def test_group_lasso_atom():
ps = np.array([0]*5 + [3]*3)
weights = {3:2., 0:2.3}
lagrange = 1.5
lipschitz = 0.2
p = gl.group_lasso(ps, lagrange, weights)
z = 30 * np.random.standard_normal(8)
q = rr.identity_quadratic(lipschitz, z, 0, 0)
x = p.solve(q)
a = gl.prox_group_lasso(z, lagrange, lipschitz, np.array([],np.int), np.array([],np.int), np.array([], np.int), np.array([0,0,0,0,0,1,1,1]), np.array([np.sqrt(5), 2]))
result = np.zeros_like(a)
result[:5] = z[:5] / np.linalg.norm(z[:5]) * max(np.linalg.norm(z[:5]) - weights[0] * lagrange/lipschitz, 0)
result[5:] = z[5:] / np.linalg.norm(z[5:]) * max(np.linalg.norm(z[5:]) - weights[3] * lagrange/lipschitz, 0)
lipschitz = 1.
q = rr.identity_quadratic(lipschitz, z, 0, 0)
x2 = p.solve(q)
pc = p.conjugate
a2 = pc.solve(q)
np.testing.assert_allclose(z-a2, x2)
def test_group_lasso2(l1=1, **control):
"""
fits a LASSO as a group lasso with
all 2norms are one dimensional
"""
X = np.load("X.npy")
Y = np.load('Y.npy')
n, p = X.shape
XtX = np.dot(X.T, X)
M = np.linalg.eigvalsh(XtX).max() #/ (1*len(Y))
def e(i, n):
z = np.zeros(n)
z[i] = 1.
return z
p1 = lasso.gengrad((X, Y), L=M)
p1.assign_penalty(l1=l1 * n)
Dv = [(e(i, p), l1 * n) for i in range(p)]
p2 = group.group_lasso((X, Dv, Y))
p2.dualcontrol['tol'] = 1.0e-10
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts1 = t2 - t1
t1 = time.time()
opt2 = regreg.FISTA(p2)
opt2.debug = True
opt2.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts3 = t2 - t1
p3 = glasso.generalized_lasso((X, np.identity(p), Y), L=M)
p3.assign_penalty(l1=l1 * n)
p3.dualcontrol['tol'] = 1.0e-10
t1 = time.time()
opt3 = regreg.FISTA(p3)
opt3.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts3 = t2 - t1
beta1, _ = opt1.output
beta2, _ = opt2.output
beta3, _ = opt3.output
X = np.arange(n)
nose.tools.assert_true(
(np.fabs(beta1 - beta2).sum() / np.fabs(beta1).sum()) < 5.0e-04)
nose.tools.assert_true(
(np.fabs(beta1 - beta3).sum() / np.fabs(beta1).sum()) < 5.0e-04)
def test_group_lasso(l1=0.1, **control):
"""
fits a fused lasso as a group lasso approximator, i.e.
all 2norms are one dimensional
"""
Y = np.load('Y.npy')
n = Y.shape[0]
def e(i, n):
z = np.zeros(n)
z[i] = 1.
z[i + 1] = -1
return z
Dv = [(e(i, n), l1 * n) for i in range(n - 1)]
D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
M = np.linalg.eigvalsh(np.dot(D.T, D)).max()
p1 = group.group_approximator((Dv, Y), L=M)
p2 = group.group_lasso((np.identity(n), Dv, Y), L=M)
p3 = signal_approximator.signal_approximator((D, Y), L=M)
p3.assign_penalty(l1=l1 * n)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.debug = True
opt1.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts1 = t2 - t1
t1 = time.time()
opt2 = regreg.FISTA(p3)
opt2.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts3 = t2 - t1
t1 = time.time()
opt3 = regreg.FISTA(p3)
opt3.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts3 = t2 - t1
beta1, _ = opt1.output
beta2, _ = opt2.output
beta3, _ = opt3.output
X = np.arange(n)
nose.tools.assert_true(
(np.fabs(beta1 - beta3).sum() / np.fabs(beta1).sum()) < 1.0e-04)
nose.tools.assert_true(
(np.fabs(beta1 - beta2).sum() / np.fabs(beta1).sum()) < 1.0e-04)
