def test_kron2sum_large_covariance():
random = RandomState(0)
n = 50
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
scale = 1e4
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lmm.fit(verbose=False)
lmm_large = Kron2Sum(Y, A, F, scale * G, restricted=False)
lmm_large.fit(verbose=False)
assert_allclose(lmm_large.lml(), lmm.lml())
assert_allclose(lmm_large.C0, lmm.C0 / (scale**2), rtol=1e-3, atol=1e-5)
assert_allclose(lmm_large.C1, lmm.C1, rtol=1e-3, atol=1e-5)
assert_allclose(lmm_large.beta, lmm.beta, rtol=1e-3, atol=1e-5)
assert_allclose(lmm_large.beta_covariance,
lmm.beta_covariance,
rtol=1e-3,
atol=1e-5)
assert_allclose(lmm_large.mean(), lmm.mean(), rtol=1e-2, atol=1e-5)
assert_allclose(lmm_large.covariance(),
lmm.covariance(),
rtol=1e-3,
atol=1e-5)
def test_kron2sum_large_outcome():
random = RandomState(2)
n = 50
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
B = random.randn(2, 3)
C0 = random.randn(3, 3)
C0 = C0 @ C0.T
C1 = random.randn(3, 3)
C1 = C1 @ C1.T
K = kron(C0, (G @ G.T)) + kron(C1, eye(n))
y = multivariate_normal(random, kron(A, F) @ vec(B), K)
Y = unvec(y, (n, 3))
Y = Y / Y.std(0)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lmm.fit(verbose=False)
assert_allclose(lmm.lml(), -12.163158697588926)
assert_allclose(lmm.C0[0, 1], -0.004781646218546575, rtol=1e-3, atol=1e-5)
assert_allclose(lmm.C1[0, 1], 0.03454122242999587, rtol=1e-3, atol=1e-5)
assert_allclose(lmm.beta[2], -0.02553979383437496, rtol=1e-3, atol=1e-5)
assert_allclose(lmm.beta_covariance[0, 1],
0.0051326042358990865,
rtol=1e-3,
atol=1e-5)
assert_allclose(lmm.mean()[3], 0.3442913781854699, rtol=1e-2, atol=1e-5)
assert_allclose(lmm.covariance()[0, 1],
0.0010745698663887468,
rtol=1e-3,
atol=1e-5)
def fit(self, verbose=True):
from glimix_core.lmm import Kron2Sum
self._lmm = Kron2Sum(self._y, [[1]], self._M, self._W, restricted=True)
self._lmm.fit(verbose=verbose)
self._covarparam0 = self._lmm.C0[0, 0]
self._covarparam1 = self._lmm.C1[0, 0]
def test_kron2sum_gradient_unrestricted():
random = RandomState(2)
Y = random.randn(5, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(5, 2)
G = random.randn(5, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lmm._cov.C0.Lu = random.randn(3)
lmm._cov.C1.Lu = random.randn(6)
def func(x):
lmm._cov.C0.Lu = x[:3]
lmm._cov.C1.Lu = x[3:9]
return lmm.lml()
def grad(x):
lmm._cov.C0.Lu = x[:3]
lmm._cov.C1.Lu = x[3:9]
D = lmm.gradient()
return concatenate((D["C0.Lu"], D["C1.Lu"]))
assert_allclose(check_grad(func, grad, random.randn(9), epsilon=1e-8),
0,
atol=1e-3)
def test_kron2sum_insufficient_sample_size():
random = RandomState(0)
n = 2
Y = random.randn(n, 2)
A = random.randn(2, 2)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 6)
with pytest.warns(UserWarning):
Kron2Sum(Y, A, F, G)
def test_kron2sum_fit_C1_well_cond_redutant_F_unrestricted():
random = RandomState(0)
Y = random.randn(5, 2)
A = random.randn(2, 2)
A = A @ A.T
F = random.randn(5, 2)
F = concatenate((F, F), axis=1)
G = random.randn(5, 2)
with pytest.warns(UserWarning):
Kron2Sum(Y, A, F, G, restricted=False)
def test_lmm_kron_scan():
random = RandomState(0)
n = 20
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 6)
lmm = Kron2Sum(Y, A, F, G, restricted=True)
lmm.fit(verbose=False)
scan = lmm.get_fast_scanner()
m = lmm.mean()
K = lmm.covariance()
def func(scale):
mv = st.multivariate_normal(m, scale * K)
return -mv.logpdf(vec(Y))
s = minimize(func, 1e-3, 5.0, 1e-5)[0]
assert_allclose(scan.null_lml(),
st.multivariate_normal(m, s * K).logpdf(vec(Y)))
assert_allclose(kron(A, F) @ scan.null_beta, m)
A1 = random.randn(3, 2)
F1 = random.randn(n, 4)
r = scan.scan(A1, F1)
assert_allclose(r["scale"], 0.7365021111700154, rtol=1e-3)
m = kron(A, F) @ vec(r["effsizes0"]) + kron(A1, F1) @ vec(r["effsizes1"])
def func(scale):
mv = st.multivariate_normal(m, scale * K)
return -mv.logpdf(vec(Y))
s = minimize(func, 1e-3, 5.0, 1e-5)[0]
assert_allclose(r["lml"], st.multivariate_normal(m, s * K).logpdf(vec(Y)))
r = scan.scan(empty((3, 0)), F1)
assert_allclose(r["lml"], -85.36667704747371, rtol=1e-4)
assert_allclose(r["scale"], 0.8999995537936586, rtol=1e-3)
assert_allclose(
r["effsizes0"],
[
[0.21489119796865844, 0.6412947101778663, -0.7176143380221816],
[0.8866722740598517, -0.18731140321348416, -0.26118052682069],
],
rtol=1e-2,
atol=1e-2,
)
assert_allclose(r["effsizes1"], [])
def test_kron2sum_fit_C1_well_cond_redundant_Y_unrestricted():
random = RandomState(0)
Y = random.randn(5, 2)
Y = concatenate((Y, Y), axis=1)
A = random.randn(4, 4)
A = A @ A.T
F = random.randn(5, 2)
G = random.randn(5, 2)
with pytest.warns(UserWarning):
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lml = lmm.lml()
assert_allclose(lml, -39.59627521826263)
def test_lmm_kron_scan_unrestricted():
random = RandomState(0)
n = 15
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 6)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lmm.fit(verbose=False)
scan = lmm.get_fast_scanner()
assert_allclose(scan.null_scale, 1.0, rtol=1e-3)
assert_allclose(lmm.beta_covariance, scan.null_beta_covariance, rtol=1e-3)
def _fit_lmm_multi_trait(self, verbose):
from numpy import sqrt, asarray
from glimix_core.lmm import Kron2Sum
from numpy_sugar.linalg import economic_qs, ddot
X = asarray(self._M, float)
QS = economic_qs(self._covariance[0]._K)
G = ddot(QS[0][0], sqrt(QS[1]))
lmm = Kron2Sum(self._y, self._mean.A, X, G, rank=1, restricted=True)
lmm.fit(verbose=verbose)
self._glmm = lmm
self._covariance[0]._set_kron2sum(lmm)
self._covariance[1]._set_kron2sum(lmm)
self._mean.B = lmm.B
def test_kron2sum_fit_C1_well_cond_C0_fullrank_unrestricted():
random = RandomState(0)
Y = random.randn(5, 2)
A = random.randn(2, 2)
A = A @ A.T
F = random.randn(5, 2)
G = random.randn(5, 6)
lmm = Kron2Sum(Y, A, F, G, rank=2, restricted=False)
lml0 = lmm.lml()
lmm.fit(verbose=False)
lml1 = lmm.lml()
assert_allclose([lml0, lml1], [-18.201106294121434, -11.853021889285362])
grad = lmm.gradient()
vars = grad.keys()
assert_allclose(concatenate([grad[var] for var in vars]), [0] * 7,
atol=1e-2)
def test_kron2sum_fit_C1_well_cond_unrestricted():
random = RandomState(0)
Y = random.randn(5, 2)
A = random.randn(2, 2)
A = A @ A.T
F = random.randn(5, 2)
G = random.randn(5, 6)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lml0 = lmm.lml()
lmm.fit(verbose=False)
lml1 = lmm.lml()
assert_allclose([lml0, lml1], [-17.87016217772149, -11.853022179263597],
rtol=1e-5)
grad = lmm.gradient()
vars = grad.keys()
assert_allclose(concatenate([grad[var] for var in vars]), [0] * 5,
atol=1e-2)
def test_kron2sum_fit_ill_conditioned_unrestricted():
random = RandomState(0)
n = 30
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lml0 = lmm.lml()
lmm.fit(verbose=False)
lml1 = lmm.lml()
assert_allclose([lml0, lml1], [-154.73966241953627, -122.97307227633186])
grad = lmm.gradient()
vars = grad.keys()
assert_allclose(concatenate([grad[var] for var in vars]), [0] * 9,
atol=1e-2)
def _mt_lmm(Y, A, M, QS, verbose):
from glimix_core.lmm import Kron2Sum
from numpy_sugar.linalg import ddot
from numpy import sqrt, zeros
if QS is None:
KG = zeros((Y.shape[0], 1))
else:
KG = ddot(QS[0][0], sqrt(QS[1]))
lmm = Kron2Sum(Y.values, A, M.values, KG, restricted=False)
lmm.fit(verbose=verbose)
sys.stdout.flush()
C0 = lmm.C0
C1 = lmm.C1
return lmm.get_fast_scanner(), C0, C1
def test_lmm_kron_scan_redundant():
random = RandomState(0)
n = 30
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 6)
G = concatenate([G, G], axis=1)
lmm = Kron2Sum(Y, A, F, G, restricted=True)
lmm.fit(verbose=False)
scan = lmm.get_fast_scanner()
m = lmm.mean()
K = lmm.covariance()
def func(scale):
mv = st.multivariate_normal(m, scale * K)
return -mv.logpdf(vec(Y))
s = minimize(func, 1e-3, 5.0, 1e-5)[0]
assert_allclose(scan.null_lml(),
st.multivariate_normal(m, s * K).logpdf(vec(Y)))
assert_allclose(kron(A, F) @ scan.null_beta, m)
A1 = random.randn(3, 2)
F1 = random.randn(n, 4)
F1 = concatenate([F1, F1], axis=1)
r = scan.scan(A1, F1)
assert_allclose(r["scale"], 0.8843540849467378, rtol=1e-3)
m = kron(A, F) @ vec(r["effsizes0"]) + kron(A1, F1) @ vec(r["effsizes1"])
def func(scale):
mv = st.multivariate_normal(m, scale * K)
return -mv.logpdf(vec(Y))
s = minimize(func, 1e-3, 5.0, 1e-5)[0]
assert_allclose(r["lml"], st.multivariate_normal(m, s * K).logpdf(vec(Y)))
def test_kron2sum_unrestricted_lml():
random = RandomState(0)
Y = random.randn(5, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(5, 2)
G = random.randn(5, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
y = vec(lmm._Y)
m = lmm.mean()
K = lmm.covariance()
assert_allclose(lmm.lml(), st.multivariate_normal(m, K).logpdf(y))
lmm._cov.C0.Lu = random.randn(3)
m = lmm.mean()
K = lmm.covariance()
assert_allclose(lmm.lml(), st.multivariate_normal(m, K).logpdf(y))
lmm._cov.C1.Lu = random.randn(6)
m = lmm.mean()
K = lmm.covariance()
assert_allclose(lmm.lml(), st.multivariate_normal(m, K).logpdf(y))
def test_lmm_kron_scan_with_lmm():
random = RandomState(0)
n = 15
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 6)
klmm = Kron2Sum(Y, A, F, G, restricted=True)
klmm.fit(verbose=False)
kscan = klmm.get_fast_scanner()
K = klmm.covariance()
X = kron(A, F)
QS = economic_qs(K)
scan = FastScanner(vec(Y), X, QS, 0.0)
assert_allclose(klmm.covariance(), K)
assert_allclose(kscan.null_scale, scan.null_scale)
assert_allclose(kscan.null_beta, scan.null_beta)
assert_allclose(kscan.null_lml(), scan.null_lml())
assert_allclose(kscan.null_beta_covariance, scan.null_beta_covariance)
A1 = random.randn(3, 2)
F1 = random.randn(n, 2)
M = kron(A1, F1)
kr = kscan.scan(A1, F1)
r = scan.scan(M)
assert_allclose(kr["lml"], r["lml"])
assert_allclose(kr["scale"], r["scale"])
assert_allclose(vec(kr["effsizes0"]), r["effsizes0"])
assert_allclose(vec(kr["effsizes1"]), r["effsizes1"])
assert_allclose(vec(kr["effsizes0_se"]), r["effsizes0_se"])
assert_allclose(vec(kr["effsizes1_se"]), r["effsizes1_se"])
def test_kron2sum_restricted():
random = RandomState(0)
n = 5
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=True)
assert_allclose(lmm.lml(), -16.081058762513514)
assert_allclose(lmm._check_grad(step=1e-7), 0, atol=1e-4)
assert_equal(lmm.nsamples, n)
assert_equal(lmm.ntraits, 3)
assert_equal(lmm.ncovariates, 2)
n = 5
Y = random.randn(n, 1)
A = random.randn(1, 1)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=True)
lmm.name = "KronSum"
assert_allclose(lmm.lml(), -3.7547099473445003)
assert_allclose(lmm._check_grad(step=1e-7), 0, atol=1e-4)
assert_allclose([lmm.mean()[0], lmm.mean()[1]],
[0.06452826276050515, 0.4855196092646256])
assert_allclose(
lmm.covariance(),
[
[
1.9379300845374776,
-0.02014070399890988,
-0.7399969689595782,
-0.1402228534612341,
-0.4690219904509089,
],
[
-0.02014070399890988,
1.4797056135059965,
0.0916295591269426,
-0.3210581381149237,
0.2558220662032061,
],
[
-0.7399969689595782,
0.0916295591269426,
1.6313538475715865,
-0.07164808824303559,
0.5063738410283093,
],
[
-0.1402228534612341,
-0.3210581381149237,
-0.07164808824303559,
3.333140431376828,
0.3424485007527981,
],
[
-0.4690219904509089,
0.2558220662032061,
0.5063738410283093,
0.3424485007527981,
2.023907116315917,
],
],
)
assert_equal(lmm.nsamples, n)
assert_equal(lmm.ntraits, 1)
assert_equal(lmm.name, "KronSum")
lmm.fit(verbose=False)
grad = lmm.gradient()
assert_allclose(grad["C0.Lu"], [0], atol=1e-4)
assert_allclose(grad["C1.Lu"], [0], atol=1e-4)
assert_allclose(lmm.lml(), -0.6930197328322949, rtol=1e-5)
A = lmm.beta_covariance
assert_allclose(
A,
[
[4.831901045051292, -2.1320785310203645],
[-2.1320785310203645, 0.9438229054009741],
],
atol=1e-5,
rtol=1e-5,
)
def test_kron2sum_unrestricted():
random = RandomState(0)
n = 5
Y = random.randn(n, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
assert_allclose(lmm.lml(), -21.917751466118062)
assert_allclose(lmm._check_grad(step=1e-7), 0, atol=1e-4)
assert_equal(lmm.nsamples, n)
assert_equal(lmm.ntraits, 3)
assert_equal(lmm.ncovariates, 2)
n = 5
Y = random.randn(n, 1)
A = random.randn(1, 1)
A = A @ A.T
F = random.randn(n, 2)
G = random.randn(n, 4)
lmm = Kron2Sum(Y, A, F, G, restricted=False)
lmm.name = "KronSum"
assert_allclose(lmm.lml(), -6.293806054115431)
assert_allclose(lmm._check_grad(step=1e-7), 0, atol=1e-4)
assert_allclose(
lmm.mean(),
[
0.06452826276050515,
0.4855196092646256,
0.1396748241908668,
-0.264600249205993,
-0.08238891336460354,
],
)
assert_allclose(
lmm.covariance(),
[
[
1.9379300845374776,
-0.02014070399890988,
-0.7399969689595782,
-0.1402228534612341,
-0.4690219904509089,
],
[
-0.02014070399890988,
1.4797056135059965,
0.0916295591269426,
-0.3210581381149237,
0.2558220662032061,
],
[
-0.7399969689595782,
0.0916295591269426,
1.6313538475715865,
-0.07164808824303559,
0.5063738410283093,
],
[
-0.1402228534612341,
-0.3210581381149237,
-0.07164808824303559,
3.333140431376828,
0.3424485007527981,
],
[
-0.4690219904509089,
0.2558220662032061,
0.5063738410283093,
0.3424485007527981,
2.023907116315917,
],
],
)
assert_equal(lmm.nsamples, n)
assert_equal(lmm.ntraits, 1)
assert_equal(lmm.name, "KronSum")
lmm.fit(verbose=False)
grad = lmm.gradient()
assert_allclose(grad["C0.Lu"], [0], atol=1e-4)
assert_allclose(grad["C1.Lu"], [0], atol=1e-4)
assert_allclose(lmm.lml(), 2.3394131683065957, rtol=1e-5)
A = [
[3.621700765362852, -1.5979882078099437],
[-1.5979882078099474, 0.7081144405074323],
]
assert_allclose(lmm.beta_covariance, A, atol=1e-5, rtol=1e-5)
def test_kron2sum_interface():
random = RandomState(2)
Y = random.randn(2, 3)
A = random.randn(3, 3)
A = A @ A.T
F = random.randn(2, 2)
G = random.randn(2, 4)
with pytest.warns(UserWarning):
lmm = Kron2Sum(Y, A, F, G, restricted=False)
assert_allclose(
lmm.covariance(),
[
[
14.086388186569708,
2.460064191520785,
14.086373285408515,
2.460064191520785,
14.086373285408515,
2.460064191520785,
],
[
2.460064191520785,
24.620081892940938,
2.460064191520785,
24.620066991779744,
2.460064191520785,
24.620066991779744,
],
[
14.086373285408515,
2.460064191520785,
15.086388186569708,
2.460064191520785,
15.086373285408515,
2.460064191520785,
],
[
2.460064191520785,
24.620066991779744,
2.460064191520785,
25.620081892940938,
2.460064191520785,
25.620066991779744,
],
[
14.086373285408515,
2.460064191520785,
15.086373285408515,
2.460064191520785,
16.086388186569707,
2.460064191520785,
],
[
2.460064191520785,
24.620066991779744,
2.460064191520785,
25.620066991779744,
2.460064191520785,
26.620081892940938,
],
],
atol=1e-7,
)
assert_allclose(
lmm.mean(),
[
-0.4167578796040061,
1.6402707883933658,
-0.05626685903041562,
-1.7934356050990345,
-2.1361961254498922,
-0.8417473850096115,
],
atol=1e-7,
)
assert_allclose(lmm.lml(), -8.429274310765745, atol=1e-7)
assert_allclose(lmm.value(), lmm.lml(), atol=1e-7)
assert_allclose(
lmm.A,
[
[2.9228950357645274, -3.568888742838519, 0.8427306809792194],
[-3.568888742838519, 6.384613981254706, 0.58138966904566],
[0.8427306809792194, 0.58138966904566, 1.5420666949903108],
],
atol=1e-7,
)
assert_allclose(
lmm.B,
[
[-155.30629394331186, -98.10725907737903, 124.05223343020717],
[-371.5199454125782, -234.2023411372212, 295.50286962569464],
],
atol=1e-7,
)
assert_allclose(
lmm.X,
[
[-0.596159699806467, -0.019130496521151476],
[1.175001219500291, -0.7478709492938624],
],
atol=1e-7,
)
assert_allclose(
lmm.M,
[
[
-1.7425122270871933,
-0.05591643331338421,
2.127627641573291,
0.06827461367924896,
-0.5024020697902709,
-0.016121856360740573,
],
[
3.4344052314946665,
-2.1859482850835352,
-4.193448625096121,
2.6690682120308225,
0.9902095778608936,
-0.630253794382992,
],
[
2.127627641573291,
0.06827461367924896,
-3.8062495544449777,
-0.12214083555728823,
-0.34660109056884186,
-0.011122273041111408,
],
[
-4.193448625096121,
2.6690682120308225,
7.501929214012888,
-4.774867319035823,
0.6831335701335212,
-0.43480444369882226,
],
[
-0.5024020697902709,
-0.016121856360740573,
-0.34660109056884186,
-0.011122273041111408,
-0.9193180179669744,
-0.029500501543895694,
],
[
0.9902095778608936,
-0.630253794382992,
0.6831335701335212,
-0.43480444369882226,
1.8119302471643985,
-1.1532668830568527,
],
],
atol=1e-7,
)
assert_allclose(
lmm.C0,
[
[15.191012511337567, 15.191012511337567, 15.191012511337567],
[15.191012511337567, 15.191012511337567, 15.191012511337567],
[15.191012511337567, 15.191012511337567, 15.191012511337567],
],
atol=1e-7,
)
assert_allclose(
lmm.C1,
[
[1.0000149011611938, 1.0, 1.0],
[1.0, 2.000014901161194, 2.0],
[1.0, 2.0, 3.000014901161194],
],
atol=1e-7,
)
assert_allclose(
lmm.beta,
[
-155.3062975390569,
-371.5199529125092,
-98.10726134921538,
-234.20234587581533,
124.0522362217501,
295.5028754471357,
],
atol=1e-7,
)
assert_allclose(
lmm.beta_covariance,
[
[
180454.5259497599,
301884.9772469587,
114011.82157538977,
190733.14284940425,
-140134.13859849886,
-234404.7154325302,
],
[
301884.97720675723,
720240.068298505,
190733.1428240255,
455058.3880442711,
-234404.7154008012,
-559111.09170418,
],
[
114011.82157538975,
190733.14284942497,
72033.11947254256,
120506.65851010302,
-88536.94418846158,
-148098.13529283906,
],
[
190733.14282400408,
455058.38804427016,
120506.6584940551,
287512.77822660643,
-148098.13527277583,
-353253.7315868218,
],
[
-140134.13859850125,
-234404.71543202398,
-88536.94418846308,
-148098.13529250308,
108827.80847946613,
182016.00480204573,
],
[
-234404.71540133483,
-559111.0917042121,
-148098.13527312962,
-353253.7315868427,
182016.00477781752,
434044.7463389145,
],
],
atol=1e-7,
)
assert_equal(lmm.ncovariates, 2)
assert_equal(lmm.nsamples, 2)
assert_equal(lmm.ntraits, 3)
assert_equal(lmm.name, "Kron2Sum")
