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_marg_k():
np.random.seed(1)
# Generate data
D = 10
N_1 = 10
X_1 = 5 * np.random.rand(N_1, D) - 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)])
gmm = GaussianComponentsDiag(X_1, prior, assignments=assignments)
# Calculate marginal for component by hand
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_log_marg = (-N_1 * D / 2. * math.log(np.pi) +
D / 2. * math.log(k_0) - D / 2. * math.log(k_N) +
v_0 / 2. * np.log(S_0).sum() -
v_N / 2. * np.log(S_N).sum() + D *
(gammaln(v_N / 2.) - gammaln(v_0 / 2.)))
npt.assert_almost_equal(gmm.log_marg_k(0), expected_log_marg)
def test_log_post_pred():
# Data generated with np.random.seed(2); np.random.rand(11, 4)
X = np.array([[0.4359949, 0.02592623, 0.54966248, 0.43532239],
[0.4203678, 0.33033482, 0.20464863, 0.61927097],
[0.29965467, 0.26682728, 0.62113383, 0.52914209],
[0.13457995, 0.51357812, 0.18443987, 0.78533515],
[0.85397529, 0.49423684, 0.84656149, 0.07964548],
[0.50524609, 0.0652865, 0.42812233, 0.09653092],
[0.12715997, 0.59674531, 0.226012, 0.10694568],
[0.22030621, 0.34982629, 0.46778748, 0.20174323],
[0.64040673, 0.48306984, 0.50523672, 0.38689265],
[0.79363745, 0.58000418, 0.1622986, 0.70075235],
[0.96455108, 0.50000836, 0.88952006, 0.34161365]])
N, D = X.shape
# Setup densities
m_0 = X.mean(axis=0)
k_0 = 0.05
v_0 = D + 10
S_0 = 0.5 * np.ones(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponentsDiag(X, prior, [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1])
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_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_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_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_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)