def test_lasso(n=100):
l1 = 1.
sparsity1 = l1norm(n, l=l1*0.75)
sparsity2 = l1norm(n, l=l1*0.25)
sparsity = l1norm(n, l=l1)
X = np.random.standard_normal((5000,n))
Y = np.random.standard_normal((5000,))
regloss = squaredloss(X,Y)
#p=regloss.add_seminorm(sparsity)
#p=regloss.add_seminorm(seminorm(sparsity1,sparsity2),initial=np.zeros(n))
p=regloss.add_seminorm(seminorm(sparsity),initial=np.zeros(n))
solver=FISTA(p)
solver.debug = True
t1 = time.time()
vals1 = solver.fit(max_its=800,tol=1e-18,set_prox_tol=True)
t2 = time.time()
dt1 = t2 - t1
soln = solver.problem.coefs
time.sleep(5)
p2 = lasso.gengrad((X, Y))#,initial_coefs = np.random.normal(0,1,n))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
t1 = time.time()
vals2 = opt.fit(tol=1e-18,max_its=800)
t2 = time.time()
dt2 = t2 - t1
beta = opt.problem.coefs
print soln[range(10)]
print beta[range(10)]
print p.obj(soln), p.obj(beta)
print p2.obj(soln), p2.obj(beta)
print "Times", dt1, dt2
return [vals1, vals2]
def lasso_example(compare=False):
l1 = 20.
sparsity = l1norm(500, l=l1 / 2.)
X = np.random.standard_normal((1000, 500))
Y = np.random.standard_normal((1000, ))
regloss = squaredloss(X, Y)
sparsity2 = l1norm(500, l=l1 / 2.)
#p=regloss.add_seminorm(sparsity)
p = regloss.add_seminorm(seminorm(sparsity, sparsity2))
solver = FISTA(p)
solver.debug = True
vals = solver.fit(max_its=2000, min_its=100)
soln = solver.problem.coefs
if not compare:
# solution
pylab.figure(num=1)
pylab.clf()
pylab.plot(soln, c='g')
# objective values
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
else:
p2 = lasso.gengrad((X, Y))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
opt.fit(tol=1e-10, max_its=5000)
beta = opt.problem.coefs
print "Terminal error with seminorm:", np.min(
vals), "\tTerminal error with lasso", p.obj(
beta), "\nTerminal relative error:", (
np.min(vals) - p.obj(beta)) / p.obj(beta)
pylab.figure(num=1)
pylab.clf()
#pylab.plot(soln, c='g')
pylab.scatter(soln, beta)
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
def test_1d_fused_lasso(n=100):
l1 = 1.
sparsity1 = l1norm(n, l=l1)
D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
extra = np.zeros(n)
extra[0] = 1.
D = np.vstack([D,extra])
D = sparse.csr_matrix(D)
fused = seminorm(l1norm(D, l=l1))
X = np.random.standard_normal((2*n,n))
Y = np.random.standard_normal((2*n,))
regloss = squaredloss(X,Y)
p=regloss.add_seminorm(fused)
solver=FISTA(p)
solver.debug = True
vals1 = solver.fit(max_its=25000, tol=1e-12)
soln1 = solver.problem.coefs
B = np.array(sparse.tril(np.ones((n,n))).todense())
X2 = np.dot(X,B)
time.sleep(3)
D2 = np.diag(np.ones(n))
p2 = lasso.gengrad((X2, Y))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
opt.fit(tol=1e-12,max_its=25000)
beta = opt.problem.coefs
soln2 = np.dot(B,beta)
print soln1[range(10)]
print soln2[range(10)]
print p.obj(soln1), p.obj(soln2)
#np.testing.assert_almost_equal(soln1,soln2)
return vals1
def lasso_example(compare=False):
l1 = 20.
sparsity = l1norm(500, l=l1/2.)
X = np.random.standard_normal((1000,500))
Y = np.random.standard_normal((1000,))
regloss = squaredloss(X,Y)
sparsity2 = l1norm(500, l=l1/2.)
#p=regloss.add_seminorm(sparsity)
p=regloss.add_seminorm(seminorm(sparsity,sparsity2))
solver=FISTA(p)
solver.debug = True
vals = solver.fit(max_its=2000, min_its = 100)
soln = solver.problem.coefs
if not compare:
# solution
pylab.figure(num=1)
pylab.clf()
pylab.plot(soln, c='g')
# objective values
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
else:
p2 = lasso.gengrad((X, Y))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
opt.fit(tol=1e-10,max_its=5000)
beta = opt.problem.coefs
print "Terminal error with seminorm:", np.min(vals), "\tTerminal error with lasso", p.obj(beta) ,"\nTerminal relative error:", (np.min(vals) - p.obj(beta))/p.obj(beta)
pylab.figure(num=1)
pylab.clf()
#pylab.plot(soln, c='g')
pylab.scatter(soln,beta)
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
def test_lasso(n=100):
l1 = 1.
sparsity1 = l1norm(n, l=l1 * 0.75)
sparsity2 = l1norm(n, l=l1 * 0.25)
sparsity = l1norm(n, l=l1)
X = np.random.standard_normal((5000, n))
Y = np.random.standard_normal((5000, ))
regloss = squaredloss(X, Y)
#p=regloss.add_seminorm(sparsity)
#p=regloss.add_seminorm(seminorm(sparsity1,sparsity2),initial=np.zeros(n))
p = regloss.add_seminorm(seminorm(sparsity), initial=np.zeros(n))
solver = FISTA(p)
solver.debug = True
t1 = time.time()
vals1 = solver.fit(max_its=800, tol=1e-18, set_prox_tol=True)
t2 = time.time()
dt1 = t2 - t1
soln = solver.problem.coefs
time.sleep(5)
p2 = lasso.gengrad((X, Y)) #,initial_coefs = np.random.normal(0,1,n))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
t1 = time.time()
vals2 = opt.fit(tol=1e-18, max_its=800)
t2 = time.time()
dt2 = t2 - t1
beta = opt.problem.coefs
print soln[range(10)]
print beta[range(10)]
print p.obj(soln), p.obj(beta)
print p2.obj(soln), p2.obj(beta)
print "Times", dt1, dt2
return [vals1, vals2]
def test_1d_fused_lasso(n=100):
l1 = 1.
sparsity1 = l1norm(n, l=l1)
D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:]
extra = np.zeros(n)
extra[0] = 1.
D = np.vstack([D, extra])
D = sparse.csr_matrix(D)
fused = seminorm(l1norm(D, l=l1))
X = np.random.standard_normal((2 * n, n))
Y = np.random.standard_normal((2 * n, ))
regloss = squaredloss(X, Y)
p = regloss.add_seminorm(fused)
solver = FISTA(p)
solver.debug = True
vals1 = solver.fit(max_its=25000, tol=1e-12)
soln1 = solver.problem.coefs
B = np.array(sparse.tril(np.ones((n, n))).todense())
X2 = np.dot(X, B)
time.sleep(3)
D2 = np.diag(np.ones(n))
p2 = lasso.gengrad((X2, Y))
p2.assign_penalty(l1=l1)
opt = FISTA(p2)
opt.debug = True
opt.fit(tol=1e-12, max_its=25000)
beta = opt.problem.coefs
soln2 = np.dot(B, beta)
print soln1[range(10)]
print soln2[range(10)]
print p.obj(soln1), p.obj(soln2)
#np.testing.assert_almost_equal(soln1,soln2)
return vals1