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)
