def test_changepoint_scaled():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(np.sqrt(M.sizes) * X.adjoint_map(Y) / (1 + np.sqrt(np.log(M.sizes)))).max()
penalty = rr.weighted_l1norm((1 + np.sqrt(np.log(M.sizes))) / np.sqrt(M.sizes), lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
if INTERACTIVE:
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
plt.show()
def test_nesta_nonnegative():
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
A = np.random.standard_normal((q, p))
coef = 10 * np.fabs(np.random.standard_normal(q)) + 1
coef[:2] = -0.2
beta = np.dot(np.linalg.pinv(A), coef)
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X, Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss,
penalty,
constraint,
max_iters=300,
coef_tol=1.e-4,
tol=1.e-4)
print np.dot(A, primal)
assert_almost_nonnegative(np.dot(A, primal), tol=1.e-3)
def test_nesta_nonnegative():
state = np.random.get_state()
np.random.seed(10)
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
A = np.random.standard_normal((q, p))
coef = 10 * np.fabs(np.random.standard_normal(q)) + 1
coef[:2] = -0.2
beta = np.dot(np.linalg.pinv(A), coef)
print(r'\beta', beta)
print(r'A\beta', np.dot(A, beta))
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X, Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss,
penalty,
constraint,
max_iters=300,
coef_tol=1.e-10,
tol=1.e-10)
print(r'A \hat{\beta}', np.dot(A, primal))
assert_almost_nonnegative(np.dot(A, primal), tol=1.e-3)
np.random.set_state(state)
def test_outputs_SLOPE_weights(n=500, p=100, signal_fac=1., s=5, sigma=3., rho=0.35):
inst = gaussian_instance
signal = np.sqrt(signal_fac * 2. * np.log(p))
X, Y, beta = inst(n=n,
p=p,
signal=signal,
s=s,
equicorrelated=False,
rho=rho,
sigma=sigma,
random_signs=True)[:3]
sigma_ = np.sqrt(np.linalg.norm(Y - X.dot(np.linalg.pinv(X).dot(Y))) ** 2 / (n - p))
r_beta, r_E, r_lambda_seq, r_sigma = slope_R(X,
Y,
W = None,
normalize = True,
choice_weights = "gaussian",
sigma = sigma_)
print("estimated sigma", sigma_, r_sigma)
print("weights output by R", r_lambda_seq)
print("output of est coefs R", r_beta)
pen = slope_atom(r_sigma * r_lambda_seq, lagrange=1.)
loss = rr.squared_error(X, Y)
problem = rr.simple_problem(loss, pen)
soln = problem.solve()
print("output of est coefs python", soln)
print("relative difference in solns", np.linalg.norm(soln-r_beta)/np.linalg.norm(r_beta))
def test_using_SLOPE_weights():
n, p = 500, 50
X = np.random.standard_normal((n, p))
#Y = np.random.standard_normal(n)
X -= X.mean(0)[None, :]
X /= (X.std(0)[None, :] * np.sqrt(n))
beta = np.zeros(p)
beta[:5] = 5.
Y = X.dot(beta) + np.random.standard_normal(n)
output_R = fit_slope_R(X, Y, W = None, normalize = True, choice_weights = "bhq")
r_beta = output_R[0]
r_lambda_seq = output_R[2]
W = r_lambda_seq
pen = slope(W, lagrange=1.)
loss = rr.squared_error(X, Y)
problem = rr.simple_problem(loss, pen)
soln = problem.solve(tol=1.e-14, min_its=500)
# we get a better objective value
nt.assert_true(problem.objective(soln) < problem.objective(np.asarray(r_beta)))
nt.assert_true(np.linalg.norm(soln - r_beta) < 1.e-6 * np.linalg.norm(soln))
def test_nesta_lasso():
n, p = 1000, 20
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 30
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X, Y)
penalty = rr.l1norm(p, lagrange=4.)
# using nesta
z = rr.zero(p)
primal, dual = rr.nesta(loss,
z,
penalty,
tol=1.e-10,
epsilon=2.**(-np.arange(30)))
# using simple problem
problem = rr.simple_problem(loss, penalty)
problem.solve()
nt.assert_true(
np.linalg.norm(primal - problem.coefs) /
np.linalg.norm(problem.coefs) < 1.e-3)
def test_conjugate_sqerror():
"""
This verifies the conjugate class can compute the conjugate
of a quadratic function.
"""
ridge_coef = 0.4
X = np.random.standard_normal((10,4))
Y = np.random.standard_normal(10)
l = rr.squared_error(X, Y)
q = rr.identity_quadratic(ridge_coef,0,0,0)
atom_conj = rr.conjugate(l, q, tol=1.e-12, min_its=100)
w = np.random.standard_normal(4)
u11, u12 = atom_conj.smooth_objective(w)
# check that objective is half of squared error
np.testing.assert_allclose(l.smooth_objective(w, mode='func'), 0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
np.testing.assert_allclose(atom_conj.atom.smooth_objective(w, mode='func'), 0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
XTX = np.dot(X.T, X)
XTXi = np.linalg.pinv(XTX)
quadratic_term = XTX + ridge_coef * np.identity(4)
linear_term = np.dot(X.T, Y) + w
b = u22 = np.linalg.solve(quadratic_term, linear_term)
u21 = (w*u12).sum() - l.smooth_objective(u12, mode='func') - q.objective(u12, mode='func')
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
np.testing.assert_approx_equal(u11, u21)
def test_using_SLOPE_weights():
n, p = 500, 50
X = np.random.standard_normal((n, p))
#Y = np.random.standard_normal(n)
X -= X.mean(0)[None, :]
X /= (X.std(0)[None, :] * np.sqrt(n))
beta = np.zeros(p)
beta[:5] = 5.
Y = X.dot(beta) + np.random.standard_normal(n)
output_R = fit_slope_R(X, Y)
r_beta = np.squeeze(output_R[0])[:, 3]
r_lambda_seq = np.array(output_R[2]).reshape(-1)
alpha = output_R[-1]
W = np.asarray(r_lambda_seq * alpha[3]).reshape(-1)
pen = slope(W, lagrange=1.)
loss = rr.squared_error(X, Y)
problem = rr.simple_problem(loss, pen)
soln = problem.solve(tol=1.e-14, min_its=500)
# we get a better objective value
nt.assert_true(
problem.objective(soln) < problem.objective(np.asarray(r_beta)))
nt.assert_true(
np.linalg.norm(soln - r_beta) < 1.e-6 * np.linalg.norm(soln))
def test_nesta_nonnegative():
state = np.random.get_state()
np.random.seed(10)
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
A = np.random.standard_normal((q,p))
coef = 10 * np.fabs(np.random.standard_normal(q)) + 1
coef[:2] = -0.2
beta = np.dot(np.linalg.pinv(A), coef)
print(r'\beta', beta)
print(r'A\beta', np.dot(A, beta))
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X,Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss, penalty, constraint, max_iters=300, coef_tol=1.e-10, tol=1.e-10)
print(r'A \hat{\beta}', np.dot(A, primal))
assert_almost_nonnegative(np.dot(A,primal), tol=1.e-3)
np.random.set_state(state)
def test_nesta_lasso():
n, p = 1000, 20
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 30
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X,Y)
penalty = rr.l1norm(p, lagrange=2.)
# using nesta
z = rr.zero(p)
primal, dual = rr.nesta(loss, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p))
# using simple problem
problem = rr.simple_problem(loss, penalty)
problem.solve()
nt.assert_true(np.linalg.norm(primal - problem.coefs) / np.linalg.norm(problem.coefs) < 1.e-3)
# test None as smooth_atom
rr.nesta(None, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p))
# using coefficients to stop
rr.nesta(loss, z, penalty, tol=1.e-10,
epsilon=2.**(-np.arange(30)),
initial_dual=np.zeros(p),
coef_stop=True)
def test_conjugate_sqerror():
"""
This verifies the conjugate class can compute the conjugate
of a quadratic function.
"""
ridge_coef = 0.4
X = np.random.standard_normal((10, 4))
Y = np.random.standard_normal(10)
l = rr.squared_error(X, Y)
q = rr.identity_quadratic(ridge_coef, 0, 0, 0)
atom_conj = rr.conjugate(l, q, tol=1.e-12, min_its=100)
w = np.random.standard_normal(4)
u11, u12 = atom_conj.smooth_objective(w)
# check that objective is half of squared error
np.testing.assert_allclose(l.smooth_objective(w, mode='func'),
0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
np.testing.assert_allclose(atom_conj.atom.smooth_objective(w, mode='func'),
0.5 * np.linalg.norm(Y - np.dot(X, w))**2)
XTX = np.dot(X.T, X)
XTXi = np.linalg.pinv(XTX)
quadratic_term = XTX + ridge_coef * np.identity(4)
linear_term = np.dot(X.T, Y) + w
b = u22 = np.linalg.solve(quadratic_term, linear_term)
u21 = (w * u12).sum() - l.smooth_objective(u12, mode='func') - q.objective(
u12, mode='func')
np.testing.assert_allclose(u12, u22, rtol=1.0e-05)
np.testing.assert_approx_equal(u11, u21)
def __init__(self, X, Y):
self.X = X
n, p = X.shape
self.Y = Y
self._constant_term = (Y**2).sum()
if n > p:
self._quadratic_term = X.T.dot(X)
self._linear_term = -2 * X.T.dot(Y)
self._sqerror = rr.squared_error(X, Y)
def __init__(self, X, Y):
self.X = rr.astransform(X)
n, p = self.X.output_shape[0], self.X.input_shape[0]
self.Y = Y
if n > p:
self._quadratic_term = np.dot(X.T, X)
self._linear_term = -2 * np.dot(X.T, Y)
self._constant_term = (Y**2).sum()
self._sqerror = rr.squared_error(X, Y)
def test_weighted_l1_bound_loose():
n, p = 100, 10
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
beta = np.linalg.pinv(X).dot(Y)
bound = 2 * np.fabs(beta).sum()
atom = rr.weighted_l1norm(np.ones(p), bound=bound)
loss = rr.squared_error(X, Y)
problem = rr.simple_problem(loss, atom)
soln = problem.solve(tol=1.e-12, min_its=100)
npt.assert_allclose(soln, beta)
def test_path_group_lasso():
'''
this test looks at the paths of three different parameterizations
of the same problem
'''
n = 100
X = np.random.standard_normal((n, 10))
U = np.random.standard_normal((n, 2))
Y = np.random.standard_normal(100)
betaX = np.array([3, 4, 5, 0, 0] + [0] * 5)
betaU = np.array([10, -5])
Y += (np.dot(X, betaX) + np.dot(U, betaU)) * 5
Xn = rr.normalize(np.hstack([np.ones((100, 1)), X]),
inplace=True,
center=True,
scale=True,
intercept_column=0).normalized_array()
lasso = rr.lasso.squared_error(Xn[:, 1:],
Y,
penalty_structure=[0] * 7 + [1] * 3,
nstep=10)
sol = lasso.main(inner_tol=1.e-12, verbose=True)
beta = np.array(sol['beta'].todense())
sols = []
sols_sep = []
for l in sol['lagrange']:
loss = rr.squared_error(Xn, Y, coef=1. / n)
penalty = rr.group_lasso([rr.UNPENALIZED] + [0] * 7 + [1] * 3,
l) # matrix contains an intercept...
problem = rr.simple_problem(loss, penalty)
sols.append(problem.solve(tol=1.e-12).copy())
sep = rr.separable((11, ), [
rr.l2norm((7, ),
np.sqrt(7) * l),
rr.l2norm((3, ),
np.sqrt(3) * l)
], [np.arange(1, 8), np.arange(8, 11)])
sep_problem = rr.simple_problem(loss, sep)
sols_sep.append(sep_problem.solve(tol=1.e-12).copy())
sols = np.array(sols).T
sols_sep = np.array(sols_sep).T
nt.assert_true(
np.linalg.norm(beta - sols) / (1 + np.linalg.norm(beta)) <= 1.e-4)
nt.assert_true(
np.linalg.norm(beta - sols_sep) / (1 + np.linalg.norm(beta)) <= 1.e-4)
def __init__(self, X, Y, quadratic=None, initial=None, offset=None):
rr.smooth_atom.__init__(self,
rr.astransform(X).input_shape,
coef=1.,
offset=offset,
quadratic=quadratic,
initial=initial)
self.X = X
self.Y = Y
self.data = (X, Y)
self._sqerror = rr.squared_error(X, Y)
def __init__(self, X, Y,
quadratic=None,
initial=None,
offset=None):
rr.smooth_atom.__init__(self,
X.input_shape,
coef=1.,
offset=offset,
quadratic=quadratic,
initial=initial)
self.X = X
self.Y = Y
self._sqerror = rr.squared_error(X, Y)
def test_nesta_nonnegative():
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 3
Y = np.random.standard_normal(n) + np.dot(X, beta)
A = np.random.standard_normal((q,p))
loss = rr.squared_error(X,Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss, penalty, constraint)
assert_almost_nonnegative(np.dot(A,primal))
def test_class():
"""
runs several class methods on generic instance
"""
n, p = 100, 20
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
pen = rr.l1norm(p, lagrange=1.0)
problem = rr.simple_problem(loss, pen)
problem.latexify()
for debug, coef_stop, max_its in product([True, False], [True, False], [5, 100]):
rr.gengrad(problem, rr.power_L(X) ** 2, max_its=max_its, debug=debug, coef_stop=coef_stop)
def test_admm(n=100, p=10):
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
D = np.identity(p)
pen = rr.l1norm(p, lagrange=1.5)
ADMM = admm_problem(loss, pen, ra.astransform(D), 0.5)
ADMM.solve(niter=1000)
coef1 = ADMM.atom_coefs
problem2 = rr.simple_problem(loss, pen)
coef2 = problem2.solve(tol=1.e-12, min_its=500)
np.testing.assert_allclose(coef1, coef2, rtol=1.e-3, atol=1.e-4)
def test_nesta_nonnegative():
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
beta = np.zeros(p)
beta[:4] = 3
Y = np.random.standard_normal(n) + np.dot(X, beta)
A = np.random.standard_normal((q, p))
loss = rr.squared_error(X, Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss, penalty, constraint)
assert_almost_nonnegative(np.dot(A, primal))
def test_solve_QP():
"""
Check the R coordinate descent LASSO solver
"""
n, p = 100, 200
lam = 10
np.random.seed(0)
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
pen = rr.l1norm(p, lagrange=lam)
problem = rr.simple_problem(loss, pen)
soln = problem.solve(min_its=500, tol=1.e-12)
import rpy2.robjects.numpy2ri
rpy2.robjects.numpy2ri.activate()
tol = 1.e-5
rpy.r.assign('X', X)
rpy.r.assign('Y', Y)
rpy.r.assign('lam', lam)
R_code = """
library(selectiveInference)
p = ncol(X)
soln_R = rep(0, p)
grad = -t(X) %*% Y
ever_active = c(1, rep(0, p-1))
nactive = as.integer(1)
kkt_tol = 1.e-12
objective_tol = 1.e-12
maxiter = 500
soln_R = selectiveInference:::solve_QP(t(X) %*% X, lam, maxiter, soln_R, -t(X) %*% Y, grad, ever_active, nactive, kkt_tol, objective_tol, p)$soln
"""
rpy.r(R_code)
soln_R = np.asarray(rpy.r('soln_R'))
rpy2.robjects.numpy2ri.deactivate()
yield np.testing.assert_allclose, soln, soln_R, tol, tol, False, 'checking coordinate QP solver'
def test_path_group_lasso():
"""
this test looks at the paths of three different parameterizations
of the same problem
"""
n = 100
X = np.random.standard_normal((n, 10))
U = np.random.standard_normal((n, 2))
Y = np.random.standard_normal(100)
betaX = np.array([3, 4, 5, 0, 0] + [0] * 5)
betaU = np.array([10, -5])
Y += (np.dot(X, betaX) + np.dot(U, betaU)) * 5
Xn = rr.normalize(
np.hstack([np.ones((100, 1)), X]), inplace=True, center=True, scale=True, intercept_column=0
).normalized_array()
lasso = rr.lasso.squared_error(Xn[:, 1:], Y, penalty_structure=[0] * 7 + [1] * 3, nstep=10)
sol = lasso.main(inner_tol=1.0e-12, verbose=True)
beta = np.array(sol["beta"].todense())
sols = []
sols_sep = []
for l in sol["lagrange"]:
loss = rr.squared_error(Xn, Y, coef=1.0 / n)
penalty = rr.mixed_lasso([rr.UNPENALIZED] + [0] * 7 + [1] * 3, lagrange=l) # matrix contains an intercept...
problem = rr.simple_problem(loss, penalty)
sols.append(problem.solve(tol=1.0e-12).copy())
sep = rr.separable(
(11,),
[rr.l2norm((7,), np.sqrt(7) * l), rr.l2norm((3,), np.sqrt(3) * l)],
[np.arange(1, 8), np.arange(8, 11)],
)
sep_problem = rr.simple_problem(loss, sep)
sols_sep.append(sep_problem.solve(tol=1.0e-12).copy())
sols = np.array(sols).T
sols_sep = np.array(sols_sep).T
nt.assert_true(np.linalg.norm(beta - sols) / (1 + np.linalg.norm(beta)) <= 1.0e-4)
nt.assert_true(np.linalg.norm(beta - sols_sep) / (1 + np.linalg.norm(beta)) <= 1.0e-4)
def test_nesta_nonnegative():
n, p, q = 1000, 20, 5
X = np.random.standard_normal((n, p))
A = np.random.standard_normal((q,p))
coef = 10 * np.fabs(np.random.standard_normal(q)) + 1
coef[:2] = -0.2
beta = np.dot(np.linalg.pinv(A), coef)
Y = np.random.standard_normal(n) + np.dot(X, beta)
loss = rr.squared_error(X,Y)
penalty = rr.l1norm(p, lagrange=0.2)
constraint = rr.nonnegative.linear(A)
primal, dual = rr.nesta(loss, penalty, constraint, max_iters=300, coef_tol=1.e-4, tol=1.e-4)
print np.dot(A, primal)
assert_almost_nonnegative(np.dot(A,primal), tol=1.e-3)
def test_choose_parameter(delta=2, p=60):
signal = np.zeros(p)
signal[(p//2):] += delta
Z = np.random.standard_normal(p) + signal
p = Z.shape[0]
M = multiscale(p)
M.scaling = np.sqrt(M.sizes)
lam = choose_tuning_parameter(M)
weights = (lam + np.sqrt(2 * np.log(p / M.sizes))) / np.sqrt(p)
Z0 = Z - Z.mean()
loss = rr.squared_error(ra.adjoint(M), Z0)
penalty = rr.weighted_l1norm(weights, lagrange=1.)
problem = rr.simple_problem(loss, penalty)
coef = problem.solve()
active = coef != 0
if active.sum():
X = M.form_matrix(M.slices[active])[0]
def __init__(self, X, Y, l_theory, l_min, l_1se, sigma_reid):
parametric_method.__init__(self, X, Y, l_theory, l_min, l_1se, sigma_reid)
self.lagrange = l_1se * np.ones(X.shape[1])
n, p = self.X.shape
n1 = int(self.selection_frac * n)
X1, X2 = self.X1, self.X2 = self.X[:n1], self.X[n1:]
Y1, Y2 = self.Y1, self.Y2 = self.Y[:n1], self.Y[n1:]
pen = rr.weighted_l1norm(np.sqrt(n1) * self.lagrange, lagrange=1.)
loss = rr.squared_error(X1, Y1)
problem = rr.simple_problem(loss, pen)
soln = problem.solve()
self.active_set = np.nonzero(soln)[0]
self.signs = np.sign(soln)[self.active_set]
self._fit = True
def test_class():
'''
runs several class methods on generic instance
'''
n, p = 100, 20
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y)
pen = rr.l1norm(p, lagrange=1.)
problem = rr.simple_problem(loss, pen)
problem.latexify()
for debug, coef_stop, max_its in product([True, False], [True, False],
[5, 100]):
rr.gengrad(problem,
rr.power_L(X)**2,
max_its=max_its,
debug=debug,
coef_stop=coef_stop)
def test_changepoint():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(X.adjoint_map(Y)).max()
penalty = rr.l1norm(X.input_shape, lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
def test_changepoint():
p = 150
M = multiscale(p)
M.minsize = 10
X = ra.adjoint(M)
Y = np.random.standard_normal(p)
Y[20:50] += 8
Y += 2
meanY = Y.mean()
lammax = np.fabs(X.adjoint_map(Y)).max()
penalty = rr.l1norm(X.input_shape, lagrange=0.5*lammax)
loss = rr.squared_error(X, Y - meanY)
problem = rr.simple_problem(loss, penalty)
soln = problem.solve()
Yhat = X.linear_map(soln)
Yhat += meanY
plt.scatter(np.arange(p), Y)
plt.plot(np.arange(p), Yhat)
plt.show()
def highdim_model_inference(X,
y,
truth,
selection_algorithm,
sampler,
lam_min,
dispersion,
success_params=(1, 1),
fit_probability=keras_fit,
fit_args={
'epochs': 10,
'sizes': [100] * 5,
'dropout': 0.,
'activation': 'relu'
},
alpha=0.1,
B=2000,
naive=True,
learner_klass=mixture_learner,
how_many=None):
n, p = X.shape
XTX = X.T.dot(X)
instance_hash = hashlib.md5()
instance_hash.update(X.tobytes())
instance_hash.update(y.tobytes())
instance_hash.update(truth.tobytes())
instance_id = instance_hash.hexdigest()
# run selection algorithm
observed_set = repeat_selection(selection_algorithm, sampler,
*success_params)
observed_list = sorted(observed_set)
# observed debiased LASSO estimate
loss = rr.squared_error(X, y)
pen = rr.l1norm(p, lagrange=lam_min)
problem = rr.simple_problem(loss, pen)
soln = problem.solve()
grad = X.T.dot(X.dot(soln) - y) # gradient at beta_hat
M = pseudoinverse_debiasing_matrix(X, observed_list)
observed_target = soln[observed_list] - M.dot(grad)
tmp = X.dot(M.T)
target_cov = tmp.T.dot(tmp) * dispersion
cross_cov = np.identity(p)[:, observed_list] * dispersion
if len(observed_list) > 0:
if how_many is None:
how_many = len(observed_list)
observed_list = observed_list[:how_many]
# find the target, based on the observed outcome
(pivots, covered, lengths, pvalues, lower,
upper) = [], [], [], [], [], []
targets = []
true_target = truth[observed_list]
results = infer_set_target(selection_algorithm,
observed_set,
observed_list,
sampler,
observed_target,
target_cov,
cross_cov,
hypothesis=true_target,
fit_probability=fit_probability,
fit_args=fit_args,
success_params=success_params,
alpha=alpha,
B=B,
learner_klass=learner_klass)
for i, result in enumerate(results):
(pivot, interval, pvalue, _) = result
pvalues.append(pvalue)
pivots.append(pivot)
covered.append((interval[0] < true_target[i]) *
(interval[1] > true_target[i]))
lengths.append(interval[1] - interval[0])
lower.append(interval[0])
upper.append(interval[1])
if len(pvalues) > 0:
df = pd.DataFrame({
'pivot': pivots,
'pvalue': pvalues,
'coverage': covered,
'length': lengths,
'upper': upper,
'lower': lower,
'id': [instance_id] * len(pvalues),
'target': true_target,
'variable': observed_list,
'B': [B] * len(pvalues)
})
if naive:
(naive_pvalues, naive_pivots, naive_covered, naive_lengths,
naive_upper, naive_lower) = [], [], [], [], [], []
for j, idx in enumerate(observed_list):
true_target = truth[idx]
target_sd = np.sqrt(target_cov[j, j])
observed_target_j = observed_target[j]
quantile = normal_dbn.ppf(1 - 0.5 * alpha)
naive_interval = (observed_target_j - quantile * target_sd,
observed_target_j + quantile * target_sd)
naive_upper.append(naive_interval[1])
naive_lower.append(naive_interval[0])
naive_pivot = (1 - normal_dbn.cdf(
(observed_target_j - true_target) / target_sd))
naive_pivot = 2 * min(naive_pivot, 1 - naive_pivot)
naive_pivots.append(naive_pivot)
naive_pvalue = (
1 - normal_dbn.cdf(observed_target_j / target_sd))
naive_pvalue = 2 * min(naive_pvalue, 1 - naive_pvalue)
naive_pvalues.append(naive_pvalue)
naive_covered.append((naive_interval[0] < true_target) *
(naive_interval[1] > true_target))
naive_lengths.append(naive_interval[1] - naive_interval[0])
naive_df = pd.DataFrame({
'naive_pivot': naive_pivots,
'naive_pvalue': naive_pvalues,
'naive_coverage': naive_covered,
'naive_length': naive_lengths,
'naive_upper': naive_upper,
'naive_lower': naive_lower,
'variable': observed_list,
})
df = pd.merge(df, naive_df, on='variable')
return df
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)
def test_solve_QP():
"""
Check the R coordinate descent LASSO solver
"""
n, p = 100, 50
lam = 0.08
X = np.random.standard_normal((n, p))
loss = rr.squared_error(X, np.zeros(n), coef=1. / n)
pen = rr.l1norm(p, lagrange=lam)
E = np.zeros(p)
E[2] = 1
Q = rr.identity_quadratic(0, 0, E, 0)
problem = rr.simple_problem(loss, pen)
soln = problem.solve(Q, min_its=500, tol=1.e-12)
numpy2ri.activate()
rpy.r.assign('X', X)
rpy.r.assign('E', E)
rpy.r.assign('lam', lam)
R_code = """
library(selectiveInference)
p = ncol(X)
n = nrow(X)
soln_R = rep(0, p)
grad = 1. * E
ever_active = as.integer(c(1, rep(0, p-1)))
nactive = as.integer(1)
kkt_tol = 1.e-12
objective_tol = 1.e-16
parameter_tol = 1.e-10
maxiter = 500
soln_R = selectiveInference:::solve_QP(t(X) %*% X / n,
lam,
maxiter,
soln_R,
E,
grad,
ever_active,
nactive,
kkt_tol,
objective_tol,
parameter_tol,
p,
TRUE,
TRUE,
TRUE)$soln
# test wide solver
Xtheta = rep(0, n)
nactive = as.integer(1)
ever_active = as.integer(c(1, rep(0, p-1)))
soln_R_wide = rep(0, p)
grad = 1. * E
soln_R_wide = selectiveInference:::solve_QP_wide(X,
rep(lam, p),
0,
maxiter,
soln_R_wide,
E,
grad,
Xtheta,
ever_active,
nactive,
kkt_tol,
objective_tol,
parameter_tol,
p,
TRUE,
TRUE,
TRUE)$soln
"""
rpy.r(R_code)
soln_R = np.asarray(rpy.r('soln_R'))
soln_R_wide = np.asarray(rpy.r('soln_R_wide'))
numpy2ri.deactivate()
tol = 1.e-5
print(soln - soln_R)
print(soln_R - soln_R_wide)
G = X.T.dot(X).dot(soln) / n + E
yield np.testing.assert_allclose, soln, soln_R, tol, tol, False, 'checking coordinate QP solver'
yield np.testing.assert_allclose, soln, soln_R_wide, tol, tol, False, 'checking wide coordinate QP solver'
yield np.testing.assert_allclose, G[soln != 0], -np.sign(
soln[soln != 0]
) * lam, tol, tol, False, 'checking active coordinate KKT for QP solver'
yield nt.assert_true, np.fabs(
G).max() < lam * (1. + 1.e-6), 'testing linfinity norm'
def form_loss(self, active_set):
return squared_error(self.X[:,active_set], self.y)
def __init__(self, X, Y):
self.X = X
self.Y = Y
self._sqerror = rr.squared_error(X, Y)
def test_solve_QP_lasso():
"""
Check the R coordinate descent LASSO solver
"""
n, p = 100, 200
lam = 0.1
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.squared_error(X, Y, coef=1. / n)
pen = rr.l1norm(p, lagrange=lam)
problem = rr.simple_problem(loss, pen)
soln = problem.solve(min_its=500, tol=1.e-12)
numpy2ri.activate()
rpy.r.assign('X', X)
rpy.r.assign('Y', Y)
rpy.r.assign('lam', lam)
R_code = """
library(selectiveInference)
p = ncol(X)
n = nrow(X)
soln_R = rep(0, p)
grad = -t(X) %*% Y / n
ever_active = as.integer(c(1, rep(0, p-1)))
nactive = as.integer(1)
kkt_tol = 1.e-12
objective_tol = 1.e-16
parameter_tol = 1.e-10
maxiter = 500
soln_R = selectiveInference:::solve_QP(t(X) %*% X / n,
lam,
maxiter,
soln_R,
1. * grad,
grad,
ever_active,
nactive,
kkt_tol,
objective_tol,
parameter_tol,
p,
TRUE,
TRUE,
TRUE)$soln
# test wide solver
Xtheta = rep(0, n)
nactive = as.integer(1)
ever_active = as.integer(c(1, rep(0, p-1)))
soln_R_wide = rep(0, p)
grad = - t(X) %*% Y / n
soln_R_wide = selectiveInference:::solve_QP_wide(X,
rep(lam, p),
0,
maxiter,
soln_R_wide,
1. * grad,
grad,
Xtheta,
ever_active,
nactive,
kkt_tol,
objective_tol,
parameter_tol,
p,
TRUE,
TRUE,
TRUE)$soln
"""
rpy.r(R_code)
soln_R = np.asarray(rpy.r('soln_R'))
soln_R_wide = np.asarray(rpy.r('soln_R_wide'))
numpy2ri.deactivate()
tol = 1.e-5
print(soln - soln_R)
print(soln_R - soln_R_wide)
yield np.testing.assert_allclose, soln, soln_R, tol, tol, False, 'checking coordinate QP solver for LASSO problem'
yield np.testing.assert_allclose, soln, soln_R_wide, tol, tol, False, 'checking wide coordinate QP solver for LASSO problem'
def __init__(self, X, Y):
self.X = X
self.Y = Y
self._sqerror = rr.squared_error(X, Y)
def form_loss(self, active_set):
return squared_error(self.X[:, active_set], self.y)
