def plot_benchmark1():
"""Plot various quantities obtained for varying values of alpha."""
parameters = dict(n_var=200,
n_tasks=5,
density=0.15,
tol=1e-2,
# max_iter=50,
min_samples=100,
max_samples=150)
cache_dir = get_cache_dir(parameters, output_dir=output_dir)
gt = get_ground_truth(cache_dir)
gt['precisions'] = np.dstack(gt['precisions'])
emp_covs, n_samples = empirical_covariances(gt['signals'])
n_samples /= n_samples.sum()
alpha = []
objective = []
log_likelihood = []
ll_penalized = []
sparsity = []
kl = []
true_covs = np.empty(gt['precisions'].shape)
for k in range(gt['precisions'].shape[-1]):
true_covs[..., k] = np.linalg.inv(gt['precisions'][..., k])
for out in iter_outputs(cache_dir):
alpha.append(out['alpha'])
objective.append(- out['objective'][-1])
ll, llpen = group_sparse_scores(out['precisions'],
n_samples, true_covs, out['alpha'])
log_likelihood.append(ll)
ll_penalized.append(llpen)
sparsity.append(1. * (out['precisions'][..., 0] != 0).sum()
/ out['precisions'].shape[0] ** 2)
kl.append(distance(out['precisions'], gt['precisions']))
gt["true_sparsity"] = (1. * (gt['precisions'][..., 0] != 0).sum()
/ gt['precisions'].shape[0] ** 2)
title = (("n_var: {n_var}, n_tasks: {n_tasks}, "
+ "true sparsity: {true_sparsity:.2f} "
+ "\ntol: {tol:.2e} samples: {min_samples}-{max_samples}").format(
true_sparsity=gt["true_sparsity"],
**parameters))
plot(alpha, objective, label="objective", title=title)
plot(alpha, log_likelihood, label="log-likelihood", new_figure=False)
plot(alpha, ll_penalized, label="penalized L-L", new_figure=False)
plot(alpha, sparsity, label="sparsity", title=title)
pl.hlines(gt["true_sparsity"], min(alpha), max(alpha))
plot(alpha, kl, label="distance", title=title)
pl.show()
# estimate second-order sensibility
sens2 = np.empty(last_m.shape)
for k in range(last_m.shape[-1]):
sens2[..., k] = n_samples[k] * (
np.dot(
np.dot(last_m_inv[..., k],
derivative[..., k]),
last_m_inv[..., k])
)
sens2 = np.abs(sens2 / 2.)
matshow(np.sqrt(derivative[..., l]), title="sensitivity 1")
matshow(np.sqrt(sens2[..., l]), title="sensitivity 2")
matshow(np.sqrt(sens2[..., l] + derivative[..., l]),
title="sensitivity 1+2")
## matshow((last_m - mean)[..., l], title="difference with mean")
## matshow(topo_count[..., l], title="non-zero count")
pl.show()
if __name__ == "__main__":
output_dir = "_gsc_sensitivity"
## parameters = {"n_var": 10, "n_tasks": 40, "density": 0.1,
## "tol": 1e-4, "alpha": 0.02}
parameters = {"n_var": 100, "n_tasks": 40, "density": 0.1,
"tol": 1e-2, "alpha": 0.02}
cache_dir = get_cache_dir(parameters, output_dir)
compute_stats(cache_dir)
