def test_log_marg_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
X_1 = 5 * np.random.rand(N_1, D) - 1
# Prior
var = 10 * np.random.rand(D)
mu_0 = 5 * np.random.rand(D) - 2
var_0 = 2 * np.random.rand(D)
prior = FixedVarPrior(var, mu_0, var_0)
precision = 1. / var
precision_0 = 1. / var_0
# Setup GMM
assignments = np.concatenate([np.zeros(N_1)])
gmm = GaussianComponentsFixedVar(X_1, prior, assignments=assignments)
# Calculate marginal for component by hand
expected_log_marg = np.sum(
np.log([
np.sqrt(var[i]) / (np.sqrt(2 * np.pi * var[i])**N_1 *
np.sqrt(N_1 * var_0[i] + var[i])) *
np.exp(-0.5 * np.square(X_1).sum(axis=0)[i] / var[i] - mu_0[i]**2 /
(2 * var_0[i])) * np.exp(
(var_0[i] * N_1**2 * X_1.mean(axis=0)[i]**2 / var[i] +
var[i] * mu_0[i]**2 / var_0[i] +
2 * N_1 * X_1.mean(axis=0)[i] * mu_0[i]) /
(2. * (N_1 * var_0[i] + var[i]))) for i in range(D)
]))
npt.assert_almost_equal(gmm.log_marg_k(0), expected_log_marg)
def test_log_prod_norm():
np.random.seed(1)
# Prior
D = 10
var = 1 * np.random.rand(D)
mu_0 = 5 * np.random.rand(D) - 2
var_0 = 2 * np.random.rand(D)
prior = FixedVarPrior(var, mu_0, var_0)
# GMM will be used to access `_log_prod_norm`
x = 3 * np.random.rand(D) + 4
gmm = GaussianComponentsFixedVar(np.array([x]), prior)
expected_prior = np.sum(
[log_norm_pdf(x[i], mu_0[i], var_0[i]) for i in range(len(x))])
npt.assert_almost_equal(gmm.log_prior(0), expected_prior)