 0 * L.unbiased_estimate
v = np.zeros_like(L.active)
v[s] = 1.
P0, interval = L.hypothesis_test(v,
burnin=burnin,
ndraw=ndraw,
compute_interval=compute_interval)
target = (beta[L.active] * v).sum()
estimate = (L.unbiased_estimate[:L.active.shape[0]] * v).sum()
low, hi = interval
v = np.zeros_like(L.active)
v[0] = 1.
PA, _ = L.hypothesis_test(v,
burnin=burnin,
ndraw=ndraw,
compute_interval=compute_interval)
return P0, PA, L
def test_logistic_saturated_active_coordinate():
s, n, p = 5, 200, 20
randomizer = randomization.laplace((p, ), scale=1.)
X, y, beta, _ = logistic_instance(n=n, p=p, s=s, rho=0.1, snr=14)
nonzero = np.where(beta)[0]
lam_frac = 1.
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
penalty = rr.group_lasso(np.arange(p),
weights=dict(zip(np.arange(p), W)),
lagrange=1.)
print(lam)
# our randomization
M_est1 = glm_group_lasso(loss, epsilon, penalty, randomizer)
mv = multiple_queries([M_est1])
mv.solve()
active = M_est1.selection_variable['variables']
nactive = active.sum()
if set(nonzero).issubset(np.nonzero(active)[0]):
active_set = np.nonzero(active)[0]
inactive_selected = I = [
i for i in np.arange(active_set.shape[0])
if active_set[i] not in nonzero
]
active_selected = A = [
i for i in np.arange(active_set.shape[0])
if active_set[i] in nonzero
]
idx = A[0]
inactive = ~M_est1.selection_variable['variables']
boot_target, target_observed = pairs_bootstrap_glm(loss,
active,
inactive=inactive)
def active_target(indices):
result = boot_target(indices)
return result[idx]
active_observed = np.zeros(1)
active_observed[0] = target_observed[idx]
# the active_observed[1:] is only used as a
# starting point for chain -- could be 0
# active_observed[1:] = target_observed[nactive:]
form_covariances = glm_nonparametric_bootstrap(n, n)
mv.setup_sampler(form_covariances)
target_sampler = mv.setup_target(active_target, active_observed)
test_stat = lambda x: x[0]
pval = target_sampler.hypothesis_test(
test_stat, test_stat(active_observed), burnin=10000,
ndraw=10000) # twosided by default
return pval, True
def test_overall_null_two_queries():
s, n, p = 5, 200, 20
randomizer = randomization.laplace((p, ), scale=0.5)
X, y, beta, _ = logistic_instance(n=n, p=p, s=s, rho=0.1, snr=14)
nonzero = np.where(beta)[0]
lam_frac = 1.
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, 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.)
# first randomization
M_est1 = glm_group_lasso(loss, epsilon, penalty, randomizer)
M_est1.solve()
bootstrap_score1 = M_est1.setup_sampler(scaling=2.)
# second randomization
M_est2 = glm_group_lasso(loss, epsilon, penalty, randomizer)
M_est2.solve()
bootstrap_score2 = M_est2.setup_sampler(scaling=2.)
# we take target to be union of two active sets
active = M_est1.selection_variable[
'variables'] + M_est2.selection_variable['variables']
if set(nonzero).issubset(np.nonzero(active)[0]):
boot_target, target_observed = pairs_bootstrap_glm(loss, active)
# target are all true null coefficients selected
sampler = lambda: np.random.choice(n, size=(n, ), replace=True)
target_cov, cov1, cov2 = bootstrap_cov(sampler,
boot_target,
cross_terms=(bootstrap_score1,
bootstrap_score2))
active_set = np.nonzero(active)[0]
inactive_selected = I = [
i for i in np.arange(active_set.shape[0])
if active_set[i] not in nonzero
]
# is it enough only to bootstrap the inactive ones?
# seems so...
if not I:
return None
A1, b1 = M_est1.linear_decomposition(cov1[I], target_cov[I][:, I],
target_observed[I])
A2, b2 = M_est2.linear_decomposition(cov2[I], target_cov[I][:, I],
target_observed[I])
target_inv_cov = np.linalg.inv(target_cov[I][:, I])
initial_state = np.hstack([
target_observed[I], M_est1.observed_opt_state,
M_est2.observed_opt_state
])
ntarget = len(I)
target_slice = slice(0, ntarget)
opt_slice1 = slice(ntarget, p + ntarget)
opt_slice2 = slice(p + ntarget, 2 * p + ntarget)
def target_gradient(state):
# with many samplers, we will add up the `target_slice` component
# many target_grads
# and only once do the Gaussian addition of full_grad
target = state[target_slice]
opt_state1 = state[opt_slice1]
opt_state2 = state[opt_slice2]
target_grad1 = M_est1.randomization_gradient(
target, (A1, b1), opt_state1)
target_grad2 = M_est2.randomization_gradient(
target, (A2, b2), opt_state2)
full_grad = np.zeros_like(state)
full_grad[opt_slice1] = -target_grad1[1]
full_grad[opt_slice2] = -target_grad2[1]
full_grad[target_slice] -= target_grad1[0] + target_grad2[0]
full_grad[target_slice] -= target_inv_cov.dot(target)
return full_grad
def target_projection(state):
opt_state1 = state[opt_slice1]
state[opt_slice1] = M_est1.projection(opt_state1)
opt_state2 = state[opt_slice2]
state[opt_slice2] = M_est2.projection(opt_state2)
return state
target_langevin = projected_langevin(initial_state, target_gradient,
target_projection,
.5 / (2 * p + 1))
Langevin_steps = 10000
burning = 2000
samples = []
for i in range(Langevin_steps):
target_langevin.next()
if (i >= burning):
samples.append(target_langevin.state[target_slice].copy())
test_stat = lambda x: np.linalg.norm(x)
observed = test_stat(target_observed[I])
sample_test_stat = np.array([test_stat(x) for x in samples])
family = discrete_family(sample_test_stat,
np.ones_like(sample_test_stat))
pval = family.ccdf(0, observed)
return pval, False
def test_one_inactive_coordinate_handcoded():
s, n, p = 5, 200, 20
randomizer = randomization.laplace((p, ), scale=1.)
X, y, beta, _ = logistic_instance(n=n, p=p, s=s, rho=0.1, snr=14)
nonzero = np.where(beta)[0]
lam_frac = 1.
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 += lam * np.arange(p) / 200
W[0] = 0
penalty = rr.group_lasso(np.arange(p),
weights=dict(zip(np.arange(p), W)),
lagrange=1.)
print(lam)
# our randomization
M_est1 = glm_group_lasso(loss, epsilon, penalty, randomizer)
M_est1.solve()
bootstrap_score1 = M_est1.setup_sampler()
active = M_est1.selection_variable['variables']
if set(nonzero).issubset(np.nonzero(active)[0]):
boot_target, target_observed = pairs_bootstrap_glm(loss, active)
# target are all true null coefficients selected
sampler = lambda: np.random.choice(n, size=(n, ), replace=True)
target_cov, cov1 = bootstrap_cov(sampler,
boot_target,
cross_terms=(bootstrap_score1, ))
# have checked that covariance up to here agrees with other test_glm_langevin example
active_set = np.nonzero(active)[0]
inactive_selected = I = [
i for i in np.arange(active_set.shape[0])
if active_set[i] not in nonzero
]
# is it enough only to bootstrap the inactive ones?
# seems so...
if not I:
return None
# take the first inactive one
I = I[:1]
A1, b1 = M_est1.linear_decomposition(cov1[I], target_cov[I][:, I],
target_observed[I])
print(I, 'I', target_observed[I])
target_inv_cov = np.linalg.inv(target_cov[I][:, I])
initial_state = np.hstack(
[target_observed[I], M_est1.observed_opt_state])
ntarget = len(I)
target_slice = slice(0, ntarget)
opt_slice1 = slice(ntarget, p + ntarget)
def target_gradient(state):
# with many samplers, we will add up the `target_slice` component
# many target_grads
# and only once do the Gaussian addition of full_grad
target = state[target_slice]
opt_state1 = state[opt_slice1]
target_grad1 = M_est1.randomization_gradient(
target, (A1, b1), opt_state1)
full_grad = np.zeros_like(state)
full_grad[opt_slice1] = -target_grad1[1]
full_grad[target_slice] -= target_grad1[0]
full_grad[target_slice] -= target_inv_cov.dot(target)
return full_grad
def target_projection(state):
opt_state1 = state[opt_slice1]
state[opt_slice1] = M_est1.projection(opt_state1)
return state
target_langevin = projected_langevin(initial_state, target_gradient,
target_projection, 1. / p)
Langevin_steps = 10000
burning = 2000
samples = []
for i in range(Langevin_steps + burning):
target_langevin.next()
if (i > burning):
samples.append(target_langevin.state[target_slice].copy())
test_stat = lambda x: x
observed = test_stat(target_observed[I])
sample_test_stat = np.array([test_stat(x) for x in samples])
family = discrete_family(sample_test_stat,
np.ones_like(sample_test_stat))
pval = family.ccdf(0, observed)
pval = 2 * min(pval, 1 - pval)
_i = I[0]
naive_Z = target_observed[_i] / np.sqrt(target_cov[_i, _i])
naive_pval = ndist.sf(np.fabs(naive_Z))
naive_pval = 2 * min(naive_pval, 1 - naive_pval)
print('naive Z', naive_Z, naive_pval)
return pval, naive_pval, False
