Note
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Benchmark of Frank-Wolfe variants for sparse logistic regressionΒΆ
Speed of convergence of different Frank-Wolfe variants on various
problems with a logistic regression loss (copt.utils.LogLoss()
)
and a L1 ball constraint (copt.utils.L1Ball()
).
Out:
Running on the Gisette dataset
/usr/local/google/home/pedregosa/dev/copt/copt/frank_wolfe.py:115: RuntimeWarning: Exhausted line search iterations in minimize_frank_wolfe
"Exhausted line search iterations in minimize_frank_wolfe", RuntimeWarning
Sparsity of solution: 0.0034
Running on the RCV1 dataset
Sparsity of solution: 0.0006774494029977136
Running on the Madelon dataset
Sparsity of solution: 0.248
Running on the Covtype dataset
/usr/local/google/home/pedregosa/dev/copt/copt/frank_wolfe.py:115: RuntimeWarning: Exhausted line search iterations in minimize_frank_wolfe
"Exhausted line search iterations in minimize_frank_wolfe", RuntimeWarning
Sparsity of solution: 0.25925925925925924
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 = [
["adaptive", "adaptive step-size", "s"],
["adaptive_scipy", "scipy linesearch step-size", "^"],
["adaptive_scipy+", "linesearch+ step-size", "s"],
# ["adaptive3", "adaptive3 step-size", "+"],
# ["adaptive4", "adaptive4 step-size", "x"],
["panj", "geoff's step-size", ">"],
["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_size, 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_size=step_size,
lipschitz=f.lipschitz,
# max_iter=1000
)
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: ( 46 minutes 47.690 seconds)
Estimated memory usage: 1469 MB