def test_consistency_of_inferring_sigma(self):
""" Checks that the same knockoffs are produced
whether you infer the covariance matrix first and
pass it to the gaussian_knockoffs generator, or
you let the generator do the work for you
"""
n = 25
p = 300
rho = 0.5
X, _, _, _, _ = graphs.sample_data(n=n, p=p, rho=rho, method='AR1')
# Method 1: infer cov first
V, _ = utilities.estimate_covariance(X, tol=1e-2)
np.random.seed(110)
Xk1 = knockoffs.gaussian_knockoffs(X=X,
Sigma=V,
method='sdp',
max_epochs=1)
# Method 2: Infer during
np.random.seed(110)
Xk2 = knockoffs.gaussian_knockoffs(X=X, method='sdp', max_epochs=1)
np.testing.assert_array_almost_equal(
Xk1, Xk2, 5, err_msg='Knockoff gen is inconsistent')
def fx_knockoffs_low_n():
knockoffs.gaussian_knockoffs(
X=X,
Sigma=corr_matrix,
S=None,
fixedX=True,
)
def check_valid_mxknockoffs(self,
X,
mu=None,
Sigma=None,
msg='',
**kwargs):
# S matrix
all_knockoffs, S = knockoffs.gaussian_knockoffs(X=X,
mu=mu,
Sigma=Sigma,
return_S=True,
verbose=True,
**kwargs)
# Extract knockoffs
Xk = all_knockoffs[:, :, -1]
# Test knockoff mean
if mu is None:
mu = X.mean(axis=0)
outmsg = "Knockoffs have incorrect means "
outmsg += f"for MX knockoffs for {msg}"
np.testing.assert_array_almost_equal(Xk.mean(axis=0), mu, 2, outmsg)
# Sigma should be
if Sigma is None:
Sigma, _ = utilities.estimate_covariance(X, tol=1e-2)
# Also rescale X/Xk so S makes sense
scale = np.sqrt(np.diag(Sigma))
X = X / scale.reshape(1, -1)
if mu is None:
mu = X.mean(axis=0)
else:
mu = mu / scale
Xk = Xk / scale.reshape(1, -1)
Sigma = Sigma / np.outer(scale, scale)
S = S / np.outer(scale, scale)
# Empirical FK correlation matrix
features = np.concatenate([X, Xk], axis=1)
G_hat = np.cov(features.T)
# Calculate population version
G = np.concatenate([
np.concatenate([Sigma, Sigma - S]),
np.concatenate([Sigma - S, Sigma])
],
axis=1)
# Test G has correct structure
outmsg = f"Feature-knockoff cov matrix has incorrect values "
outmsg += f"for MX knockoffs for {msg} graph "
np.testing.assert_array_almost_equal(G_hat, G, 2, outmsg)
def test_FX_knockoff_dist(self):
# Test knockoff construction for mvr and SDP
# on equicorrelated matrices
n = 500
p = 5
for rho in [0.1, 0.9]:
for gamma in [0.5, 1]:
for method in ['mvr', 'sdp']:
# X values
X, _, _, _, corr_matrix, _ = graphs.daibarber2016_graph(
n=n, p=p, gamma=gamma, rho=rho)
# S matrix
trivial_groups = np.arange(0, p, 1) + 1
all_knockoffs, S = knockoffs.gaussian_knockoffs(
X=X,
fixedX=True,
copies=int(gamma) + 1,
method=method,
return_S=True,
verbose=False)
# Scale properly so we can calculate
scale = np.sqrt(np.diag(np.dot(X.T, X)).reshape(1, -1))
X = X / scale
knockoff_copy = all_knockoffs[:, :, -1] / scale
S = S / np.outer(scale, scale)
# # Compute empirical (scaled) cov matrix
features = np.concatenate([X, knockoff_copy], axis=1)
G_hat = np.dot(features.T, features)
# Calculate what this should be
Sigma = np.dot(X.T, X)
G = np.concatenate([
np.concatenate([Sigma, Sigma - S]),
np.concatenate([Sigma - S, Sigma])
],
axis=1)
# Test G has correct structure
msg = f"Feature-knockoff cov matrix has incorrect values "
msg += f"for daibarber graph, FX knockoffs, rho = {rho}, gamma = {gamma}"
np.testing.assert_array_almost_equal(G_hat, G, 5, msg)
def fdr_vio_knockoffs():
knockoffs.gaussian_knockoffs(X=X,
Sigma=corr_matrix,
S=S_bad,
verbose=False)
def test_easy_sdp(self):
# Test non-group SDP first
n = 200
p = 50
X, _, _, _, corr_matrix, groups = graphs.daibarber2016_graph(n=n,
p=p,
gamma=0.3)
# S matrix
trivial_groups = np.arange(0, p, 1) + 1
S_triv = knockoffs.compute_S_matrix(
Sigma=corr_matrix,
groups=trivial_groups,
method='sdp',
verbose=True,
)
np.testing.assert_array_almost_equal(
S_triv,
np.eye(p),
decimal=2,
err_msg=
'solve_group_SDP does not produce optimal S matrix (daibarber graphs)'
)
self.check_S_properties(corr_matrix, S_triv, trivial_groups)
# Repeat for gaussian_knockoffs method
_, S_triv2 = knockoffs.gaussian_knockoffs(
X=X,
Sigma=corr_matrix,
groups=trivial_groups,
return_S=True,
verbose=False,
method='sdp',
)
np.testing.assert_array_almost_equal(
S_triv2,
np.eye(p),
decimal=2,
err_msg=
'solve_group_SDP does not produce optimal S matrix (daibarber graphs)'
)
self.check_S_properties(corr_matrix, S_triv2, trivial_groups)
# Test slightly harder case
_, _, _, _, expected_out, _ = graphs.daibarber2016_graph(n=n,
p=p,
gamma=0)
_, S_harder = knockoffs.gaussian_knockoffs(X=X,
Sigma=corr_matrix,
groups=groups,
return_S=True,
verbose=False,
method='sdp')
np.testing.assert_almost_equal(
S_harder,
expected_out,
decimal=2,
err_msg=
'solve_group_SDP does not produce optimal S matrix (daibarber graphs)'
)
self.check_S_properties(corr_matrix, S_harder, groups)
# Repeat for ASDP
_, S_harder_ASDP = knockoffs.gaussian_knockoffs(X=X,
Sigma=corr_matrix,
groups=groups,
method='ASDP',
return_S=True,
verbose=False,
max_block=10)
np.testing.assert_almost_equal(
S_harder_ASDP,
expected_out,
decimal=2,
err_msg=
'solve_group_ASDP does not produce optimal S matrix (daibarber graphs)'
)
self.check_S_properties(corr_matrix, S_harder_ASDP, groups)