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.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1])
npt.assert_almost_equal(log_post_pred_unvectorized(gmm, 10), gmm.log_post_pred(10))
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.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0, 1, 0, 1, 3, 4, 3, 2, -1])
npt.assert_almost_equal(log_post_pred_unvectorized(gmm, 10),
gmm.log_post_pred(10))
def test_log_post_pred_k():
# Setup densities
prior = NIW(m_0=np.array([0.0, 0.0]), k_0=2.0, v_0=5.0, S_0=5.0 * np.eye(2))
gmm = GaussianComponents(np.array([[1.2, 0.9], [-0.1, 0.8], [0.5, 0.4]]), prior)
# Add data vectors to a single component
gmm.add_item(0, 0)
gmm.add_item(1, 0)
# Calculate log predictave
lp = gmm.log_post_pred_k(2, 0)
lp_expected = -2.07325364088
npt.assert_almost_equal(lp, lp_expected)
def test_map():
# Setup densities
prior = NIW(m_0=np.array([0.0, 0.0]), k_0=2.0, v_0=5.0, S_0=5.0 * np.eye(2))
gmm = GaussianComponents(np.array([[1.2, 0.9], [-0.1, 0.8]]), prior)
gmm.add_item(0, 0)
gmm.add_item(1, 0)
mu_expected = np.array([0.275, 0.425])
sigma_expected = np.array([[0.55886364, 0.04840909], [0.04840909, 0.52068182]])
# Calculate the posterior MAP of the parameters
mu, sigma = gmm.map(0)
npt.assert_almost_equal(mu, mu_expected)
npt.assert_almost_equal(sigma, sigma_expected)
def test_log_post_pred_k():
# Setup densities
prior = NIW(m_0=np.array([0.0, 0.0]), k_0=2., v_0=5., S_0=5. * np.eye(2))
gmm = GaussianComponents(np.array([[1.2, 0.9], [-0.1, 0.8], [0.5, 0.4]]),
prior)
# Add data vectors to a single component
gmm.add_item(0, 0)
gmm.add_item(1, 0)
# Calculate log predictave
lp = gmm.log_post_pred_k(2, 0)
lp_expected = -2.07325364088
npt.assert_almost_equal(lp, lp_expected)
def test_log_prior_3d():
# Data
X = np.array([[-0.3406, -0.0593, -0.0686]])
N, D = X.shape
# Setup densities
m_0 = np.zeros(D)
k_0 = 0.05
v_0 = D + 1
S_0 = 0.001 * np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior)
# Calculate log predictave under prior alone
lp = gmm.log_prior(0)
lp_expected = -0.472067277015
npt.assert_almost_equal(lp, lp_expected)
def test_log_prior_3d():
# Data
X = np.array([[-0.3406, -0.0593, -0.0686]])
N, D = X.shape
# Setup densities
m_0 = np.zeros(D)
k_0 = 0.05
v_0 = D + 1
S_0 = 0.001 * np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior)
# Calculate log predictave under prior alone
lp = gmm.log_prior(0)
lp_expected = -0.472067277015
npt.assert_almost_equal(lp, lp_expected)
def test_log_marg_k():
# Data
X = np.array([[-0.3406, -0.3593, -0.0686], [-0.3381, 0.2993, 0.925], [-0.5, -0.101, 0.75]])
N, D = X.shape
# Setup densities
m_0 = np.zeros(D)
k_0 = 0.05
v_0 = D + 3
S_0 = 0.5 * np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0])
log_marg_expected = -8.42365141729
# Calculate log marginal of data
log_marg = gmm.log_marg_k(0)
npt.assert_almost_equal(log_marg, log_marg_expected)
def test_map():
# Setup densities
prior = NIW(m_0=np.array([0.0, 0.0]),
k_0=2.0,
v_0=5.0,
S_0=5.0 * np.eye(2))
gmm = GaussianComponents(np.array([[1.2, 0.9], [-0.1, 0.8]]), prior)
gmm.add_item(0, 0)
gmm.add_item(1, 0)
mu_expected = np.array([0.275, 0.425])
sigma_expected = np.array([[0.55886364, 0.04840909],
[0.04840909, 0.52068182]])
# Calculate the posterior MAP of the parameters
mu, sigma = gmm.map(0)
npt.assert_almost_equal(mu, mu_expected)
npt.assert_almost_equal(sigma, sigma_expected)
def test_log_marg_k():
# Data
X = np.array([[-0.3406, -0.3593, -0.0686], [-0.3381, 0.2993, 0.925],
[-0.5, -0.101, 0.75]])
N, D = X.shape
# Setup densities
m_0 = np.zeros(D)
k_0 = 0.05
v_0 = D + 3
S_0 = 0.5 * np.eye(D)
prior = NIW(m_0, k_0, v_0, S_0)
gmm = GaussianComponents(X, prior, [0, 0, 0])
log_marg_expected = -8.42365141729
# Calculate log marginal of data
log_marg = gmm.log_marg_k(0)
npt.assert_almost_equal(log_marg, log_marg_expected)
