def test_gowl_vs_glasso_duality_gap_3(self):
"""
Duality Gap goes negative in this case. Should that happen?
"""
np.random.seed(680)
p = 10
blocks = [
Block(dim=p,
idx=0,
block_min_size=2,
block_max_size=6,
block_value=0.9),
Block(dim=p,
idx=1,
block_min_size=2,
block_max_size=6,
block_value=-0.9),
Block(dim=p,
idx=3,
block_min_size=2,
block_max_size=6,
block_value=-0.5),
]
theta_star, blocks, theta_blocks = generate_theta_star_gowl(p=p,
alpha=0.5,
noise=0.1,
blocks=blocks)
lam1 = 0.001 # controls sparsity
lam2 = 0.01 # encourages equality of coefficients
rho = oscar_weights(lam1, lam2, (p ** 2 - p) / 2)
theta_star = theta_star[0]
sigma = np.linalg.inv(theta_star)
n = 100
X = np.random.multivariate_normal(np.zeros(p), sigma, n)
X = standardize(X)
S = np.cov(X.T)
theta_0 = np.linalg.inv(S)
model = GOWLModel(X, S, theta_0, lam1, lam2, 'backtracking', max_iters=100000)
model.fit()
theta_gowl = model.theta_hat
gl = GraphicalLasso(max_iter=200)
gl.fit(S)
theta_glasso = gl.get_precision()
print('Non zero entries in precision matrix {}'.format(np.count_nonzero(theta_gowl)))
plot_multiple_theta_matrices_2d([theta_blocks, theta_star, theta_glasso, theta_gowl],
[f"Blocks: {len(blocks)}", 'True Theta', 'GLASSO', 'GOWL'])
_fit_evaluations(theta_star, theta_glasso, 3, 'GLASSO')
_fit_evaluations(theta_star, theta_gowl, 3, 'GOWL')
y_hat_gowl = spectral_clustering(theta=theta_gowl, K=4)
y_hat_glasso = spectral_clustering(theta=theta_glasso, K=4)
y_true = spectral_clustering(theta=theta_blocks, K=4).flatten()
_cluster_evaluations(y_true, y_hat_gowl, 'GOWL')
_cluster_evaluations(y_true, y_hat_glasso, 'GLASSO')
def test_gowl_vs_grab_1(self):
np.random.seed(680)
p = 10
n_blocks = 1
theta_star, blocks, theta_blocks = generate_theta_star_gowl(p=p,
alpha=0.5,
noise=0.1,
n_blocks=n_blocks,
block_min_size=2,
block_max_size=6)
theta_star = theta_star[0]
sigma = np.linalg.inv(theta_star)
n = 100
X = np.random.multivariate_normal(np.zeros(p), sigma, n)
X = standardize(X)
S = np.cov(X.T)
lam1 = 0.001 # controls sparsity
lam2 = 0.01 # encourages equality of coefficients
lmbda = .2
K = 10
o_size = .3 # The size of overlap, as an input parameter
max_iter = 20
tol = 1e-4
dual_max_iter = 600
dual_tol = 1e-4
theta_grab, blocks = grab.BCD(S,
lmbda=lmbda,
K=K,
o_size=o_size,
max_iter=max_iter,
tol=tol,
dual_max_iter=dual_max_iter,
dual_tol=dual_tol)
theta_grab = np.asarray(theta_grab)
model = GOWLModel(X, S, lam1, lam2, 'backtracking', max_iters=100000)
model.fit()
theta_gowl = model.theta_hat
print('Non zero entries in precision matrix {}'.format(np.count_nonzero(theta_gowl)))
plot_multiple_theta_matrices_2d([theta_blocks, theta_star, theta_grab, theta_gowl],
[f"1 Block of Size 2", 'True Theta', 'GRAB', 'GOWL'])
_fit_evaluations(theta_star, theta_grab, 1, 'GRAB')
_fit_evaluations(theta_star, theta_gowl, 1, 'GOWL')
y_hat_gowl = spectral_clustering(theta=theta_gowl, K=2)
y_hat_grab = spectral_clustering(theta=theta_grab, K=2)
y_true = spectral_clustering(theta=theta_blocks, K=2).flatten()
_cluster_evaluations(y_true, y_hat_gowl, 'GOWL')
_cluster_evaluations(y_true, y_hat_grab, 'GRAB')
def test_gowl_vs_grab_n(self):
np.random.seed(680)
p = 50
block_percentage = 0.1
alpha = 0.5
noise = 0.1
K = int(p * block_percentage)
block_min_size = p * 0.1
block_max_size = p * 0.4
ccl_1 = 0.01
ccl_2 = 0.0001
thetas_with_noise, theta_blocks, scov_matrices, X_matrices = generate_synthetic_data(K,
p,
block_min_size,
block_max_size,
alpha,
noise,
1)
S = scov_matrices[0]
model = GOWLModel(X_matrices, S, ccl_1, ccl_2, 'backtracking')
model.fit()
theta_gowl = model.theta_hat
lmbda = .2
K = 10
o_size = .3 # The size of overlap, as an input parameter
max_iter = 20
tol = 1e-4
dual_max_iter = 600
dual_tol = 1e-4
theta_grab, blocks = grab.BCD(S,
lmbda=lmbda,
K=K,
o_size=o_size,
max_iter=max_iter,
tol=tol,
dual_max_iter=dual_max_iter,
dual_tol=dual_tol)
theta_grab = np.asarray(theta_grab)
plot_multiple_theta_matrices_2d([S, theta_blocks, thetas_with_noise[0], theta_grab, theta_gowl],
['Sample Covariance', f"Blocks: {len(blocks)}", 'True Theta', 'GRAB', 'GOWL'])
_fit_evaluations(theta_blocks, theta_grab, 1, 'GRAB')
_fit_evaluations(theta_blocks, theta_gowl, 1, 'GOWL')
y_hat_gowl = spectral_clustering(theta=theta_gowl, K=2)
y_hat_grab = spectral_clustering(theta=theta_grab, K=2)
y_true = spectral_clustering(theta=theta_blocks, K=2).flatten()
_cluster_evaluations(y_true, y_hat_gowl, 'GOWL')
_cluster_evaluations(y_true, y_hat_grab, 'GRAB')