def test_nonnegative_positive_part(debug=False):
"""
This test verifies that using nonnegative constraint
with a linear term, with some unpenalized terms yields the same result
as using separable with constrained_positive_part and nonnegative
"""
import numpy as np
import regreg.api as rr
import regreg.atoms as rra
# N - number of data points
# P - number of columns in design == number of betas
N, P = 40, 30
# an arbitrary positive offset for data and design
offset = 2
# data
Y = np.random.normal(size=(N, )) + offset
# design - with ones as last column
X = np.ones((N, P))
X[:, :-1] = np.random.normal(size=(N, P - 1)) + offset
# coef for loss
coef = 0.5
# lagrange for penalty
lagrange = .1
# Loss function (squared difference between fitted and actual data)
loss = rr.quadratic_loss.affine(X, -Y, coef=coef)
# Penalty using nonnegative, leave the last 5 unpenalized but
# nonnegative
weights = np.ones(P) * lagrange
weights[-5:] = 0
linq = rr.identity_quadratic(0, 0, weights, 0)
penalty = rr.nonnegative(P, quadratic=linq)
# Solution
composite_form = rr.separable_problem.singleton(penalty, loss)
solver = rr.FISTA(composite_form)
solver.debug = debug
solver.fit(tol=1.0e-12, min_its=200)
coefs = solver.composite.coefs
# using the separable penalty, only penalize the first
# 25 coefficients with constrained_positive_part
penalties_s = [
rr.constrained_positive_part(25, lagrange=lagrange),
rr.nonnegative(5)
]
groups_s = [slice(0, 25), slice(25, 30)]
penalty_s = rr.separable((P, ), penalties_s, groups_s)
composite_form_s = rr.separable_problem.singleton(penalty_s, loss)
solver_s = rr.FISTA(composite_form_s)
solver_s.debug = debug
solver_s.fit(tol=1.0e-12, min_its=200)
coefs_s = solver_s.composite.coefs
nt.assert_true(
np.linalg.norm(coefs - coefs_s) / np.linalg.norm(coefs) < 1.0e-02)
def test_nonnegative_positive_part(debug=False):
"""
This test verifies that using nonnegative constraint
with a linear term, with some unpenalized terms yields the same result
as using separable with constrained_positive_part and nonnegative
"""
import numpy as np
import regreg.api as rr
import regreg.atoms as rra
# N - number of data points
# P - number of columns in design == number of betas
N, P = 40, 30
# an arbitrary positive offset for data and design
offset = 2
# data
Y = np.random.normal(size=(N,)) + offset
# design - with ones as last column
X = np.ones((N,P))
X[:,:-1] = np.random.normal(size=(N,P-1)) + offset
# coef for loss
coef = 0.5
# lagrange for penalty
lagrange = .1
# Loss function (squared difference between fitted and actual data)
loss = rr.quadratic.affine(X, -Y, coef=coef)
# Penalty using nonnegative, leave the last 5 unpenalized but
# nonnegative
weights = np.ones(P) * lagrange
weights[-5:] = 0
linq = rr.identity_quadratic(0,0,weights,0)
penalty = rr.nonnegative(P, quadratic=linq)
# Solution
composite_form = rr.separable_problem.singleton(penalty, loss)
solver = rr.FISTA(composite_form)
solver.debug = debug
solver.fit(tol=1.0e-12, min_its=200)
coefs = solver.composite.coefs
# using the separable penalty, only penalize the first
# 25 coefficients with constrained_positive_part
penalties_s = [rr.constrained_positive_part(25, lagrange=lagrange),
rr.nonnegative(5)]
groups_s = [slice(0,25), slice(25,30)]
penalty_s = rr.separable((P,), penalties_s,
groups_s)
composite_form_s = rr.separable_problem.singleton(penalty_s, loss)
solver_s = rr.FISTA(composite_form_s)
solver_s.debug = debug
solver_s.fit(tol=1.0e-12, min_its=200)
coefs_s = solver_s.composite.coefs
nt.assert_true(np.linalg.norm(coefs - coefs_s) / np.linalg.norm(coefs) < 1.0e-02)
def test_centering_fit_inplace(debug=False):
# N - number of data points
# P - number of columns in design == number of betas
N, P = 40, 30
# an arbitrary positive offset for data and design
offset = 2
# design - with ones as last column
X = np.random.normal(size=(N, P)) + offset
L = rr.normalize(X, center=True, scale=False, inplace=True)
# X should have been normalized in place
np.testing.assert_almost_equal(np.sum(X, 0), 0)
# data
Y = np.random.normal(size=(N, )) + offset
# coef for loss
coef = 0.5
# lagrange for penalty
lagrange = .1
# Loss function (squared difference between fitted and actual data)
loss = rr.quadratic_loss.affine(L, -Y, coef=coef)
penalties = [
rr.constrained_positive_part(25, lagrange=lagrange),
rr.nonnegative(5)
]
groups = [slice(0, 25), slice(25, 30)]
penalty = rr.separable((P, ), penalties, groups)
initial = np.random.standard_normal(P)
composite_form = rr.separable_problem.fromatom(penalty, loss)
solver = rr.FISTA(composite_form)
solver.debug = debug
solver.fit(tol=1.0e-12, min_its=200)
coefs = solver.composite.coefs
# Solve the problem with X, which has been normalized in place
loss2 = rr.quadratic_loss.affine(X, -Y, coef=coef)
initial2 = np.random.standard_normal(P)
composite_form2 = rr.separable_problem.fromatom(penalty, loss2)
solver2 = rr.FISTA(composite_form2)
solver2.debug = debug
solver2.fit(tol=1.0e-12, min_its=200)
coefs2 = solver2.composite.coefs
for _ in range(10):
beta = np.random.standard_normal(P)
g1 = loss.smooth_objective(beta, mode='grad')
g2 = loss2.smooth_objective(beta, mode='grad')
np.testing.assert_almost_equal(g1, g2)
b1 = penalty.proximal(sq(1, beta, g1, 0))
b2 = penalty.proximal(sq(1, beta, g2, 0))
np.testing.assert_almost_equal(b1, b2)
f1 = composite_form.objective(beta)
f2 = composite_form2.objective(beta)
np.testing.assert_almost_equal(f1, f2)
np.testing.assert_almost_equal(composite_form.objective(coefs),
composite_form.objective(coefs2))
np.testing.assert_almost_equal(composite_form2.objective(coefs),
composite_form2.objective(coefs2))
nt.assert_true(
np.linalg.norm(coefs - coefs2) /
max(np.linalg.norm(coefs), 1) < 1.0e-04)
def test_centering_fit_inplace(debug=False):
# N - number of data points
# P - number of columns in design == number of betas
N, P = 40, 30
# an arbitrary positive offset for data and design
offset = 2
# design - with ones as last column
X = np.random.normal(size=(N,P)) + offset
L = rr.normalize(X, center=True, scale=False, inplace=True)
# X should have been normalized in place
np.testing.assert_almost_equal(np.sum(X, 0), 0)
# data
Y = np.random.normal(size=(N,)) + offset
# coef for loss
coef = 0.5
# lagrange for penalty
lagrange = .1
# Loss function (squared difference between fitted and actual data)
loss = rr.quadratic.affine(L, -Y, coef=coef)
penalties = [rr.constrained_positive_part(25, lagrange=lagrange),
rr.nonnegative(5)]
groups = [slice(0,25), slice(25,30)]
penalty = rr.separable((P,), penalties,
groups)
initial = np.random.standard_normal(P)
composite_form = rr.separable_problem.fromatom(penalty, loss)
solver = rr.FISTA(composite_form)
solver.debug = debug
solver.fit(tol=1.0e-12, min_its=200)
coefs = solver.composite.coefs
# Solve the problem with X, which has been normalized in place
loss2 = rr.quadratic.affine(X, -Y, coef=coef)
initial2 = np.random.standard_normal(P)
composite_form2 = rr.separable_problem.fromatom(penalty, loss2)
solver2 = rr.FISTA(composite_form2)
solver2.debug = debug
solver2.fit(tol=1.0e-12, min_its=200)
coefs2 = solver2.composite.coefs
for _ in range(10):
beta = np.random.standard_normal(P)
g1 = loss.smooth_objective(beta, mode='grad')
g2 = loss2.smooth_objective(beta, mode='grad')
np.testing.assert_almost_equal(g1, g2)
b1 = penalty.proximal(sq(1, beta, g1,0))
b2 = penalty.proximal(sq(1, beta, g2,0))
np.testing.assert_almost_equal(b1, b2)
f1 = composite_form.objective(beta)
f2 = composite_form2.objective(beta)
np.testing.assert_almost_equal(f1, f2)
np.testing.assert_almost_equal(composite_form.objective(coefs), composite_form.objective(coefs2))
np.testing.assert_almost_equal(composite_form2.objective(coefs), composite_form2.objective(coefs2))
nt.assert_true(np.linalg.norm(coefs - coefs2) / max(np.linalg.norm(coefs),1) < 1.0e-04)
def test_scaling_and_centering_intercept_fit(debug=False):
# N - number of data points
# P - number of columns in design == number of betas
N, P = 40, 30
# an arbitrary positive offset for data and design
offset = 2
# design - with ones as last column
X = np.random.normal(size=(N, P)) + 0 * offset
X2 = X - X.mean(0)[None, :]
X2 = X2 / np.std(X2, 0, ddof=1)[None, :]
X2 = np.hstack([np.ones((X2.shape[0], 1)), X2])
L = rr.normalize(X, center=True, scale=True, intercept=True)
# data
Y = np.random.normal(size=(N, )) + offset
# lagrange for penalty
lagrange = .1
# Loss function (squared difference between fitted and actual data)
loss = rr.squared_error(L, Y)
penalties = [
rr.constrained_positive_part(25, lagrange=lagrange),
rr.nonnegative(5)
]
groups = [slice(0, 25), slice(25, 30)]
penalty = rr.separable((P + 1, ), penalties, groups)
initial = np.random.standard_normal(P + 1)
composite_form = rr.separable_problem.fromatom(penalty, loss)
solver = rr.FISTA(composite_form)
solver.debug = debug
solver.fit(tol=1.0e-12, min_its=200)
coefs = solver.composite.coefs
# Solve the problem with X2
loss2 = rr.squared_error(X2, Y)
initial2 = np.random.standard_normal(P + 1)
composite_form2 = rr.separable_problem.fromatom(penalty, loss2)
solver2 = rr.FISTA(composite_form2)
solver2.debug = debug
solver2.fit(tol=1.0e-12, min_its=200)
coefs2 = solver2.composite.coefs
for _ in range(10):
beta = np.random.standard_normal(P + 1)
g1 = loss.smooth_objective(beta, mode='grad')
g2 = loss2.smooth_objective(beta, mode='grad')
np.testing.assert_almost_equal(g1, g2)
b1 = penalty.proximal(sq(1, beta, g1, 0))
b2 = penalty.proximal(sq(1, beta, g2, 0))
np.testing.assert_almost_equal(b1, b2)
f1 = composite_form.objective(beta)
f2 = composite_form2.objective(beta)
np.testing.assert_almost_equal(f1, f2)
np.testing.assert_almost_equal(composite_form.objective(coefs),
composite_form.objective(coefs2))
np.testing.assert_almost_equal(composite_form2.objective(coefs),
composite_form2.objective(coefs2))
nt.assert_true(
np.linalg.norm(coefs - coefs2) /
max(np.linalg.norm(coefs), 1) < 1.0e-04)