def test_sparse_linear_trend(n=500, l1=2., ratio=0.1, control=control):
D1 = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
D2 = np.dot(D1[1:, 1:], D1)
D = np.vstack([D2, ratio * np.identity(n)])
M = np.linalg.eigvalsh(np.dot(D.T, D)).max()
Y = np.random.standard_normal(n) * 0.1
X = np.linspace(0, 1, n)
mu = 0 * Y
mu[int(0.1 *
n):int(0.3 *
n)] += (X[int(0.1 * n):int(0.3 * n)] - X[int(0.1 * n)]) * 6
mu[int(0.3 * n):int(0.5 * n)] += (X[int(0.3 * n):int(0.5 * n)] -
X[int(0.3 * n)]) * (-6) + 1.2
Y += mu
p1 = sapprox.signal_approximator((D, Y), L=M)
p1.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2 - t1
beta, _ = opt1.output
if control['plot']:
pylab.clf()
pylab.plot(X, beta, linewidth=3, c='red')
pylab.scatter(X, Y)
pylab.plot(X, mu)
pylab.show()
def test_sparse_fused_lasso(n=500, l1=2., ratio=1., control=control):
D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
D = np.vstack([D, ratio * np.identity(n)])
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)] += 3.
p1 = sapprox.signal_approximator((D, Y), L=M)
p1.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2 - t1
beta, _ = opt1.output
X = np.arange(n)
if control['plot']:
pylab.clf()
pylab.step(X, beta, linewidth=3, c='red')
pylab.scatter(X, Y)
pylab.show()
def test_sparse_linear_trend(n=500,l1=2., ratio=0.1, control=control):
D1 = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
D2 = np.dot(D1[1:,1:], D1)
D = np.vstack([D2, ratio*np.identity(n)])
M = np.linalg.eigvalsh(np.dot(D.T, D)).max()
Y = np.random.standard_normal(n) * 0.1
X = np.linspace(0,1,n)
mu = 0 * Y
mu[int(0.1*n):int(0.3*n)] += (X[int(0.1*n):int(0.3*n)] - X[int(0.1*n)]) * 6
mu[int(0.3*n):int(0.5*n)] += (X[int(0.3*n):int(0.5*n)] - X[int(0.3*n)]) * (-6) + 1.2
Y += mu
p1 = sapprox.signal_approximator((D, Y),L=M)
p1.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2-t1
beta, _ = opt1.output
if control['plot']:
pylab.clf()
pylab.plot(X, beta, linewidth=3, c='red')
pylab.scatter(X, Y)
pylab.plot(X, mu)
pylab.show()
def test_sparse_fused_lasso(n=500,l1=2.,ratio=1.,control=control):
D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
D = np.vstack([D, ratio*np.identity(n)])
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)] += 3.
p1 = sapprox.signal_approximator((D, Y),L=M)
p1.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2-t1
beta, _ = opt1.output
X = np.arange(n)
if control['plot']:
pylab.clf()
pylab.step(X, beta, linewidth=3, c='red')
pylab.scatter(X, Y)
pylab.show()
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)
def test_group_lasso_approximator1(l1=0.1, **control):
Y = np.load('Y.npy')
n = Y.shape[0]
def e(i, n):
z = np.zeros(n)
z[i] = 1.
return z
Dv = [(e(i, n), l1 * n) for i in range(n)]
p1 = group.group_approximator((Dv, Y))
p2 = lasso.gengrad((np.identity(n), Y))
p2.assign_penalty(l1=l1 * n)
p3 = signal_approximator.signal_approximator((np.identity(n), Y))
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(p2)
opt2.fit(tol=control['tol'], max_its=control['max_its'])
t2 = time.time()
ts2 = 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)
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()