def test_3component_with_delete_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
m_0 = 5 * np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2 * np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Setup GMM
assignments = np.concatenate(
[np.zeros(N_1), np.ones(N_2), 2 * np.ones(N_3)])
gmm = GaussianComponentsDiag(X, prior, assignments=assignments)
# Remove everything from component 2
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]
k_N = k_0 + N_1
v_N = v_0 + N_1
m_N = (k_0 * m_0 + N_1 * X_1.mean(axis=0)) / k_N
S_N = S_0 + np.square(X_1).sum(
axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x_1[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
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_1 = X_3[0]
k_N = k_0 + N_3
v_N = v_0 + N_3
m_N = (k_0 * m_0 + N_3 * X_3.mean(axis=0)) / k_N
S_N = S_0 + np.square(X_3).sum(
axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x_1[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
for i in range(len(x_1))
])
npt.assert_almost_equal(gmm.log_post_pred_k(N_1 + N_2, 1),
expected_posterior)
def test_2component_post_pred_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
N_2 = 5
X = 5 * np.random.rand(N_1 + N_2, D) - 1
X_1 = X[:N_1]
X_2 = X[N_1:]
# Prior
m_0 = 5 * np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2 * np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Setup GMM
assignments = np.concatenate([np.zeros(N_1), np.ones(N_2)])
gmm = GaussianComponentsDiag(X, prior, assignments=assignments)
# Remove one item (as additional check)
gmm.del_item(N_1 + N_2 - 1)
X_2 = X_2[:-1]
N_2 -= 1
# Calculate posterior for first component by hand
x_1 = X_1[0]
k_N = k_0 + N_1
v_N = v_0 + N_1
m_N = (k_0 * m_0 + N_1 * X_1.mean(axis=0)) / k_N
S_N = S_0 + np.square(X_1).sum(
axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x_1[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
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_1 = X_2[0]
k_N = k_0 + N_2
v_N = v_0 + N_2
m_N = (k_0 * m_0 + N_2 * X_2.mean(axis=0)) / k_N
S_N = S_0 + np.square(X_2).sum(
axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x_1[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
for i in range(len(x_1))
])
npt.assert_almost_equal(gmm.log_post_pred_k(N_1, 1), expected_posterior)
def test_3component_with_delete_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
m_0 = 5*np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2*np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Setup GMM
assignments = np.concatenate([np.zeros(N_1), np.ones(N_2), 2*np.ones(N_3)])
gmm = GaussianComponentsDiag(X, prior, assignments=assignments)
# Remove everything from component 2
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]
k_N = k_0 + N_1
v_N = v_0 + N_1
m_N = (k_0*m_0 + N_1*X_1.mean(axis=0))/k_N
S_N = S_0 + np.square(X_1).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x_1[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) 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_1 = X_3[0]
k_N = k_0 + N_3
v_N = v_0 + N_3
m_N = (k_0*m_0 + N_3*X_3.mean(axis=0))/k_N
S_N = S_0 + np.square(X_3).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x_1[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) for i in range(len(x_1))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(N_1 + N_2, 1), expected_posterior)
def test_2component_post_pred_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
N_2 = 5
X = 5*np.random.rand(N_1 + N_2, D) - 1
X_1 = X[:N_1]
X_2 = X[N_1:]
# Prior
m_0 = 5*np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2*np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Setup GMM
assignments = np.concatenate([np.zeros(N_1), np.ones(N_2)])
gmm = GaussianComponentsDiag(X, prior, assignments=assignments)
# Remove one item (as additional check)
gmm.del_item(N_1 + N_2 - 1)
X_2 = X_2[:-1]
N_2 -= 1
# Calculate posterior for first component by hand
x_1 = X_1[0]
k_N = k_0 + N_1
v_N = v_0 + N_1
m_N = (k_0*m_0 + N_1*X_1.mean(axis=0))/k_N
S_N = S_0 + np.square(X_1).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x_1[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) 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_1 = X_2[0]
k_N = k_0 + N_2
v_N = v_0 + N_2
m_N = (k_0*m_0 + N_2*X_2.mean(axis=0))/k_N
S_N = S_0 + np.square(X_2).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x_1[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) for i in range(len(x_1))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(N_1, 1), expected_posterior)
def test_log_post_pred_k():
np.random.seed(1)
# Prior
D = 10
m_0 = 5 * np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2 * np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Data
N = 12
X = 5 * np.random.rand(N, D) - 1
# Setup GMM
gmm = GaussianComponentsDiag(X, prior)
for i in range(N):
gmm.add_item(i, 0)
# Calculate posterior by hand
x = X[0]
k_N = k_0 + N
v_N = v_0 + N
m_N = (k_0 * m_0 + N * X[:N].mean(axis=0)) / k_N
S_N = S_0 + np.square(
X[:N]).sum(axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
for i in range(len(x))
])
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
def test_log_post_pred_k():
np.random.seed(1)
# Prior
D = 10
m_0 = 5*np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2*np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Data
N = 12
X = 5*np.random.rand(N, D) - 1
# Setup GMM
gmm = GaussianComponentsDiag(X, prior)
for i in range(N):
gmm.add_item(i, 0)
# Calculate posterior by hand
x = X[0]
k_N = k_0 + N
v_N = v_0 + N
m_N = (k_0*m_0 + N*X[:N].mean(axis=0))/k_N
S_N = S_0 + np.square(X[:N]).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) for i in range(len(x))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
def test_del_item():
np.random.seed(1)
# Prior
D = 10
m_0 = 5 * np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2 * np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Data
N = 12
X = 5 * np.random.rand(N, D) - 1
# Setup GMM
gmm = GaussianComponentsDiag(X, prior)
for i in range(N):
gmm.add_item(i, 0)
# Remove 5 random items
del_items = set(np.random.randint(1, N, size=5))
for i in del_items:
gmm.del_item(i)
indices = list(set(range(N)).difference(del_items))
# Calculate posterior by hand
X = X[indices]
N, _ = X.shape
x = X[0]
k_N = k_0 + N
v_N = v_0 + N
m_N = (k_0 * m_0 + N * X[:N].mean(axis=0)) / k_N
S_N = S_0 + np.square(
X[:N]).sum(axis=0) + k_0 * np.square(m_0) - k_N * np.square(m_N)
var = S_N * (k_N + 1) / (k_N * v_N)
expected_posterior = np.sum([
students_t(x[i], m_N[i], S_N[i] * (k_N + 1) / (k_N * v_N), v_N)
for i in range(len(x))
])
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
def test_del_item():
np.random.seed(1)
# Prior
D = 10
m_0 = 5*np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2*np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# Data
N = 12
X = 5*np.random.rand(N, D) - 1
# Setup GMM
gmm = GaussianComponentsDiag(X, prior)
for i in range(N):
gmm.add_item(i, 0)
# Remove 5 random items
del_items = set(np.random.randint(1, N, size=5))
for i in del_items:
gmm.del_item(i)
indices = list(set(range(N)).difference(del_items))
# Calculate posterior by hand
X = X[indices]
N, _ = X.shape
x = X[0]
k_N = k_0 + N
v_N = v_0 + N
m_N = (k_0*m_0 + N*X[:N].mean(axis=0))/k_N
S_N = S_0 + np.square(X[:N]).sum(axis=0) + k_0*np.square(m_0) - k_N*np.square(m_N)
var = S_N*(k_N + 1)/(k_N*v_N)
expected_posterior = np.sum(
[students_t(x[i], m_N[i], S_N[i]*(k_N + 1)/(k_N*v_N), v_N) for i in range(len(x))]
)
npt.assert_almost_equal(gmm.log_post_pred_k(0, 0), expected_posterior)
def test_log_prod_students_t():
np.random.seed(1)
# Prior
D = 10
m_0 = 5*np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2*np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# GMM we will use to access `_log_prod_students_t`
x = 3*np.random.rand(D) + 4
gmm = GaussianComponentsDiag(np.array([x]), prior)
expected_prior = np.sum(
[students_t(x[i], m_0[i], S_0[i]*(k_0 + 1)/(k_0 * v_0), v_0) for i in range(len(x))]
)
npt.assert_almost_equal(gmm.log_prior(0), expected_prior)
def test_log_prod_students_t():
np.random.seed(1)
# Prior
D = 10
m_0 = 5 * np.random.rand(D) - 2
k_0 = np.random.randint(15)
v_0 = D + np.random.randint(5)
S_0 = 2 * np.random.rand(D) + 3
prior = NIW(m_0=m_0, k_0=k_0, v_0=v_0, S_0=S_0)
# GMM we will use to access `_log_prod_students_t`
x = 3 * np.random.rand(D) + 4
gmm = GaussianComponentsDiag(np.array([x]), prior)
expected_prior = np.sum([
students_t(x[i], m_0[i], S_0[i] * (k_0 + 1) / (k_0 * v_0), v_0)
for i in range(len(x))
])
npt.assert_almost_equal(gmm.log_prior(0), expected_prior)
