def test_logitnormal_moments(self):
# global parameters for computing lognormals
gh_loc, gh_weights = hermgauss(4)
# log normal parameters
lognorm_means = np.random.random((5, 3)) # should work for arrays now
lognorm_infos = np.random.random((5, 3))**2 + 1
alpha = 2 # dp parameter
# draw samples
num_draws = 10**5
samples = np.random.normal(lognorm_means,
1/np.sqrt(lognorm_infos), size = (num_draws, 5, 3))
logit_norm_samples = sp.special.expit(samples)
# test lognormal means
np_test.assert_allclose(
np.mean(logit_norm_samples, axis = 0),
ef.get_e_logitnormal(
lognorm_means, lognorm_infos, gh_loc, gh_weights),
atol = 3 * np.std(logit_norm_samples) / np.sqrt(num_draws))
# test Elog(x) and Elog(1-x)
log_logistic_norm = np.mean(np.log(logit_norm_samples), axis = 0)
log_1m_logistic_norm = np.mean(np.log(1 - logit_norm_samples), axis = 0)
tol1 = 3 * np.std(np.log(logit_norm_samples))/ np.sqrt(num_draws)
tol2 = 3 * np.std(np.log(1 - logit_norm_samples))/ np.sqrt(num_draws)
np_test.assert_allclose(
log_logistic_norm,
ef.get_e_log_logitnormal(
lognorm_means, lognorm_infos, gh_loc, gh_weights)[0],
atol = tol1)
np_test.assert_allclose(
log_1m_logistic_norm,
ef.get_e_log_logitnormal(
lognorm_means, lognorm_infos, gh_loc, gh_weights)[1],
atol = tol2)
# test prior
prior_samples = np.mean((alpha - 1) *
np.log(1 - logit_norm_samples), axis = 0)
tol3 = 3 * np.std((alpha - 1) * np.log(1 - logit_norm_samples)) \
/np.sqrt(num_draws)
np_test.assert_allclose(
prior_samples,
ef.get_e_dp_prior_logitnorm_approx(
alpha, lognorm_means, lognorm_infos, gh_loc, gh_weights),
atol = tol3)
x = np.random.normal(0, 1e2, size = 10)
def e_log_v(x):
return np.sum(ef.get_e_log_logitnormal(\
x[0:5], np.abs(x[5:10]), gh_loc, gh_weights)[0])
check_grads(e_log_v, order=2)(x)
def get_e_cluster_probabilities(stick_propn_mean, stick_propn_info,
gh_loc, gh_weights):
e_stick_lengths = \
ef.get_e_logitnormal(stick_propn_mean, stick_propn_info, gh_loc, gh_weights)
return get_mixture_weights_from_stick_break_propns(e_stick_lengths)
