Note
Click here to download the full example code
Benchmark of Frank-Wolfe variants for sparse logistic regressionΒΆ
Comparison of different Frank-Wolfe variants on various
problems with a logistic regression loss (copt.utils.LogLoss()
)
and a L1 ball constraint (copt.utils.L1Ball()
).
Traceback (most recent call last):
File "/home/pedregosa/dev/sphinx-gallery/sphinx_gallery/gen_rst.py", line 435, in _memory_usage
multiprocess=True)
File "/home/pedregosa/dev/memory_profiler/memory_profiler.py", line 343, in memory_usage
returned = f(*args, **kw)
File "/home/pedregosa/dev/sphinx-gallery/sphinx_gallery/gen_rst.py", line 426, in __call__
exec(self.code, self.globals)
File "/home/pedregosa/dev/copt/examples/frank_wolfe/plot_sparse_benchmark.py", line 32, in <module>
X, y = load_data()
File "/home/pedregosa/dev/copt/copt/datasets.py", line 155, in load_madelon
return _load_dataset("madelon", subset, data_dir)
File "/home/pedregosa/dev/copt/copt/datasets.py", line 54, in _load_dataset
makedirs(dataset_dir)
File "/home/pedregosa/anaconda3/lib/python3.7/os.py", line 221, in makedirs
mkdir(name, mode)
FileExistsError: [Errno 17] File exists: '/home/pedregosa/copt_data/madelon'
import matplotlib.pyplot as plt
import numpy as np
import copt as cp
# .. datasets and their loading functions ..
datasets = [
("Gisette", cp.datasets.load_gisette, 6e3),
("RCV1", cp.datasets.load_rcv1, 2e4),
("Madelon", cp.datasets.load_madelon, 20.0),
("Covtype", cp.datasets.load_covtype, 200.0),
]
variants_fw = [
["backtracking", "adaptive step-size", "s"],
["DR", "Lipschitz step-size", "<"],
]
for dataset_title, load_data, alpha in datasets:
plt.figure()
print("Running on the %s dataset" % dataset_title)
X, y = load_data()
n_samples, n_features = X.shape
l1_ball = cp.utils.L1Ball(alpha)
f = cp.utils.LogLoss(X, y)
x0 = np.zeros(n_features)
for step, label, marker in variants_fw:
cb = cp.utils.Trace(f)
sol = cp.minimize_frank_wolfe(
f.f_grad, x0, l1_ball.lmo, callback=cb, step=step, lipschitz=f.lipschitz
)
plt.plot(cb.trace_time, cb.trace_fx, label=label, marker=marker, markevery=10)
print("Sparsity of solution: %s" % np.mean(np.abs(sol.x) > 1e-8))
plt.legend()
plt.xlabel("Time (in seconds)")
plt.ylabel("Objective function")
plt.title(dataset_title)
plt.tight_layout() # otherwise the right y-label is slightly clipped
plt.xlim((0, 0.7 * cb.trace_time[-1])) # for aesthetics
plt.grid()
plt.show()
Total running time of the script: ( 11 minutes 46.105 seconds)
Estimated memory usage: 8 MB