def group_lasso_example():
def selector(p, slice):
return np.identity(p)[slice]
penalties = [l2norm(selector(500, slice(i*100,(i+1)*100)), l=.1) for i in range(5)]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
X = np.random.standard_normal((1000,500))
Y = np.random.standard_normal((1000,))
regloss = squaredloss(X,Y)
p=regloss.add_seminorm(group_lasso)
solver=FISTA(p)
solver.debug = True
vals = solver.fit(max_its=2000, min_its=20,tol=1e-10)
soln = solver.problem.coefs
# solution
pylab.figure(num=1)
pylab.clf()
pylab.plot(soln, c='g')
# objective values
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
def group_lasso_example():
def selector(p, slice):
return np.identity(p)[slice]
penalties = [
l2norm(selector(500, slice(i * 100, (i + 1) * 100)), l=.1)
for i in range(5)
]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
X = np.random.standard_normal((1000, 500))
Y = np.random.standard_normal((1000, ))
regloss = squaredloss(X, Y)
p = regloss.add_seminorm(group_lasso)
solver = FISTA(p)
solver.debug = True
vals = solver.fit(max_its=2000, min_its=20, tol=1e-10)
soln = solver.problem.coefs
# solution
pylab.figure(num=1)
pylab.clf()
pylab.plot(soln, c='g')
# objective values
pylab.figure(num=2)
pylab.clf()
pylab.plot(vals)
class conjugate(composite):
def __init__(self, atom, quadratic=None, tol=1e-8):
# we copy the atom because we will modify its quadratic part
self.atom = copy(atom)
if self.atom.quadratic is None:
self.atom.set_quadratic(0, None, None, 0)
if quadratic is not None:
totalq = self.atom.quadratic + quadratic
self.atom.set_quadratic(totalq.coef,
totalq.offset,
totalq.linear_term,
totalq.constant_term)
if self.atom.quadratic in [0, None]:
raise ValueError('quadratic coefficient must be non-zero')
self.solver = FISTA(self.atom)
self.tol = tol
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(self.atom, "lipschitz"):
self._backtrack = False
# self._smooth_function_linear.lipschitz = atom.lipschitz + self.atom.quadratic.coef
else:
self._backtrack = True
self._have_solved_once = False
def smooth_objective(self, x, mode='both', check_feasibility=False):
"""
Evaluate the conjugate function and/or its gradient
if mode == 'both', return both function value and gradient
if mode == 'grad', return only the gradient
if mode == 'func', return only the function value
"""
self.solver.debug = False
self.atom.quadratic.linear_term -= x.T
self.solver.fit(max_its=5000, tol=self.tol, backtrack=self._backtrack)
minimizer = self.atom.coefs
# retain a reference
self.argmin = minimizer
if mode == 'both':
v = self.atom.objective(minimizer)
return -v, minimizer
elif mode == 'func':
v = self.atom.objective(minimizer)
return -v
elif mode == 'grad':
return minimizer
else:
raise ValueError("mode incorrectly specified")
self.atom.quadratic.linear_term += x
def __init__(self, atom, quadratic=None, tol=1e-8):
# we copy the atom because we will modify its quadratic part
self.atom = copy(atom)
if self.atom.quadratic is None:
self.atom.set_quadratic(0, None, None, 0)
if quadratic is not None:
totalq = self.atom.quadratic + quadratic
self.atom.set_quadratic(totalq.coef,
totalq.offset,
totalq.linear_term,
totalq.constant_term)
if self.atom.quadratic in [0, None]:
raise ValueError('quadratic coefficient must be non-zero')
self.solver = FISTA(self.atom)
self.tol = tol
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(self.atom, "lipschitz"):
self._backtrack = False
# self._smooth_function_linear.lipschitz = atom.lipschitz + self.atom.quadratic.coef
else:
self._backtrack = True
self._have_solved_once = False
def __init__(self, smooth_f, epsilon=0.01):
self._smooth_function = smooth_f
self._linear = linear(np.zeros(smooth_f.primal_shape))
self._quadratic = l2normsq(smooth_f.primal_shape, l=epsilon / 2.)
self._smooth_function_linear = smooth_function(smooth_f, self._linear,
self._quadratic)
self._solver = FISTA(self._smooth_function_linear)
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(smooth_f, "L"):
self._backtrack = False
self._smooth_function_linear.L = smooth_f.L + epsilon
else:
self._backtrack = True
self._have_solved_once = False
self.epsilon = epsilon
class conjugate(object):
def __init__(self, smooth_f, epsilon=0.01):
self._smooth_function = smooth_f
self._linear = linear(np.zeros(smooth_f.primal_shape))
self._quadratic = l2normsq(smooth_f.primal_shape, l=epsilon / 2.)
self._smooth_function_linear = smooth_function(smooth_f, self._linear,
self._quadratic)
self._solver = FISTA(self._smooth_function_linear)
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(smooth_f, "L"):
self._backtrack = False
self._smooth_function_linear.L = smooth_f.L + epsilon
else:
self._backtrack = True
self._have_solved_once = False
self.epsilon = epsilon
def smooth_eval(self, x, mode='both'):
"""
Evaluate the conjugate function and/or its gradient
if mode == 'both', return both function value and gradient
if mode == 'grad', return only the gradient
if mode == 'func', return only the function value
"""
self._solver.debug = False
self._linear.vector[:] = -x
self._solver.fit(max_its=1000, tol=1.0e-08, backtrack=self._backtrack)
minimizer = self._smooth_function_linear.coefs
if mode == 'both':
v = self._smooth_function_linear.smooth_eval(minimizer,
mode='func')
return -v, minimizer
elif mode == 'func':
v = self._smooth_function_linear.smooth_eval(minimizer,
mode='func')
return -v
elif mode == 'grad':
return minimizer
else:
raise ValueError("mode incorrectly specified")
class conjugate(object):
def __init__(self, smooth_f, epsilon=0.01):
self._smooth_function = smooth_f
self._linear = linear(np.zeros(smooth_f.primal_shape))
self._quadratic = l2normsq(smooth_f.primal_shape, l=epsilon/2.)
self._smooth_function_linear = smooth_function(smooth_f, self._linear, self._quadratic)
self._solver = FISTA(self._smooth_function_linear)
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(smooth_f, "L"):
self._backtrack = False
self._smooth_function_linear.L = smooth_f.L + epsilon
else:
self._backtrack = True
self._have_solved_once = False
self.epsilon = epsilon
def smooth_eval(self, x, mode='both'):
"""
Evaluate the conjugate function and/or its gradient
if mode == 'both', return both function value and gradient
if mode == 'grad', return only the gradient
if mode == 'func', return only the function value
"""
self._solver.debug = False
self._linear.vector[:] = -x
self._solver.fit(max_its=1000, tol=1.0e-08, backtrack=self._backtrack)
minimizer = self._smooth_function_linear.coefs
if mode == 'both':
v = self._smooth_function_linear.smooth_eval(minimizer, mode='func')
return -v, minimizer
elif mode == 'func':
v = self._smooth_function_linear.smooth_eval(minimizer, mode='func')
return -v
elif mode == 'grad':
return minimizer
else:
raise ValueError("mode incorrectly specified")
def test_group_lasso_sparse(n=100):
def selector(p, slice):
return np.identity(p)[slice]
def selector_sparse(p, slice):
return sparse.csr_matrix(np.identity(p)[slice])
X = np.random.standard_normal((1000, 500))
Y = np.random.standard_normal((1000, ))
penalties = [
l2norm(selector(500, slice(i * 100, (i + 1) * 100)), l=.1)
for i in range(5)
]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
regloss = squaredloss(X, Y)
p = regloss.add_seminorm(group_lasso)
solver = FISTA(p)
solver.debug = True
t1 = time.time()
vals = solver.fit(max_its=2000, min_its=20, tol=1e-8)
soln1 = solver.problem.coefs
t2 = time.time()
dt1 = t2 - t1
penalties = [
l2norm(selector_sparse(500, slice(i * 100, (i + 1) * 100)), l=.1)
for i in range(5)
]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
regloss = squaredloss(X, Y)
p = regloss.add_seminorm(group_lasso)
solver = FISTA(p)
solver.debug = True
t1 = time.time()
vals = solver.fit(max_its=2000, min_its=20, tol=1e-8)
soln2 = solver.problem.coefs
t2 = time.time()
dt2 = t2 - t1
print "Times", dt1, dt2
print soln1[range(10)]
print soln2[range(10)]
np.testing.assert_almost_equal(soln1, soln2)
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 __init__(self, smooth_f, epsilon=0.01):
self._smooth_function = smooth_f
self._linear = linear(np.zeros(smooth_f.primal_shape))
self._quadratic = l2normsq(smooth_f.primal_shape, l=epsilon/2.)
self._smooth_function_linear = smooth_function(smooth_f, self._linear, self._quadratic)
self._solver = FISTA(self._smooth_function_linear)
#XXX we need a better way to pass around the Lipschitz constant
# should go in the container class
if hasattr(smooth_f, "L"):
self._backtrack = False
self._smooth_function_linear.L = smooth_f.L + epsilon
else:
self._backtrack = True
self._have_solved_once = False
self.epsilon = epsilon
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_group_lasso_sparse(n=100):
def selector(p, slice):
return np.identity(p)[slice]
def selector_sparse(p, slice):
return sparse.csr_matrix(np.identity(p)[slice])
X = np.random.standard_normal((1000,500))
Y = np.random.standard_normal((1000,))
penalties = [l2norm(selector(500, slice(i*100,(i+1)*100)), l=.1) for i in range(5)]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
regloss = squaredloss(X,Y)
p=regloss.add_seminorm(group_lasso)
solver=FISTA(p)
solver.debug = True
t1 = time.time()
vals = solver.fit(max_its=2000, min_its=20,tol=1e-8)
soln1 = solver.problem.coefs
t2 = time.time()
dt1 = t2 - t1
penalties = [l2norm(selector_sparse(500, slice(i*100,(i+1)*100)), l=.1) for i in range(5)]
penalties[0].l = 250.
penalties[1].l = 225.
penalties[2].l = 150.
penalties[3].l = 100.
group_lasso = seminorm(*penalties)
regloss = squaredloss(X,Y)
p=regloss.add_seminorm(group_lasso)
solver=FISTA(p)
solver.debug = True
t1 = time.time()
vals = solver.fit(max_its=2000, min_its=20,tol=1e-8)
soln2 = solver.problem.coefs
t2 = time.time()
dt2 = t2- t1
print "Times", dt1, dt2
print soln1[range(10)]
print soln2[range(10)]
np.testing.assert_almost_equal(soln1,soln2)
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]
