def find_latent_gaussian(bin_means, bin_cov, accuracy=1e-10):
"""
Compute parameters for the hidden Gaussian random vector U generating the
binary Bernulli vector X with mean m and covariances c according to
X = 0 <=> U < -g
X = 1 <=> U > -g
Adapted from `<www.kyb.mpg.de/bethgegroup/code/efficientsampling>`_
Parameters
----------
bin_means : Type
Description
bin_cov : Type
Description
accuracy : int, optional
Description (default 1e-10)
Returns
-------
Value : Type
Description
"""
from statsmodels.sandbox.distributions.multivariate import mvstdnormcdf
if np.any(bin_means < 0) or np.any(bin_means >= 1):
raise Exception("Mean for Gaussians has to be between 0 and 1!")
d = len(bin_means)
gauss_mean = np.array([ltqnorm(m) for m in bin_means])
gauss_cov = np.eye(d)
for i in range(d):
for j in range(i + 1, d):
c_min = -1
c_max = 1
# constant
pn = bin_means[[i, j]].prod()
# check whether DG distribution for covariance exists
if (bin_cov[i, j] - mvstdnormcdf(-gauss_mean[[i, j]], np.array([np.inf, np.inf]), -1) + pn) < -1e-3 or \
(bin_cov[i, j] - mvstdnormcdf(-gauss_mean[[i, j]], np.array([np.inf, np.inf]), 1) + pn) > 1e-3:
raise Exception(
'A joint Bernoulli distribution with the given covariance matrix does not exist!'
)
# determine Lambda_ij iteratively by bisection (Psi is monotonous in rho)
while c_max - c_min > accuracy:
c_new = (c_max + c_min) / 2.
if bin_cov[i, j] > mvstdnormcdf(-gauss_mean[[i, j]],
np.array([np.inf, np.inf]),
c_new) - pn:
c_min = c_new
else:
c_max = c_new
gauss_cov[i, j] = gauss_cov[j, i] = c_max
return gauss_mean.reshape(len(bin_means), 1), gauss_cov
def find_latent_gaussian(bin_means, bin_cov, accuracy=1e-10):
"""
Compute parameters for the hidden Gaussian random vector U generating the
binary Bernulli vector X with mean m and covariances c according to
X = 0 <=> U < -g
X = 1 <=> U > -g
Adapted from `<www.kyb.mpg.de/bethgegroup/code/efficientsampling>`_
Parameters
----------
bin_means : Type
Description
bin_cov : Type
Description
accuracy : int, optional
Description (default 1e-10)
Returns
-------
Value : Type
Description
"""
from statsmodels.sandbox.distributions.multivariate import mvstdnormcdf
if np.any(bin_means < 0) or np.any(bin_means >= 1):
raise Exception("Mean for Gaussians has to be between 0 and 1!")
d = len(bin_means)
gauss_mean = np.array([ltqnorm(m) for m in bin_means])
gauss_cov = np.eye(d)
for i in range(d):
for j in range(i + 1, d):
c_min = -1
c_max = 1
# constant
pn = bin_means[[i, j]].prod()
# check whether DG distribution for covariance exists
if (bin_cov[i, j] - mvstdnormcdf(-gauss_mean[[i, j]], np.array([np.inf, np.inf]), -1) + pn) < -1e-3 or \
(bin_cov[i, j] - mvstdnormcdf(-gauss_mean[[i, j]], np.array([np.inf, np.inf]), 1) + pn) > 1e-3:
raise Exception('A joint Bernoulli distribution with the given covariance matrix does not exist!')
# determine Lambda_ij iteratively by bisection (Psi is monotonous in rho)
while c_max - c_min > accuracy:
c_new = (c_max + c_min) / 2.
if bin_cov[i, j] > mvstdnormcdf(-gauss_mean[[i, j]], np.array([np.inf, np.inf]), c_new) - pn:
c_min = c_new
else:
c_max = c_new
gauss_cov[i, j] = gauss_cov[j, i] = c_max
return gauss_mean.reshape(len(bin_means), 1), gauss_cov
def test_mvn_mvt_1(self):
a, b = self.a, self.b
df = self.df
corr_equal = self.corr_equal
#result from R, mvtnorm with option
#algorithm = GenzBretz(maxpts = 100000, abseps = 0.000001, releps = 0)
# or higher
probmvt_R = 0.60414 #report, ed error approx. 7.5e-06
probmvn_R = 0.673970 #reported error approx. 6.4e-07
assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr_equal, df), 4)
assert_almost_equal(probmvn_R,
mvstdnormcdf(a, b, corr_equal, abseps=1e-5), 4)
mvn_high = mvstdnormcdf(a, b, corr_equal, abseps=1e-8, maxpts=10000000)
assert_almost_equal(probmvn_R, mvn_high, 5)
def test_mvn_mvt_1(self):
a, b = self.a, self.b
df = self.df
corr_equal = self.corr_equal
#result from R, mvtnorm with option
#algorithm = GenzBretz(maxpts = 100000, abseps = 0.000001, releps = 0)
# or higher
probmvt_R = 0.60414 #report, ed error approx. 7.5e-06
probmvn_R = 0.673970 #reported error approx. 6.4e-07
assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr_equal, df), 4)
assert_almost_equal(probmvn_R,
mvstdnormcdf(a, b, corr_equal, abseps=1e-5), 4)
mvn_high = mvstdnormcdf(a, b, corr_equal, abseps=1e-8, maxpts=10000000)
assert_almost_equal(probmvn_R, mvn_high, 5)
def test_mvn_mvt_2(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
probmvn_R = 0.6472497 #reported error approx. 7.7e-08
probmvt_R = 0.5881863 #highest reported error up to approx. 1.99e-06
assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr2, df), 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a, b, corr2, abseps=1e-5), 4)
def test_mvn_mvt_2(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
probmvn_R = 0.6472497 #reported error approx. 7.7e-08
probmvt_R = 0.5881863 #highest reported error up to approx. 1.99e-06
assert_almost_equal(probmvt_R, mvstdtprob(a, b, corr2, df), 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a, b, corr2, abseps=1e-5), 4)
def test_mvn_mvt_5(self):
a, bl = self.a, self.b
df = self.df
corr2 = self.corr2
#unequal integration bounds
#print "ue"
a3 = np.array([0.5, -0.5, 0.5])
probmvn_R = 0.06910487 #using higher precision in R, error approx. 3.5e-08
probmvt_R = 0.05797867 #using higher precision in R, error approx. 5.8e-08
assert_almost_equal(mvstdtprob(a3, a3+1, corr2, df), probmvt_R, 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a3, a3+1, corr2,
maxpts=100000, abseps=1e-5), 4)
def test_mvn_mvt_5(self):
a, bl = self.a, self.b
df = self.df
corr2 = self.corr2
#unequal integration bounds
#print "ue"
a3 = np.array([0.5, -0.5, 0.5])
probmvn_R = 0.06910487 #using higher precision in R, error approx. 3.5e-08
probmvt_R = 0.05797867 #using higher precision in R, error approx. 5.8e-08
assert_almost_equal(mvstdtprob(a3, a3+1, corr2, df), probmvt_R, 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a3, a3+1, corr2,
maxpts=100000, abseps=1e-5), 4)
def test_mvn_mvt_3(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
#from -inf
#print 'from -inf'
a2 = a.copy()
a2[:] = -np.inf
probmvn_R = 0.9961141 #using higher precision in R, error approx. 6.866163e-07
probmvt_R = 0.9522146 #using higher precision in R, error approx. 1.6e-07
assert_almost_equal(probmvt_R, mvstdtprob(a2, b, corr2, df), 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a2, b, corr2, maxpts=100000,
abseps=1e-5), 4)
def test_mvn_mvt_3(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
#from -inf
#print 'from -inf'
a2 = a.copy()
a2[:] = -np.inf
probmvn_R = 0.9961141 #using higher precision in R, error approx. 6.866163e-07
probmvt_R = 0.9522146 #using higher precision in R, error approx. 1.6e-07
assert_almost_equal(probmvt_R, mvstdtprob(a2, b, corr2, df), 4)
assert_almost_equal(probmvn_R, mvstdnormcdf(a2, b, corr2, maxpts=100000,
abseps=1e-5), 4)
def test_mvn_mvt_4(self):
a, bl = self.a, self.b
df = self.df
corr2 = self.corr2
#from 0 to inf
#print '0 inf'
a2 = a.copy()
a2[:] = -np.inf
probmvn_R = 0.1666667 #error approx. 6.1e-08
probmvt_R = 0.1666667 #error approx. 8.2e-08
assert_almost_equal(probmvt_R, mvstdtprob(np.zeros(3), -a2, corr2, df), 4)
assert_almost_equal(probmvn_R,
mvstdnormcdf(np.zeros(3), -a2, corr2,
maxpts=100000, abseps=1e-5), 4)
def test_mvn_mvt_4(self):
a, bl = self.a, self.b
df = self.df
corr2 = self.corr2
#from 0 to inf
#print '0 inf'
a2 = a.copy()
a2[:] = -np.inf
probmvn_R = 0.1666667 #error approx. 6.1e-08
probmvt_R = 0.1666667 #error approx. 8.2e-08
assert_almost_equal(probmvt_R, mvstdtprob(np.zeros(3), -a2, corr2, df), 4)
assert_almost_equal(probmvn_R,
mvstdnormcdf(np.zeros(3), -a2, corr2,
maxpts=100000, abseps=1e-5), 4)
def test_mvn_mvt_3(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
a2 = a.copy()
a2[:] = -np.inf
# using higher precision in R, error approx. 6.866163e-07
probmvn_R = 0.9961141
# using higher precision in R, error approx. 1.6e-07
probmvt_R = 0.9522146
quadkwds = {'epsabs': 1e-08}
probmvt = mvstdtprob(a2, b, corr2, df, quadkwds=quadkwds)
assert_allclose(probmvt_R, probmvt, atol=5e-4)
probmvn = mvstdnormcdf(a2, b, corr2, maxpts=100000, abseps=1e-5)
assert_allclose(probmvn_R, probmvn, atol=1e-4)
def test_mvn_mvt_3(self):
a, b = self.a, self.b
df = self.df
corr2 = self.corr2
a2 = a.copy()
a2[:] = -np.inf
# using higher precision in R, error approx. 6.866163e-07
probmvn_R = 0.9961141
# using higher precision in R, error approx. 1.6e-07
probmvt_R = 0.9522146
quadkwds = {'epsabs': 1e-08}
probmvt = mvstdtprob(a2, b, corr2, df, quadkwds=quadkwds)
assert_allclose(probmvt_R, probmvt, atol=5e-4)
probmvn = mvstdnormcdf(a2, b, corr2, maxpts=100000, abseps=1e-5)
assert_allclose(probmvn_R, probmvn, atol=1e-4)