def test_glmmexpfam_optimize():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
z = random.multivariate_normal(0.2 * ones(nsamples), K)
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm.lml(), -29.102168129099287, atol=ATOL, rtol=RTOL)
glmm.fix("beta")
glmm.fix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -27.635788105778012, atol=ATOL, rtol=RTOL)
glmm.unfix("beta")
glmm.unfix("scale")
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -19.68486269551159, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_predict():
random = RandomState(4)
n = 100
p = n + 1
X = ones((n, 2))
X[:, 1] = random.randn(n)
G = random.randn(n, p)
G /= G.std(0)
G -= G.mean(0)
G /= sqrt(p)
K = dot(G, G.T)
i = asarray(arange(0, n), int)
si = random.choice(i, n, replace=False)
ntest = int(n // 5)
itrain = si[:-ntest]
itest = si[-ntest:]
Xtrain = X[itrain, :]
Ktrain = K[itrain, :][:, itrain]
Xtest = X[itest, :]
beta = random.randn(2)
z = random.multivariate_normal(dot(X, beta), 0.9 * K + 0.1 * eye(n))
ntri = random.randint(1, 100, n)
nsuc = zeros(n, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
QStrain = economic_qs(Ktrain)
nsuc_train = ascontiguousarray(nsuc[itrain])
ntri_train = ascontiguousarray(ntri[itrain])
nsuc_test = ascontiguousarray(nsuc[itest])
ntri_test = ascontiguousarray(ntri[itest])
glmm = GLMMExpFam(nsuc_train, ("binomial", ntri_train), Xtrain, QStrain)
glmm.fit(verbose=False)
ks = K[itest, :][:, itrain]
kss = asarray([K[i, i] for i in itest])
pm = glmm.predictive_mean(Xtest, ks, kss)
pk = glmm.predictive_covariance(Xtest, ks, kss)
r = nsuc_test / ntri_test
assert_(corrcoef([pm, r])[0, 1] > 0.8)
assert_allclose(pk[0], 54.263705682514846)
def _fit_glmm_simple_model(self, verbose):
from numpy_sugar.linalg import economic_qs
from glimix_core.glmm import GLMMExpFam
from numpy import asarray
K = self._get_matrix_simple_model()
y = asarray(self._y, float).ravel()
QS = None
if K is not None:
QS = economic_qs(K)
glmm = GLMMExpFam(y, self._lik, self._M, QS)
glmm.fit(verbose=verbose)
self._set_simple_model_variances(glmm.v0, glmm.v1)
self._glmm = glmm
def test_glmmexpfam_poisson():
from numpy import ones, stack, exp, zeros
from numpy.random import RandomState
from numpy_sugar.linalg import economic_qs
from pandas import DataFrame
random = RandomState(1)
# sample size
n = 30
# covariates
offset = ones(n) * random.randn()
age = random.randint(16, 75, n)
M = stack((offset, age), axis=1)
M = DataFrame(stack([offset, age], axis=1), columns=["offset", "age"])
M["sample"] = [f"sample{i}" for i in range(n)]
M = M.set_index("sample")
# genetic variants
G = random.randn(n, 4)
# sampling the phenotype
alpha = random.randn(2)
beta = random.randn(4)
eps = random.randn(n)
y = M @ alpha + G @ beta + eps
# Whole genotype of each sample.
X = random.randn(n, 50)
# Estimate a kinship relationship between samples.
X_ = (X - X.mean(0)) / X.std(0) / sqrt(X.shape[1])
K = X_ @ X_.T + eye(n) * 0.1
# Update the phenotype
y += random.multivariate_normal(zeros(n), K)
y = (y - y.mean()) / y.std()
z = y.copy()
y = random.poisson(exp(z))
M = M - M.mean(0)
QS = economic_qs(K)
glmm = GLMMExpFam(y, "poisson", M, QS)
assert_allclose(glmm.lml(), -52.479557279193585)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -34.09720756737648)
def _glmm(y, lik, M, QS, verbose):
from glimix_core.glmm import GLMMExpFam, GLMMNormal
glmm = GLMMExpFam(y.ravel(), lik, M, QS)
glmm.fit(verbose=verbose)
v0 = glmm.v0
v1 = glmm.v1
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M, QS)
gnormal.fit(verbose=verbose)
scanner = ScannerWrapper(gnormal.get_fast_scanner())
return scanner, v0, v1
def test_glmmexpfam_binomial_large_ntrials():
random = RandomState(0)
n = 10
X = random.randn(n, 2)
G = random.randn(n, 100)
K = dot(G, G.T)
ntrials = random.randint(1, 100000, n)
z = dot(G, random.randn(100)) / sqrt(100)
successes = zeros(len(ntrials), int)
for i in range(len(ntrials)):
for _ in range(ntrials[i]):
successes[i] += int(z[i] + 0.1 * random.randn() > 0)
QS = economic_qs(K)
glmm = GLMMExpFam(successes, ("binomial", ntrials), X, QS)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -43.067433588125446)
def test_glmmexpfam_optimize_low_rank():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = dot(X, X.T)
z = dot(X, 0.2 * random.randn(5))
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm.lml(), -18.60476792256323, atol=ATOL, rtol=RTOL)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -7.800621320491801, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_bernoulli_probit_assure_delta_fixed():
random = RandomState(1)
N = 10
G = random.randn(N, N + 50)
y = bernoulli_sample(0.0, G, random_state=random)
G = ascontiguousarray(G, dtype=float)
_stdnorm(G, 0, out=G)
G /= sqrt(G.shape[1])
QS = economic_qs_linear(G)
S0 = QS[1]
S0 /= S0.mean()
X = ones((len(y), 1))
model = GLMMExpFam(y, "probit", X, QS=(QS[0], QS[1]))
model.fit(verbose=False)
assert_allclose(model.lml(), -6.108751595773174, rtol=RTOL)
assert_allclose(model.delta, 1.4901161193847673e-08, atol=1e-5)
assert_(model._isfixed("logitdelta"))
def _perform_glmm(y, lik, M, K, QS, G, verbose):
from glimix_core.glmm import GLMMExpFam, GLMMNormal
from pandas import Series
from xarray import DataArray
glmm = GLMMExpFam(y.ravel(), lik, M.values, QS)
glmm.fit(verbose=verbose)
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M.values, QS)
gnormal.fit(verbose=verbose)
beta = gnormal.beta
covariates = list(M.coords["covariate"].values)
ncov_effsizes = Series(beta, covariates)
flmm = gnormal.get_fast_scanner()
flmm.set_scale(1.0)
null_lml = flmm.null_lml()
if hasattr(G, "data"):
values = G.data
else:
values = G.values
alt_lmls, effsizes = flmm.fast_scan(values, verbose=verbose)
coords = {
k: ("candidate", G.coords[k].values)
for k in G.coords.keys()
if G.coords[k].dims[0] == "candidate"
}
alt_lmls = DataArray(alt_lmls, dims=["candidate"], coords=coords)
effsizes = DataArray(effsizes, dims=["candidate"], coords=coords)
return QTLModel(null_lml, alt_lmls, effsizes, ncov_effsizes)
def test_glmmexpfam_bernoulli_probit_problematic():
random = RandomState(1)
N = 30
G = random.randn(N, N + 50)
y = bernoulli_sample(0.0, G, random_state=random)
G = ascontiguousarray(G, dtype=float)
_stdnorm(G, 0, out=G)
G /= sqrt(G.shape[1])
QS = economic_qs_linear(G)
S0 = QS[1]
S0 /= S0.mean()
X = ones((len(y), 1))
model = GLMMExpFam(y, "probit", X, QS=(QS[0], QS[1]))
model.delta = 0
model.fix("delta")
model.fit(verbose=False)
assert_allclose(model.lml(), -20.725623168378615, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0.0001220703125, atol=1e-3)
assert_allclose(model.scale, 0.33022865011938707, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.002617161564786044], atol=ATOL, rtol=RTOL)
h20 = model.scale * (1 - model.delta) / (model.scale + 1)
model.unfix("delta")
model.delta = 0.5
model.scale = 1.0
model.fit(verbose=False)
assert_allclose(model.lml(), -20.725623168378522, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0.5017852859580029, atol=1e-3)
assert_allclose(model.scale, 0.9928931515372, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.003203427206253548], atol=ATOL, rtol=RTOL)
h21 = model.scale * (1 - model.delta) / (model.scale + 1)
assert_allclose(h20, h21, atol=ATOL, rtol=RTOL)
def test_glmmexpfam_poisson():
random = RandomState(1)
# sample size
n = 30
# covariates
offset = ones(n) * random.randn()
age = random.randint(16, 75, n)
M = stack((offset, age), axis=1)
# genetic variants
G = random.randn(n, 4)
# sampling the phenotype
alpha = random.randn(2)
beta = random.randn(4)
eps = random.randn(n)
y = M @ alpha + G @ beta + eps
# Whole genotype of each sample.
X = random.randn(n, 50)
# Estimate a kinship relationship between samples.
X_ = (X - X.mean(0)) / X.std(0) / sqrt(X.shape[1])
K = X_ @ X_.T + eye(n) * 0.1
# Update the phenotype
y += random.multivariate_normal(zeros(n), K)
y = (y - y.mean()) / y.std()
z = y.copy()
y = random.poisson(exp(z))
M = M - M.mean(0)
QS = economic_qs(K)
glmm = GLMMExpFam(y, "poisson", M, QS)
assert_allclose(glmm.lml(), -52.479557279193585)
glmm.fit(verbose=False)
assert_allclose(glmm.lml(), -34.09720756737648)
def _st_glmm(y, lik, M, QS, verbose):
from numpy import nan
from glimix_core.glmm import GLMMExpFam, GLMMNormal
glmm = GLMMExpFam(y, lik, M, QS)
glmm.fit(verbose=verbose)
if QS is None:
v0 = nan
else:
v0 = glmm.v0
v1 = glmm.v1
sys.stdout.flush()
eta = glmm.site.eta
tau = glmm.site.tau
gnormal = GLMMNormal(eta, tau, M, QS)
gnormal.fit(verbose=verbose)
return gnormal.get_fast_scanner(), v0, v1
def test_glmmexpfam_bernoulli_problematic():
random = RandomState(1)
N = 30
G = random.randn(N, N + 50)
y = bernoulli_sample(0.0, G, random_state=random)
G = ascontiguousarray(G, dtype=float)
_stdnorm(G, 0, out=G)
G /= sqrt(G.shape[1])
QS = economic_qs_linear(G)
S0 = QS[1]
S0 /= S0.mean()
X = ones((len(y), 1))
model = GLMMExpFam(y, "bernoulli", X, QS=(QS[0], QS[1]))
model.delta = 0
model.fix("delta")
model.fit(verbose=False)
assert_allclose(model.lml(), -20.727007958026853, atol=ATOL, rtol=RTOL)
assert_allclose(model.delta, 0, atol=1e-3)
assert_allclose(model.scale, 0.879915823030081, atol=ATOL, rtol=RTOL)
assert_allclose(model.beta, [-0.00247856564728], atol=ATOL, rtol=RTOL)
def test_glmmexpfam_copy():
nsamples = 10
random = RandomState(0)
X = random.randn(nsamples, 5)
K = linear_eye_cov().value()
z = random.multivariate_normal(0.2 * ones(nsamples), K)
QS = economic_qs(K)
ntri = random.randint(1, 30, nsamples)
nsuc = zeros(nsamples, dtype=int)
for (i, ni) in enumerate(ntri):
nsuc[i] += sum(z[i] + 0.2 * random.randn(ni) > 0)
ntri = ascontiguousarray(ntri)
glmm0 = GLMMExpFam(nsuc, ("binomial", ntri), X, QS)
assert_allclose(glmm0.lml(), -29.10216812909928, atol=ATOL, rtol=RTOL)
glmm0.fit(verbose=False)
v = -19.575736562427252
assert_allclose(glmm0.lml(), v)
glmm1 = glmm0.copy()
assert_allclose(glmm1.lml(), v)
glmm1.scale = 0.92
assert_allclose(glmm0.lml(), v, atol=ATOL, rtol=RTOL)
assert_allclose(glmm1.lml(), -30.832831740038056, atol=ATOL, rtol=RTOL)
glmm0.fit(verbose=False)
glmm1.fit(verbose=False)
v = -19.575736562378573
assert_allclose(glmm0.lml(), v)
assert_allclose(glmm1.lml(), v)
import numpy as np
import numpy_sugar as ns
from glimix_core.glmm import GLMMExpFam
from time import time
G = np.load('null_G.npy')
ntri = np.load('null_ntri.npy')
nsuc = np.load('null_nsuc.npy')
N, P = G.shape
QS = ns.linalg.economic_qs(G.dot(G.T))
X = np.ones((N, 1))
ntri = np.asarray(ntri, float)
nsuc = np.asarray(nsuc, float)
start = time()
glmm = GLMMExpFam((nsuc, ntri), "binomial", X, QS)
glmm.fit(verbose=True)
stop = time()
elapsed = stop - start
print("Elapsed: {}".format(elapsed))
np.save("out/fastglmm_N{}".format(N), elapsed)