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_fused_lasso(n=100,l1=2.,**control):
D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
M = np.linalg.eigvalsh(np.dot(D.T, D)).max()
Y = np.random.standard_normal(n)
Y[int(0.1*n):int(0.3*n)] += 6.
p1 = signal_approximator((D, Y),L=M)
p1.assign_penalty(l1=l1)
p2 = glasso.generalized_lasso((np.identity(n), D, Y),L=M)
p2.assign_penalty(l1=l1)
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.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts2 = t2-t1
beta1, _ = opt1.output
beta2, _ = opt2.output
X = np.arange(n)
print (np.fabs(beta1-beta2).sum() / np.fabs(beta1).sum())
if control['plot']:
pylab.clf()
pylab.step(X, beta1, linewidth=3, c='red')
pylab.step(X, beta2, linewidth=3, c='blue')
pylab.scatter(X, Y)
pylab.show()
def test_fused_lasso(n=100, l1=2., **control):
D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
M = np.linalg.eigvalsh(np.dot(D.T, D)).max()
Y = np.random.standard_normal(n)
Y[int(0.1 * n):int(0.3 * n)] += 6.
p1 = signal_approximator((D, Y), L=M)
p1.assign_penalty(l1=l1)
p2 = glasso.generalized_lasso((np.identity(n), D, Y), L=M)
p2.assign_penalty(l1=l1)
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.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts2 = t2 - t1
beta1, _ = opt1.output
beta2, _ = opt2.output
X = np.arange(n)
print(np.fabs(beta1 - beta2).sum() / np.fabs(beta1).sum())
if control['plot']:
pylab.clf()
pylab.step(X, beta1, linewidth=3, c='red')
pylab.step(X, beta2, linewidth=3, c='blue')
pylab.scatter(X, Y)
pylab.show()
