Convergence Failure of Glasso

Demonstration of cases where graph_lasso fails to converge and quic succeeds.

“The graphical lasso: New Insights and alternatives”, by Mazumder & Hastie 2012. https://web.stanford.edu/~hastie/Papers/glassoinsights.pdf

import sys

sys.path.append("..")
sys.path.append("../inverse_covariance")

from sklearn.covariance import graph_lasso
from inverse_covariance import quic
import numpy as np

Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/skggm/envs/latest/lib/python2.7/site-packages/sphinx_gallery/gen_rst.py", line 480, in _memory_usage
    out = func()
  File "/home/docs/checkouts/readthedocs.org/user_builds/skggm/envs/latest/lib/python2.7/site-packages/sphinx_gallery/gen_rst.py", line 465, in __call__
    exec(self.code, self.globals)
  File "/home/docs/checkouts/readthedocs.org/user_builds/skggm/checkouts/latest/examples/convergence_comparison.py", line 18, in <module>
    from inverse_covariance import quic
  File "/home/docs/checkouts/readthedocs.org/user_builds/skggm/checkouts/latest/inverse_covariance/__init__.py", line 3, in <module>
    from .quic_graph_lasso import (
  File "/home/docs/checkouts/readthedocs.org/user_builds/skggm/checkouts/latest/inverse_covariance/quic_graph_lasso.py", line 12, in <module>
    from joblib import Parallel, delayed
ImportError: No module named joblib

Example 1 graph_lasso fails to converge at lam = .009 * np.max(np.abs(Shat))

X = np.loadtxt("data/Mazumder_example1.txt", delimiter=",")
Shat = np.cov(X, rowvar=0)
try:
    graph_lasso(Shat, alpha=.004)
except FloatingPointError as e:
    print("{0}".format(e))
vals = quic(Shat, .004)

Example 2 graph_lasso fails to converge at lam = .009 * np.max(np.abs(Shat))

X = np.loadtxt("data/Mazumder_example2.txt", delimiter=",")
Shat = np.cov(X, rowvar=0)
try:
    graph_lasso(Shat, alpha=.02)
except FloatingPointError as e:
    print("{0}".format(e))
vals = quic(Shat, .02)