def test_gaussian(n=100, p=20):
y = np.random.standard_normal(n)
X = np.random.standard_normal((n,p))
lam_theor = np.mean(np.fabs(np.dot(X.T, np.random.standard_normal((n, 1000)))).max(0))
Q = rr.identity_quadratic(0.01, 0, np.ones(p), 0)
weights_with_zeros = 0.5*lam_theor * np.ones(p)
weights_with_zeros[:3] = 0.
huge_weights = weights_with_zeros * 10000
for q, fw in product([Q, None],
[0.5*lam_theor, weights_with_zeros, huge_weights]):
L = lasso.gaussian(X, y, fw, 1., quadratic=Q)
L.fit()
C = L.constraints
sandwich = glm_sandwich_estimator(L.loglike, B=5000)
L = lasso.gaussian(X, y, fw, 1., quadratic=Q, covariance_estimator=sandwich)
L.fit()
C = L.constraints
S = L.summary('onesided', compute_intervals=True)
S = L.summary('twosided')
nt.assert_raises(ValueError, L.summary, 'none')
print(L.active)
yield (np.testing.assert_array_less,
np.dot(L.constraints.linear_part, L.onestep_estimator),
L.constraints.offset)
def test_gaussian_sandwich_pvals(n=200,
p=50,
s=10,
sigma=10,
rho=0.3,
snr=6.,
use_lasso_sd=False):
X, y, beta, true_active, sigma = instance(n=n,
p=p,
s=s,
sigma=sigma,
rho=rho,
snr=snr)
heteroscedastic_error = sigma * np.random.standard_normal(n) * (np.fabs(X[:,-1]) + 0.5)**2
heteroscedastic_error += sigma * np.random.standard_normal(n) * (np.fabs(X[:,-2]) + 0.2)**2
heteroscedastic_error += sigma * np.random.standard_normal(n) * (np.fabs(X[:,-3]) + 0.5)**2
y += heteroscedastic_error
# two different estimators of variance
loss = rr.glm.gaussian(X, y)
sandwich = glm_sandwich_estimator(loss, B=5000)
# make sure things work with some unpenalized columns
feature_weights = np.ones(p) * 3 * sigma
feature_weights[10:12] = 0
# try using RSS from LASSO to estimate sigma
if use_lasso_sd:
L_prelim = lasso.gaussian(X, y, feature_weights)
L_prelim.fit()
beta_lasso = L_prelim.lasso_solution
sigma_hat = np.linalg.norm(y - X.dot(beta_lasso))**2 / (n - len(L_prelim.active))
parametric = glm_parametric_estimator(loss, dispersion=sigma_hat**2)
else:
parametric = glm_parametric_estimator(loss, dispersion=None)
L_P = lasso.gaussian(X, y, feature_weights, covariance_estimator=parametric)
L_P.fit()
if set(true_active).issubset(L_P.active):
S = L_P.summary('twosided')
P_P = [p for p, v in zip(S['pval'], S['variable']) if v not in true_active]
L_S = lasso.gaussian(X, y, feature_weights, covariance_estimator=sandwich)
L_S.fit()
S = L_S.summary('twosided')
P_S = [p for p, v in zip(S['pval'], S['variable']) if v not in true_active]
return P_P, P_S, [v in true_active for v in S['variable']]