def test_blockdiag_approx_on_blockdiag(self):
# Check that blockdiag approx yields same solution
# for block-diagonal matrix.
p = 250
rho = 0.3
gamma = 0
groups = np.arange(1, p + 1, 1)
dgprocess = dgp.DGP()
_, _, _, _, V = dgprocess.sample_data(p=p,
method="blockequi",
gamma=gamma,
rho=rho)
for method in ["mvr", "maxent", "sdp"]:
# Check that S_approx is valid
S_approx = smatrix.compute_smatrix(V, method=method, max_block=10)
self.check_S_properties(V, S_approx, groups)
# In this case, should be the same as S_exact
S_exact = smatrix.compute_smatrix(V, method=method)
np.testing.assert_array_almost_equal(
S_approx,
S_exact,
2,
err_msg=
"Blockdiag approximation yields incorrect answer for blockdiag Sigma",
)
def test_agreement_on_factor_models(self):
# Random factor models
np.random.seed(110)
ks = [1, 10, 20, 50]
p = 150
for k in ks:
for method in ['mvr', 'maxent', 'sdp']:
D = np.random.uniform(low=0.01, high=1, size=(p, ))
U = np.random.randn(p, k) / np.sqrt(k)
# Rescale to correlation matrix
diag_Sigma = D + (np.power(U, 2)).sum(axis=1)
D = D / diag_Sigma
U = U / np.sqrt(diag_Sigma).reshape(-1, 1)
Sigma = np.diag(D) + np.dot(U, U.T)
# Check the factor method agrees with reg. method
S1 = smatrix.compute_smatrix(Sigma=None,
D=D,
U=U,
method=method,
how_approx='factor')
S2 = smatrix.compute_smatrix(Sigma=Sigma,
method=method,
solver='cd',
tol=0)
np.testing.assert_array_almost_equal(
S1,
S2,
decimal=2,
err_msg=
f"factored/non-factored versions for method={method}, k={k} do not agree"
)
def test_sdp_tolerance(self):
# Get graph
np.random.seed(110)
Q = dgp.ErdosRenyi(p=50, tol=1e-1)
V = utilities.cov2corr(utilities.chol2inv(Q))
groups = np.concatenate([np.zeros(10) + j for j in range(5)]) + 1
groups = groups.astype("int32")
# Solve SDP
for tol in [1e-3, 0.01, 0.02]:
S = smatrix.compute_smatrix(
Sigma=V,
groups=groups,
method="sdp",
objective="pnorm",
num_iter=10,
tol=tol,
)
G = np.hstack([np.vstack([V, V - S]), np.vstack([V - S, V])])
mineig = np.linalg.eig(G)[0].min()
self.assertTrue(
tol - mineig > -1 * tol / 10,
f"sdp solver fails to control minimum eigenvalues: tol is {tol}, val is {mineig}",
)
self.check_S_properties(V, S, groups)
def test_blockdiag_approx_on_ar1(self):
# Check that blockdiag approx yields a good soln on AR1
p = 150
a = 1
b = 1
# Create trivial and nontrivial groups
triv_groups = np.arange(1, p + 1, 1)
nontriv_groups = np.around(triv_groups / 2 + 0.01)
nontriv_groups = utilities.preprocess_groups(nontriv_groups)
# Sample data
np.random.seed(110)
dgprocess = dgp.DGP()
_, _, _, _, V = dgprocess.sample_data(p=p, method="ar1", a=a, b=b)
for groups in [triv_groups, nontriv_groups]:
for method in ["mvr", "maxent", "mmi", "sdp"]:
# Note we can't fit group mvr/maxent without pytorch
nontriv_group_flag = np.all(groups == nontriv_groups)
if not TORCH_AVAILABLE and nontriv_group_flag:
continue
# Check that S_approx is valid
S_approx = smatrix.compute_smatrix(V,
method=method,
groups=groups,
max_block=50)
self.check_S_properties(V, S_approx, groups)
# For exponentially decaying offdiags, should be quite similar
# This seems to not be true for groups, so skip that for now...
# For now, skip grouped mvr/mmi
if nontriv_group_flag:
continue
S_exact = smatrix.compute_smatrix(V,
method=method,
groups=groups)
diff = np.abs(S_approx - S_exact)
mean_diff = diff[S_exact != 0].mean()
expected = 1e-2 if CHOLDATE_AVAILABLE else 5e-2
identifier = f"for method={method}, groups={groups}"
self.assertTrue(
mean_diff < expected,
msg=
f"Blockdiag apprx is {mean_diff} > {expected} on avg. away from exact soln {identifier}",
)
def test_warnings_raised(self):
print(
f"torch={TORCH_AVAILABLE}, dsdp={DSDP_AVAILABLE}, choldate={CHOLDATE_AVAILABLE}"
)
# Sigma
p = 50
rho = 0.8
Sigma = rho * np.ones((p, p)) + (1 - rho) * np.eye(p)
for method, dependency_flag, dependency_name, suppress_kwargs in zip(
['mvr', 'maxent', 'sdp'],
[CHOLDATE_AVAILABLE, CHOLDATE_AVAILABLE, DSDP_AVAILABLE],
["choldate", "choldate", "dsdp"], [{
"choldate_warning": False
}, {
"choldate_warning": False
}, {
"dsdp_warning": False
}]):
# Check default setting
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
smatrix.compute_smatrix(Sigma, method=method)
if not dependency_flag:
self.assertTrue(dependency_name in str(w[-1].message))
else:
self.assertTrue(len(w) == 0)
# Check that it does not trigger with correct flag
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
smatrix.compute_smatrix(Sigma,
method=method,
**suppress_kwargs)
self.assertTrue(
len(w) == 0,
"warning still triggers with choldate_warning=False")
def test_cd_SDP(self):
"""
Test that CD / SDP solvers get similar answers in a hard problem
"""
np.random.seed(110)
V = utilities.cov2corr(dgp.ErdosRenyi(p=100, tol=1e-1))
S_cd = smatrix.compute_smatrix(Sigma=V,
method="sdp",
solver="cd",
verbose=True,
mu=0.95,
num_iter=100)
mac_cd = np.diag(S_cd).mean()
S_sdp = smatrix.compute_smatrix(Sigma=V, method="sdp", solver="sdp")
mac_sdp = np.diag(S_sdp).mean()
np.testing.assert_almost_equal(
mac_sdp,
mac_cd,
decimal=2,
err_msg=
f"compute_smatrix mac differs between SDP/CD solvers ({mac_sdp}, {mac_cd}, respectively"
)
def test_maxent(self):
""" Both maxent/mmi work properly """
# Sample data
dgprocess = dgp.DGP()
dgprocess.sample_data(p=50, method='ar1', a=3)
# Check solve_maxent/solve_mmi
np.random.seed(110)
S_ME = smatrix.compute_smatrix(dgprocess.Sigma, method='maxent')
np.random.seed(110)
S_MMI = smatrix.compute_smatrix(dgprocess.Sigma, method='mmi')
np.testing.assert_array_almost_equal(
S_ME,
S_MMI,
decimal=3,
err_msg=f"compute_smatrix yields diff answers for mmi, maxent")
# Check solve_maxent/solve_mmi
np.random.seed(110)
S_ME = mrc.solve_maxent(dgprocess.Sigma)
np.random.seed(110)
S_MMI = mrc.solve_mmi(dgprocess.Sigma)
np.testing.assert_array_almost_equal(
S_ME,
S_MMI,
decimal=3,
err_msg=f"solve_maxent and solve_mmi yield different answers")
# Check maxent_loss/mmi_loss
L_ME = mrc.maxent_loss(dgprocess.Sigma, S_ME)
L_MMI = mrc.mmi_loss(dgprocess.Sigma, S_MMI)
np.testing.assert_almost_equal(
L_ME,
L_MMI,
decimal=3,
err_msg=f"maxent_loss and mmi_loss yield different answers")
def test_equicorr_SDP(self):
# Test non-group SDP on equicorrelated cov matrix
p = 100
rhos = [0.6, 0.8, 0.9]
solvers = ['sdp', 'cd']
scales = [1, 5]
for scale in scales:
for rho in rhos:
V = scale * rho * np.ones(
(p, p)) + scale * (1 - rho) * np.eye(p)
for solver in solvers:
S = smatrix.compute_smatrix(Sigma=V,
method="sdp",
solver=solver,
verbose=True)
expected = (2 - 2 * rho) * np.eye(p)
np.testing.assert_almost_equal(
S / scale,
expected,
decimal=2,
err_msg=
f"compute_smatrix produces incorrect S_SDP for equicorr, rho={rho}, scale={scale}, solver={solver}",
)
def test_easy_sdp(self):
# Test non-group SDP first
n = 200
p = 50
X, _, _, _, corr_matrix, groups = dgp.block_equi_graph(n=n,
p=p,
gamma=0.3)
# S matrix
trivial_groups = np.arange(0, p, 1) + 1
S_triv = smatrix.compute_smatrix(
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 (blockequi graphs)",
)
self.check_S_properties(corr_matrix, S_triv, trivial_groups)
# Repeat for gaussian_knockoffs method
ksampler = knockoffs.GaussianSampler(
X=X,
Sigma=corr_matrix,
groups=trivial_groups,
verbose=False,
method="sdp",
)
S_triv2 = ksampler.fetch_S()
np.testing.assert_array_almost_equal(
S_triv2,
np.eye(p),
decimal=2,
err_msg=
"solve_group_SDP does not produce optimal S matrix (blockequi graphs)",
)
self.check_S_properties(corr_matrix, S_triv2, trivial_groups)
# Test slightly harder case
_, _, _, _, expected_out, _ = dgp.block_equi_graph(n=n, p=p, gamma=0)
ksampler = knockoffs.GaussianSampler(X=X,
Sigma=corr_matrix,
groups=groups,
verbose=False,
method="sdp")
S_harder = ksampler.fetch_S()
np.testing.assert_almost_equal(
S_harder,
expected_out,
decimal=2,
err_msg=
"solve_group_SDP does not produce optimal S matrix (blockequi graphs)",
)
self.check_S_properties(corr_matrix, S_harder, groups)
# Repeat for ASDP
ksampler = knockoffs.GaussianSampler(
X=X,
Sigma=corr_matrix,
groups=groups,
method="ASDP",
verbose=False,
max_block=10,
)
S_harder_ASDP = ksampler.fetch_S()
np.testing.assert_almost_equal(
S_harder_ASDP,
expected_out,
decimal=2,
err_msg=
"solve_group_ASDP does not produce optimal S matrix (blockequi graphs)",
)
self.check_S_properties(corr_matrix, S_harder_ASDP, groups)