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_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_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_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_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_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_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)
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)