def fused_lasso(n=100, l1=2., **control):
D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
Dsp = scipy.sparse.lil_matrix(D)
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 = sapprox.gengrad_sparse((Dsp, Y), L=M)
p1.assign_penalty(l1=l1)
p2 = sapprox.gengrad((D, Y), L=M)
p2.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.debug = True
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2 - t1
t1 = time.time()
opt2 = regreg.FISTA(p2)
opt2.fit(tol=control['tol'], max_its=control['max_its'])
beta2 = opt2.problem.coefs
t2 = time.time()
ts2 = t2 - t1
beta1, _ = opt1.output
beta2, _ = opt2.output
np.testing.assert_almost_equal(beta1, beta2)
X = np.arange(n)
if control['plot']:
pylab.clf()
pylab.step(X, beta1, linewidth=3, c='red')
pylab.step(X, beta2, linewidth=3, c='green')
pylab.scatter(X, Y)
pylab.show()
def fused_lasso(n=100,l1=2.,**control):
D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
Dsp = scipy.sparse.lil_matrix(D)
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 = sapprox.gengrad_sparse((Dsp, Y),L=M)
p1.assign_penalty(l1=l1)
p2 = sapprox.gengrad((D, Y),L=M)
p2.assign_penalty(l1=l1)
t1 = time.time()
opt1 = regreg.FISTA(p1)
opt1.debug=True
opt1.fit(tol=control['tol'], max_its=control['max_its'])
beta1 = opt1.problem.coefs
t2 = time.time()
ts1 = t2-t1
t1 = time.time()
opt2 = regreg.FISTA(p2)
opt2.fit(tol=control['tol'], max_its=control['max_its'])
beta2 = opt2.problem.coefs
t2 = time.time()
ts2 = t2-t1
beta1, _ = opt1.output
beta2, _ = opt2.output
np.testing.assert_almost_equal(beta1, beta2)
X = np.arange(n)
if control['plot']:
pylab.clf()
pylab.step(X, beta1, linewidth=3, c='red')
pylab.step(X, beta2, linewidth=3, c='green')
pylab.scatter(X, Y)
pylab.show()
def test_fused_lasso(n=100, l1=15., ratio=0.1):
Y = np.random.standard_normal(n)
Y[int(0.1*n):int(0.3*n)] += 6.
D1 = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
D2 = np.dot(D1[1:,1:], D1)
D2 = np.vstack([D1, ratio*np.identity(n)])
M = np.linalg.eigvalsh(np.dot(D2.T, D2)).max()
D1sp = scipy.sparse.csr_matrix(D1)
Dsp = scipy.sparse.csr_matrix(D2)
D3 = np.identity(n)
D3sp = scipy.sparse.csr_matrix(D3)
semi = seminorm(l1norm(l1)) #+ seminorm(genl1norm(D1sp,l1))
p2 = squaredloss((np.eye(n),Y),semi)
opt2 = regreg.FISTA(p2)
opt2.debug = True
obj2 = opt2.fit(tol=1.0e-10, max_its=5000)
beta2, _ = opt2.output
print beta2
p1 = sapprox.gengrad_sparse((D3sp, Y),L=M)
p1.assign_penalty(l1=l1)
opt1 = regreg.FISTA(p1)
#opt1.debug = True
obj1 = opt1.fit(tol=1.0e-10, max_its=5000, alpha=1.05)
beta1, _ = opt1.output
print beta1
print np.allclose(beta1,beta2,rtol=1e-4)
"""
