def test_prox_tvl1_approximates_prox_l1_for_lasso(size=15,
random_state=42,
decimal=4,
dgap_tol=1e-7):
rng = np.random.RandomState(random_state)
l1_ratio = 1. # pure LASSO
for ndim in range(3, 4):
shape = [size] * ndim
z = rng.randn(*shape)
for weight in np.logspace(-10, 10, num=10):
# use prox_tvl1 approximation to prox_l1
a = _prox_tvl1(z.copy(),
weight=weight,
l1_ratio=l1_ratio,
dgap_tol=dgap_tol,
max_iter=10)[0][-1].ravel()
# use exact closed-form soft shrinkage formula for prox_l1
b = _prox_l1(z.copy(), weight)[-1].ravel()
# results should be close in l-infinity norm
np.testing.assert_almost_equal(np.abs(a - b).max(),
0.,
decimal=decimal)
def test_input_args_and_kwargs():
rng = np.random.RandomState(42)
p = 125
noise_std = 1e-1
sig = np.zeros(p)
sig[[0, 2, 13, 4, 25, 32, 80, 89, 91, 93, -1]] = 1
sig[:6] = 2
sig[-7:] = 2
sig[60:75] = 1
y = sig + noise_std * rng.randn(*sig.shape)
X = np.eye(p)
mask = np.ones((p,)).astype(np.bool)
alpha = .01
alpha_ = alpha * X.shape[0]
l1_ratio = .2
l1_weight = alpha_ * l1_ratio
f1 = lambda w: _squared_loss(X, y, w, compute_grad=False)
f1_grad = lambda w: _squared_loss(X, y, w, compute_grad=True,
compute_energy=False)
f2_prox = lambda w, l, *args, **kwargs: (_prox_l1(w, l * l1_weight),
dict(converged=True))
total_energy = lambda w: f1(w) + l1_weight * np.sum(np.abs(w))
for cb_retval in [0, 1]:
for verbose in [0, 1]:
for dgap_factor in [1., None]:
best_w, objective, init = mfista(
f1_grad, f2_prox, total_energy, 1., p,
dgap_factor=dgap_factor,
callback=lambda _: cb_retval, verbose=verbose,
max_iter=100)
assert_equal(best_w.shape, mask.shape)
assert_true(isinstance(objective, list))
assert_true(isinstance(init, dict))
for key in ["w", "t", "dgap_tol", "stepsize"]:
assert_true(key in init)
def test_prox_l1_nonexpansiveness(n_features=10):
rng = np.random.RandomState(42)
x = rng.randn(n_features, 1)
tau = 0.3
s = _prox_l1(x.copy(), tau)
p = x - s # projection + shrinkage = id
# We should have ||s(a) - s(b)||^2 <= ||a - b||^2 - ||p(a) - p(b)||^2
# for all a and b (this is strong non-expansiveness
for (a, b), (pa, pb), (sa, sb) in zip(*[itertools.product(z[0], z[0]) for z in [x, p, s]]):
assert_true((sa - sb) ** 2 <= (a - b) ** 2 - (pa - pb) ** 2)
def test_prox_l1_nonexpansiveness(n_features=10):
rng = np.random.RandomState(42)
x = rng.randn(n_features, 1)
tau = .3
s = _prox_l1(x.copy(), tau)
p = x - s # projection + shrinkage = id
# We should have ||s(a) - s(b)||^2 <= ||a - b||^2 - ||p(a) - p(b)||^2
# for all a and b (this is strong non-expansiveness
for (a, b), (pa, pb), (sa, sb) in zip(*[itertools.product(z[0], z[0])
for z in [x, p, s]]):
assert_true((sa - sb) ** 2 <= (a - b) ** 2 - (pa - pb) ** 2)
def test_prox_tvl1_approximates_prox_l1_for_lasso(size=15, random_state=42, decimal=4, dgap_tol=1e-7):
rng = np.random.RandomState(random_state)
l1_ratio = 1.0 # pure LASSO
for ndim in range(3, 4):
shape = [size] * ndim
z = rng.randn(*shape)
for weight in np.logspace(-10, 10, num=10):
# use prox_tvl1 approximation to prox_l1
a = _prox_tvl1(z.copy(), weight=weight, l1_ratio=l1_ratio, dgap_tol=dgap_tol, max_iter=10)[0][-1].ravel()
# use exact closed-form soft shrinkage formula for prox_l1
b = _prox_l1(z.copy(), weight)[-1].ravel()
# results shoud be close in l-infinity norm
np.testing.assert_almost_equal(np.abs(a - b).max(), 0.0, decimal=decimal)
def test_input_args_and_kwargs():
rng = np.random.RandomState(42)
p = 125
noise_std = 1e-1
sig = np.zeros(p)
sig[[0, 2, 13, 4, 25, 32, 80, 89, 91, 93, -1]] = 1
sig[:6] = 2
sig[-7:] = 2
sig[60:75] = 1
y = sig + noise_std * rng.randn(*sig.shape)
X = np.eye(p)
mask = np.ones((p, )).astype(np.bool)
alpha = .01
alpha_ = alpha * X.shape[0]
l1_ratio = .2
l1_weight = alpha_ * l1_ratio
f1 = lambda w: _squared_loss(X, y, w, compute_grad=False)
f1_grad = lambda w: _squared_loss(
X, y, w, compute_grad=True, compute_energy=False)
f2_prox = lambda w, l, *args, **kwargs: (_prox_l1(w, l * l1_weight),
dict(converged=True))
total_energy = lambda w: f1(w) + l1_weight * np.sum(np.abs(w))
for cb_retval in [0, 1]:
for verbose in [0, 1]:
for dgap_factor in [1., None]:
best_w, objective, init = mfista(f1_grad,
f2_prox,
total_energy,
1.,
p,
dgap_factor=dgap_factor,
callback=lambda _: cb_retval,
verbose=verbose,
max_iter=100)
assert best_w.shape == mask.shape
assert isinstance(objective, list)
assert isinstance(init, dict)
for key in ["w", "t", "dgap_tol", "stepsize"]:
assert key in init
