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_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_post_pred_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
N_2 = 5
N_3 = 5
X = 5*np.random.rand(N_1 + N_2 + N_3, D) - 1
X_1 = X[:N_1]
X_2 = X[N_1:N_1 + N_2]
X_3 = X[N_1 + N_2:]
# Prior
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)
precision = 1./var
precision_0 = 1./var_0
# Setup GMM
assignments = np.concatenate([np.zeros(N_1), np.ones(N_2), 2*np.ones(N_3)])
gmm = GaussianComponentsFixedVar(X, prior, assignments=assignments)
# Remove everything from component 2 (additional check)
for i in range(N_1, N_1 + N_2):
gmm.del_item(i)
# Calculate posterior for first component by hand
x_1 = X_1[0]
precision_N_1 = precision_0 + N_1*precision
mu_N_1 = (mu_0 * precision_0 + precision*N_1*X_1.mean(axis=0)) / precision_N_1
precision_pred = 1./(1./precision_N_1 + 1./precision)
expected_posterior = np.sum(
[log_norm_pdf(x_1[i], mu_N_1[i], 1./precision_pred[i]) for i in range(len(x_1))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
# Calculate posterior for second component by hand
x_3 = X_3[0]
precision_N_3 = precision_0 + N_3*precision
mu_N_3 = (mu_0 * precision_0 + precision*N_3*X_3.mean(axis=0)) / precision_N_3
precision_pred = 1./(1./precision_N_3 + 1./precision)
expected_posterior = np.sum(
[log_norm_pdf(x_3[i], mu_N_3[i], 1./precision_pred[i]) for i in range(len(x_3))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(N_1 + N_2, 1), expected_posterior)
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)
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)
def test_log_post_pred():
np.random.seed(1)
# Generate data
X = np.random.rand(11, 10)
N, D = X.shape
# Prior
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)
# Setup GMM
assignments = [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1]
gmm = GaussianComponentsFixedVar(X, prior, assignments=assignments)
expected_log_post_pred = log_post_pred_unvectorized(gmm, 10)
npt.assert_almost_equal(gmm.log_post_pred(10), expected_log_post_pred)
def test_log_post_pred():
np.random.seed(1)
# Generate data
X = np.random.rand(11, 10)
N, D = X.shape
# Prior
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)
# Setup GMM
assignments = [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1]
gmm = GaussianComponentsFixedVar(X, prior, assignments=assignments)
expected_log_post_pred = log_post_pred_unvectorized(gmm, 10)
npt.assert_almost_equal(gmm.log_post_pred(10), expected_log_post_pred)
def test_log_post_pred_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
N_2 = 5
N_3 = 5
X = 5 * np.random.rand(N_1 + N_2 + N_3, D) - 1
X_1 = X[:N_1]
X_2 = X[N_1:N_1 + N_2]
X_3 = X[N_1 + N_2:]
# Prior
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)
precision = 1. / var
precision_0 = 1. / var_0
# Setup GMM
assignments = np.concatenate(
[np.zeros(N_1), np.ones(N_2), 2 * np.ones(N_3)])
gmm = GaussianComponentsFixedVar(X, prior, assignments=assignments)
# Remove everything from component 2 (additional check)
for i in range(N_1, N_1 + N_2):
gmm.del_item(i)
# Calculate posterior for first component by hand
x_1 = X_1[0]
precision_N_1 = precision_0 + N_1 * precision
mu_N_1 = (mu_0 * precision_0 +
precision * N_1 * X_1.mean(axis=0)) / precision_N_1
precision_pred = 1. / (1. / precision_N_1 + 1. / precision)
expected_posterior = np.sum([
log_norm_pdf(x_1[i], mu_N_1[i], 1. / precision_pred[i])
for i in range(len(x_1))
])
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
# Calculate posterior for second component by hand
x_3 = X_3[0]
precision_N_3 = precision_0 + N_3 * precision
mu_N_3 = (mu_0 * precision_0 +
precision * N_3 * X_3.mean(axis=0)) / precision_N_3
precision_pred = 1. / (1. / precision_N_3 + 1. / precision)
expected_posterior = np.sum([
log_norm_pdf(x_3[i], mu_N_3[i], 1. / precision_pred[i])
for i in range(len(x_3))
])
npt.assert_almost_equal(gmm.log_post_pred_k(N_1 + N_2, 1),
expected_posterior)