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 __init__(self, x, lam1, lam2, max_iters=10, epsilon=1e-05):
super(CCGOWLModel, self).__init__('CCGOWL', x, None)
self.nsfunc = OWL()
self.sfunc = MSE()
self.n, self.p = x.shape
self._lambdas = oscar_weights(lam1, lam2, self.p - 1)
self.max_iters = max_iters
self.epsilon = epsilon
self.beta_0 = np.zeros(x.shape[1] - 1)
self.beta = np.zeros(x.shape[1] - 1)
self.theta_hat = np.zeros((self.p, self.p))
def __init__(self,
x,
sample_cov,
lam1,
lam2,
ss_type,
dual_gap=True,
max_iters=10,
epsilon=1e-05):
super(GOWLModel, self).__init__('GOWL', x, None)
_, p = sample_cov.shape
self.S = sample_cov
self.nsfunc = GOWL()
self.sfunc = LOGDET()
self.theta0 = np.linalg.inv(sample_cov)
self._lambdas = oscar_weights(lam1, lam2, (p**2 - p) / 2)
self.dual_gap = dual_gap
self.max_iters = max_iters
self.epsilon = epsilon
self.theta_hat = np.zeros(self.S.shape)
assert ss_type in ['constant', 'backtracking'], \
"Choose a valid option: [constant, backtracking]"
self.ss_type = ss_type