def test_bernoulli_optimize():
random = RandomState(139)
nsamples = 100
nfeatures = nsamples + 10
G = random.randn(nsamples, nfeatures) / sqrt(nfeatures)
M = ones((nsamples, 1))
u = random.randn(nfeatures)
z = 0.1 + dot(G, u) + 0.5 * random.randn(nsamples)
y = empty(nsamples)
y[z > 0] = 1
y[z <= 0] = 0
(Q, S0) = economic_qs_linear(G)
lik = BernoulliProdLik(LogitLink())
lik.outcome = y
ep = ExpFamEP(lik, M, Q[0], Q[1], S0)
ep.learn(progress=False)
assert_allclose(ep.lml(), -67.67727582268618, rtol=1e-5)
assert_allclose(ep.heritability, 0.6243068813130619, rtol=1e-5)
assert_allclose(ep.beta[0], -0.2561108097463372, rtol=1e-5)
def test_binomial_optimize():
random = RandomState(139)
nsamples = 30
nfeatures = 31
G = random.randn(nsamples, nfeatures) / sqrt(nfeatures)
u = random.randn(nfeatures)
z = 0.1 + 2 * dot(G, u) + random.randn(nsamples)
ntrials = random.randint(10, 500, size=nsamples)
y = zeros(nsamples)
for i in range(len(ntrials)):
y[i] = sum(
z[i] + random.logistic(scale=pi / sqrt(3), size=ntrials[i]) > 0)
(Q, S0) = economic_qs_linear(G)
M = ones((nsamples, 1))
lik = BinomialProdLik(ntrials, LogitLink())
lik.nsuccesses = y
ep = ExpFamEP(lik, M, Q[0], Q[1], S0)
ep.learn(progress=False)
assert_allclose(ep.lml(), -144.2381842202486, rtol=1e-3)
def test_binomial_gradient_over_delta():
n = 3
M = ones((n, 1)) * 1.
G = array([[1.2, 3.4], [-.1, 1.2], [0.0, .2]])
(Q, S0) = economic_qs_linear(G)
nsuccesses = array([1., 0., 1.])
ntrials = array([1., 1., 1.])
lik = BinomialProdLik(ntrials, LogitLink())
lik.nsuccesses = nsuccesses
ep = ExpFamEP(lik, M, Q[0], Q[1], S0 + 1.0)
ep.beta = array([1.])
assert_allclose(ep.beta, array([1.]))
ep.v = 1.
ep.delta = 0.5
analytical_gradient = ep._gradient_over_delta()
lml0 = ep.lml()
step = 1e-5
ep.delta = ep.delta + step
lml1 = ep.lml()
empirical_gradient = (lml1 - lml0) / step
assert_allclose(empirical_gradient, analytical_gradient, rtol=1e-4)
def test_binomial_lml():
n = 3
M = ones((n, 1)) * 1.
G = array([[1.2, 3.4], [-.1, 1.2], [0.0, .2]])
(Q, S0) = economic_qs_linear(G)
nsuccesses = array([1., 0., 1.])
ntrials = array([1., 1., 1.])
lik = BinomialProdLik(ntrials, LogitLink())
lik.nsuccesses = nsuccesses
ep = ExpFamEP(lik, M, Q[0], Q[1], S0 + 1)
ep.beta = array([1.])
assert_allclose(ep.beta, array([1.]))
ep.v = 1.
ep.delta = 0
assert_allclose(ep.lml(), -2.3202659215368935)
def test_bernoulli_lml():
n = 3
M = ones((n, 1)) * 1.
G = array([[1.2, 3.4], [-.1, 1.2], [0.0, .2]])
(Q, S0) = economic_qs_linear(G)
y = array([1., 0., 1.])
lik = BernoulliProdLik(LogitLink())
lik.outcome = y
ep = ExpFamEP(lik, M, Q[0], Q[1], S0 + 1.0)
ep.beta = array([1.])
assert_almost_equal(ep.beta, array([1.]))
ep.v = 1.
ep.delta = 0.
assert_almost_equal(ep.lml(), -2.3202659215368935)
assert_almost_equal(ep.sigma2_epsilon, 0)
assert_almost_equal(ep.sigma2_b, 1)
def test_binomial_extreme():
import numpy as np
import os
dir_path = os.path.dirname(os.path.realpath(__file__))
data = np.load(os.path.join(dir_path, 'data', 'extreme.npz'))
from limix_inference.glmm import ExpFamEP
from limix_inference.lik import BinomialProdLik
from limix_inference.link import LogitLink
link = LogitLink()
lik = BinomialProdLik(data['ntrials'], link)
lik.nsuccesses = data['nsuccesses']
ep = ExpFamEP(lik,
data['covariates'],
Q0=data['Q0'],
Q1=data['Q1'],
S0=data['S0'])
ep.learn(progress=False)
assert_allclose(ep.lml(), -627.8816497398326, rtol=1e-3)
def test_GLMMSampler_binomial():
random = RandomState(4503)
X = random.randn(10, 15)
link = LogitLink()
lik = BinomialLik(5, link)
mean = OffsetMean()
mean.offset = 1.2
mean.set_data(10, 'sample')
cov = LinearCov()
cov.set_data((X, X), 'sample')
sampler = GLMMSampler(lik, mean, cov)
assert_equal(sampler.sample(random), [0, 5, 0, 5, 1, 1, 5, 0, 5, 5])
mean.offset = 0.
assert_equal(sampler.sample(random), [5, 4, 1, 0, 0, 1, 4, 5, 5, 0])
mean = OffsetMean()
mean.offset = 0.0
mean.set_data(10, 'sample')
cov1 = LinearCov()
cov1.set_data((X, X), 'sample')
cov2 = EyeCov()
a = arange(10)
cov2.set_data((a, a), 'sample')
cov1.scale = 1e-4
cov2.scale = 1e-4
cov = SumCov([cov1, cov2])
lik = BinomialLik(100, link)
sampler = GLMMSampler(lik, mean, cov)
assert_equal(
sampler.sample(random), [56, 56, 55, 51, 59, 45, 47, 43, 51, 38])
cov2.scale = 100.
sampler = GLMMSampler(lik, mean, cov)
assert_equal(
sampler.sample(random), [99, 93, 99, 75, 77, 0, 0, 100, 99, 12])
def test_binomial_get_normal_likelihood_trick():
random = RandomState(139)
nsamples = 30
nfeatures = 31
G = random.randn(nsamples, nfeatures) / sqrt(nfeatures)
u = random.randn(nfeatures)
z = 0.1 + 2 * dot(G, u) + random.randn(nsamples)
ntrials = random.randint(10, 500, size=nsamples)
y = zeros(nsamples)
for i in range(len(ntrials)):
y[i] = sum(
z[i] + random.logistic(scale=pi / sqrt(3), size=ntrials[i]) > 0)
(Q, S0) = economic_qs_linear(G)
M = ones((nsamples, 1))
lik = BinomialProdLik(ntrials, LogitLink())
lik.nsuccesses = y
ep = ExpFamEP(lik, M, Q[0], Q[1], S0)
ep.learn(progress=False)
nlt = ep.get_normal_likelihood_trick()
assert_allclose(nlt.fast_scan(G)[0], [
-143.48903288, -144.32031587, -144.03889888, -144.31806561,
-143.90248659, -144.303103, -144.47854112, -144.44469341, -144.285027,
-144.31240175, -143.11590263, -142.81623878, -141.67554141,
-144.4780024, -144.47780285, -144.10317082, -142.10043322,
-143.0813298, -143.99841663, -143.345783, -144.45458683, -144.37877612,
-142.56846859, -144.32923028, -144.44116855, -144.45082936,
-144.40932741, -143.0212886, -144.47902176, -143.94188634,
-143.72765373
],
rtol=1e-5)
def test_bernoulli_gradient_over_v():
n = 3
M = ones((n, 1)) * 1.
G = array([[1.2, 3.4], [-.1, 1.2], [0.0, .2]])
(Q, S0) = economic_qs_linear(G)
y = array([1., 0., 1.])
lik = BernoulliProdLik(LogitLink())
lik.outcome = y
ep = ExpFamEP(lik, M, Q[0], Q[1], S0 + 1.0)
ep.beta = array([1.])
assert_almost_equal(ep.beta, array([1.]))
ep.v = 1.
ep.delta = 0.
analytical_gradient = ep._gradient_over_v()
lml0 = ep.lml()
step = 1e-5
ep.v = ep.v + step
lml1 = ep.lml()
empirical_gradient = (lml1 - lml0) / step
assert_almost_equal(empirical_gradient, analytical_gradient, decimal=4)
def test_binomial_sampler():
random = RandomState(4503)
link = LogitLink()
binom = BinomialLik(12, link)
assert_equal(binom.sample(0, random), 7)