def test_group_lasso_weightedl1_lagrange():
n, p = 100, 50
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.glm.gaussian(X, Y)
weights = np.ones(p)
weights[-2:] = np.inf
weights[:2] = 0
weight_dict = dict([(i, w) for i, w in enumerate(weights)])
pen1 = rr.weighted_l1norm(weights, lagrange=0.5 * np.sqrt(n))
pen2 = rr.group_lasso(np.arange(p),
weights=weight_dict,
lagrange=0.5 * np.sqrt(n))
problem1 = rr.simple_problem(loss, pen1)
problem2 = rr.simple_problem(loss, pen2)
beta1 = problem1.solve(tol=1.e-14, min_its=500)
beta2 = problem2.solve(tol=1e-14, min_its=500)
npt.assert_allclose(beta1, beta2)
bound_val = pen1.seminorm(beta1, lagrange=1)
bound1 = rr.weighted_l1norm(weights, bound=bound_val)
bound2 = rr.group_lasso(np.arange(p), weights=weight_dict, bound=bound_val)
problem3 = rr.simple_problem(loss, bound1)
problem4 = rr.simple_problem(loss, bound2)
beta3 = problem3.solve(tol=1.e-14, min_its=500)
beta4 = problem4.solve(tol=1.e-14, min_its=500)
npt.assert_allclose(beta3, beta4)
npt.assert_allclose(beta3, beta1)
def __init__(
self,
loglike,
groups,
weights,
ridge_term,
randomizer,
use_lasso=True, # should lasso solver be used where applicable - defaults to True
perturb=None):
_check_groups(groups) # make sure groups looks sensible
# log likelihood : quadratic loss
self.loglike = loglike
self.nfeature = self.loglike.shape[0]
# ridge parameter
self.ridge_term = ridge_term
# group lasso penalty (from regreg)
# use regular lasso penalty if all groups are size 1
if use_lasso and groups.size == np.unique(groups).size:
# need to provide weights an an np.array rather than a dictionary
weights_np = np.array([w[1] for w in sorted(weights.items())])
self.penalty = rr.weighted_l1norm(weights=weights_np, lagrange=1.)
else:
self.penalty = rr.group_lasso(groups, weights=weights, lagrange=1.)
# store groups as a class variable since the non-group lasso doesn't
self.groups = groups
self._initial_omega = perturb
# gaussian randomization
self.randomizer = randomizer
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_weighted_l1_with_zero():
z = np.random.standard_normal(5)
a=rr.weighted_l1norm([0,1,1,1,1], lagrange=0.5)
b=a.dual[1]
c=rr.l1norm(4, lagrange=0.5)
npt.assert_equal(a.lagrange_prox(z), z-b.bound_prox(z))
npt.assert_equal(a.lagrange_prox(z)[0], z[0])
npt.assert_equal(a.lagrange_prox(z)[1:], c.lagrange_prox(z[1:]))
def __init__(self,
Q,
X,
y,
feature_weights,
ridge_term=None,
randomizer_scale=None,
perturb=None):
r"""
Create a new post-selection object for the LASSO problem
Parameters
----------
loglike : `regreg.smooth.glm.glm`
A (negative) log-likelihood as implemented in `regreg`.
feature_weights : np.ndarray
Feature weights for L-1 penalty. If a float,
it is brodcast to all features.
ridge_term : float
How big a ridge term to add?
randomizer_scale : float
Scale for IID components of randomization.
perturb : np.ndarray
Random perturbation subtracted as a linear
term in the objective function.
"""
(self.Q,
self.X,
self.y) = (Q, X, y)
self.loss = rr.quadratic_loss(Q.shape[0], Q=Q)
n, p = X.shape
self.nfeature = p
if np.asarray(feature_weights).shape == ():
feature_weights = np.ones(loglike.shape) * feature_weights
self.feature_weights = np.asarray(feature_weights)
mean_diag = np.diag(Q).mean()
if ridge_term is None:
ridge_term = np.std(y) * np.sqrt(mean_diag) / np.sqrt(n - 1)
if randomizer_scale is None:
randomizer_scale = np.sqrt(mean_diag) * 0.5 * np.std(y) * np.sqrt(n / (n - 1.))
self.randomizer = randomization.isotropic_gaussian((p,), randomizer_scale)
self.ridge_term = ridge_term
self.penalty = rr.weighted_l1norm(self.feature_weights, lagrange=1.)
self._initial_omega = perturb # random perturbation
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 solve_sqrt_lasso_fat(X,
Y,
weights=None,
initial=None,
quadratic=None,
solve_args={}):
"""
Solve the square-root LASSO optimization problem:
$$
\text{minimize}_{\beta} \|y-X\beta\|_2 + D |\beta|,
$$
where $D$ is the diagonal matrix with weights on its diagonal.
Parameters
----------
y : np.float((n,))
The target, in the model $y = X\beta$
X : np.float((n, p))
The data, in the model $y = X\beta$
weights : np.float
Coefficients of the L-1 penalty in
optimization problem, note that different
coordinates can have different coefficients.
initial : np.float(p)
Initial point for optimization.
solve_args : dict
Arguments passed to regreg solver.
quadratic : `regreg.identity_quadratic`
A quadratic term added to objective function.
"""
#X = rr.astransform(X)
#n, p = X.output_shape[0], X.input_shape[0]
n, p = X.shape
if weights is None:
lam = choose_lambda(X)
weights = lam * np.ones((p, ))
loss = sqlasso_objective(X, Y)
penalty = rr.weighted_l1norm(weights, lagrange=1.)
problem = rr.simple_problem(loss, penalty)
if initial is not None:
problem.coefs[:] = initial
soln = problem.solve(quadratic, **solve_args)
return soln, loss
def test_equivalence_sqrtlasso(n=200, p=400, s=10, sigma=3.):
"""
Check equivalent LASSO and sqrtLASSO solutions.
"""
Y = np.random.standard_normal(n) * sigma
beta = np.zeros(p)
beta[:s] = 8 * (2 * np.random.binomial(1, 0.5, size=(s, )) - 1)
X = np.random.standard_normal(
(n, p)) + 0.3 * np.random.standard_normal(n)[:, None]
X /= (X.std(0)[None, :] * np.sqrt(n))
Y += np.dot(X, beta) * sigma
lam_theor = choose_lambda(X, quantile=0.9)
weights = lam_theor * np.ones(p)
weights[:3] = 0.
soln1, loss1 = solve_sqrt_lasso(X,
Y,
weights=weights,
quadratic=None,
solve_args={
'min_its': 500,
'tol': 1.e-10
})
G1 = loss1.smooth_objective(soln1, 'grad')
# find active set, and estimate of sigma
active = (soln1 != 0)
nactive = active.sum()
subgrad = np.sign(soln1[active]) * weights[active]
X_E = X[:, active]
X_Ei = np.linalg.pinv(X_E)
sigma_E = np.linalg.norm(Y - X_E.dot(X_Ei.dot(Y))) / np.sqrt(n - nactive)
multiplier = sigma_E * np.sqrt(
(n - nactive) / (1 - np.linalg.norm(X_Ei.T.dot(subgrad))**2))
# XXX how should quadratic be changed?
# multiply everything by sigma_E?
loss2 = rr.glm.gaussian(X, Y)
penalty = rr.weighted_l1norm(weights, lagrange=multiplier)
problem = rr.simple_problem(loss2, penalty)
soln2 = problem.solve(tol=1.e-12, min_its=200)
G2 = loss2.smooth_objective(soln2, 'grad') / multiplier
np.testing.assert_allclose(G1[3:], G2[3:])
np.testing.assert_allclose(soln1, soln2)
def __init__(self,
loglike,
feature_weights,
proportion_select,
ridge_term=0,
perturb=None):
(self.loglike, self.feature_weights, self.proportion_select,
self.ridge_term) = (loglike, feature_weights, proportion_select,
ridge_term)
self.nfeature = p = self.loglike.shape[0]
self.penalty = rr.weighted_l1norm(self.feature_weights, lagrange=1.)
self._initial_omega = perturb
def solve_problem(Qbeta_bar, Q, lagrange, initial=None):
p = Qbeta_bar.shape[0]
loss = rr.quadratic_loss(
(p, ), Q=Q, quadratic=rr.identity_quadratic(0, 0, -Qbeta_bar, 0))
lagrange = np.asarray(lagrange)
if lagrange.shape in [(), (1, )]:
lagrange = np.ones(p) * lagrange
pen = rr.weighted_l1norm(lagrange, lagrange=1.)
problem = rr.simple_problem(loss, pen)
if initial is not None:
problem.coefs[:] = initial
soln = problem.solve(tol=1.e12, min_its=500)
return soln
def __init__(self,
loglike,
feature_weights,
ridge_term,
randomizer_scale,
randomizer='gaussian',
parametric_cov_estimator=False,
perturb=None):
r"""
Create a new post-selection object for the LASSO problem
Parameters
----------
loglike : `regreg.smooth.glm.glm`
A (negative) log-likelihood as implemented in `regreg`.
feature_weights : np.ndarray
Feature weights for L-1 penalty. If a float,
it is brodcast to all features.
ridge_term : float
How big a ridge term to add?
randomizer_scale : float
Scale for IID components of randomization.
randomizer : str (optional)
One of ['laplace', 'logistic', 'gaussian']
"""
self.loglike = loglike
self.nfeature = p = self.loglike.shape[0]
if np.asarray(feature_weights).shape == ():
feature_weights = np.ones(loglike.shape) * feature_weights
self.feature_weights = np.asarray(feature_weights)
self.parametric_cov_estimator = parametric_cov_estimator
if randomizer == 'laplace':
self.randomizer = randomization.laplace((p, ),
scale=randomizer_scale)
elif randomizer == 'gaussian':
self.randomizer = randomization.isotropic_gaussian(
(p, ), randomizer_scale)
elif randomizer == 'logistic':
self.randomizer = randomization.logistic((p, ),
scale=randomizer_scale)
self.ridge_term = ridge_term
self.penalty = rr.weighted_l1norm(self.feature_weights, lagrange=1.)
self._initial_omega = perturb
def solve_sqrt_lasso_fat(X, Y, weights=None, initial=None, quadratic=None, solve_args={}):
"""
Solve the square-root LASSO optimization problem:
$$
\text{minimize}_{\beta} \|y-X\beta\|_2 + D |\beta|,
$$
where $D$ is the diagonal matrix with weights on its diagonal.
Parameters
----------
y : np.float((n,))
The target, in the model $y = X\beta$
X : np.float((n, p))
The data, in the model $y = X\beta$
weights : np.float
Coefficients of the L-1 penalty in
optimization problem, note that different
coordinates can have different coefficients.
initial : np.float(p)
Initial point for optimization.
solve_args : dict
Arguments passed to regreg solver.
quadratic : `regreg.identity_quadratic`
A quadratic term added to objective function.
"""
X = rr.astransform(X)
n, p = X.output_shape[0], X.input_shape[0]
if weights is None:
lam = choose_lambda(X)
weights = lam * np.ones((p,))
loss = sqlasso_objective(X, Y)
penalty = rr.weighted_l1norm(weights, lagrange=1.)
problem = rr.simple_problem(loss, penalty)
if initial is not None:
problem.coefs[:] = initial
soln = problem.solve(quadratic, **solve_args)
return soln, loss
def test_equivalence_sqrtlasso(n=200, p=400, s=10, sigma=3.):
"""
Check equivalent LASSO and sqrtLASSO solutions.
"""
Y = np.random.standard_normal(n) * sigma
beta = np.zeros(p)
beta[:s] = 8 * (2 * np.random.binomial(1, 0.5, size=(s,)) - 1)
X = np.random.standard_normal((n,p)) + 0.3 * np.random.standard_normal(n)[:,None]
X /= (X.std(0)[None,:] * np.sqrt(n))
Y += np.dot(X, beta) * sigma
lam_theor = choose_lambda(X, quantile=0.9)
weights = lam_theor*np.ones(p)
weights[:3] = 0.
soln1, loss1 = solve_sqrt_lasso(X, Y, weights=weights, quadratic=None, solve_args={'min_its':500, 'tol':1.e-10})
G1 = loss1.smooth_objective(soln1, 'grad')
# find active set, and estimate of sigma
active = (soln1 != 0)
nactive = active.sum()
subgrad = np.sign(soln1[active]) * weights[active]
X_E = X[:,active]
X_Ei = np.linalg.pinv(X_E)
sigma_E= np.linalg.norm(Y - X_E.dot(X_Ei.dot(Y))) / np.sqrt(n - nactive)
multiplier = sigma_E * np.sqrt((n - nactive) / (1 - np.linalg.norm(X_Ei.T.dot(subgrad))**2))
# XXX how should quadratic be changed?
# multiply everything by sigma_E?
loss2 = rr.glm.gaussian(X, Y)
penalty = rr.weighted_l1norm(weights, lagrange=multiplier)
problem = rr.simple_problem(loss2, penalty)
soln2 = problem.solve(tol=1.e-12, min_its=200)
G2 = loss2.smooth_objective(soln2, 'grad') / multiplier
np.testing.assert_allclose(G1[3:], G2[3:])
np.testing.assert_allclose(soln1, soln2)
def __init__(self,
loglike,
feature_weights,
ridge_term,
randomizer,
perturb=None):
r"""
Create a new post-selection object for the LASSO problem
Parameters
----------
loglike : `regreg.smooth.glm.glm`
A (negative) log-likelihood as implemented in `regreg`.
feature_weights : np.ndarray
Feature weights for L-1 penalty. If a float,
it is brodcast to all features.
ridge_term : float
How big a ridge term to add?
randomizer : object
Randomizer -- contains representation of randomization density.
perturb : np.ndarray
Random perturbation subtracted as a linear
term in the objective function.
"""
self.loglike = loglike
self.nfeature = p = self.loglike.shape[0]
if np.asarray(feature_weights).shape == ():
feature_weights = np.ones(loglike.shape) * feature_weights
self.feature_weights = np.asarray(feature_weights)
self.ridge_term = ridge_term
self.penalty = rr.weighted_l1norm(self.feature_weights, lagrange=1.)
self._initial_omega = perturb # random perturbation
self.randomizer = randomizer
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 fit(self, **solve_args):
"""
Fit the lasso using `regreg`.
This sets the attributes `soln`, `onestep` and
forms the constraints necessary for post-selection inference
by calling `form_constraints()`.
Parameters
----------
solve_args : keyword args
Passed to `regreg.problems.simple_problem.solve`.
Returns
-------
soln : np.float
Solution to lasso.
"""
penalty = weighted_l1norm(self.feature_weights, lagrange=1.)
problem = simple_problem(self.loglike, penalty)
_soln = problem.solve(**solve_args)
self._soln = _soln
if not np.all(_soln == 0):
self.active = np.nonzero(_soln != 0)[0]
self.active_signs = np.sign(_soln[self.active])
self._active_soln = _soln[self.active]
H = self.loglike.hessian(self._soln)[self.active][:,self.active]
Hinv = np.linalg.inv(H)
G = self.loglike.gradient(self._soln)[self.active]
delta = Hinv.dot(G)
self._onestep = self._active_soln - delta
self.active_penalized = self.feature_weights[self.active] != 0
self._constraints = constraints(-np.diag(self.active_signs)[self.active_penalized],
(self.active_signs * delta)[self.active_penalized],
covariance=Hinv)
else:
self.active = []
return self._soln
def test_group_lasso_weightedl1_bound():
n, p = 100, 50
X = np.random.standard_normal((n, p))
Y = np.random.standard_normal(n)
loss = rr.glm.gaussian(X, Y)
weights = np.ones(p)
weights[-2:] = np.inf
weights[:2] = 0
weight_dict = dict([(i, w) for i, w in enumerate(weights)])
bound1 = rr.weighted_l1norm(weights, bound=2)
bound2 = rr.group_lasso(np.arange(p), weights=weight_dict, bound=2)
problem1 = rr.simple_problem(loss, bound1)
problem2 = rr.simple_problem(loss, bound2)
beta1 = problem1.solve(tol=1.e-14, min_its=500)
beta2 = problem2.solve(tol=1e-14, min_its=500)
npt.assert_allclose(beta1, beta2)
def fit(self, tol=1.e-12, min_its=50, use_full=True, **solve_args):
lasso.fit(self, tol=tol, min_its=min_its, **solve_args)
_feature_weights = self.feature_weights.copy()
_feature_weights[self.active] = 0.
_feature_weights[self.inactive] = np.inf
_unpenalized_problem = simple_problem(self.loglike_inference,
weighted_l1norm(_feature_weights, lagrange=1.))
_unpenalized = _unpenalized_problem.solve(**solve_args)
self._unpenalized_active = _unpenalized[self.active]
if use_full:
H = self.loglike_full.hessian(_unpenalized)
n_inference = self.loglike_inference.data[0].shape[0]
n_full = self.loglike_full.data[0].shape[0]
H *= (1. * n_inference / n_full)
else:
H = self.loglike_inference.hessian(_unpenalized)
H_AA = H[self.active][:,self.active]
self._cov_inference = np.linalg.inv(H_AA)
def fit(self, tol=1.e-12, min_its=50, **solve_args):
lasso.fit(self, tol=tol, min_its=min_its, **solve_args)
n1 = self.loglike.get_data()[0].shape[0]
n = self.loglike_full.get_data()[0].shape[0]
_feature_weights = self.feature_weights.copy()
_feature_weights[self.active] = 0.
_feature_weights[self.inactive] = np.inf
_unpenalized_problem = simple_problem(self.loglike_full,
weighted_l1norm(_feature_weights, lagrange=1.))
_unpenalized = _unpenalized_problem.solve(**solve_args)
_unpenalized_active = _unpenalized[self.active]
s = len(self.active)
H = self.loglike_full.hessian(_unpenalized)
H_AA = H[self.active][:,self.active]
_cov_block = np.linalg.inv(H_AA)
_subsample_block = (n * 1. / n1) * _cov_block
_carve_cov = np.zeros((2*s,2*s))
_carve_cov[:s][:,:s] = _cov_block
_carve_cov[s:][:,:s] = _subsample_block
_carve_cov[:s][:,s:] = _subsample_block
_carve_cov[s:][:,s:] = _subsample_block
_carve_linear_part = self._constraints.linear_part.dot(np.identity(2*s)[s:])
_carve_offset = self._constraints.offset
self._carve_constraints = constraints(_carve_linear_part,
_carve_offset,
covariance=_carve_cov)
self._carve_feasible = np.hstack([_unpenalized_active, self.onestep_estimator])
self._unpenalized_active = _unpenalized_active
self._carve_invcov = H_AA
def test_sqrt_highdim_lasso(n=500,
p=200,
signal_fac=1.5,
s=5,
sigma=3,
full=True,
rho=0.4,
randomizer_scale=1.,
ndraw=5000,
burnin=1000,
ridge_term=None, compare_to_lasso=True):
"""
Compare to R randomized lasso
"""
inst, const = gaussian_instance, lasso.sqrt_lasso
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]
if ridge_term is None:
mean_diag = np.mean((X**2).sum(0))
ridge_term = (np.sqrt(mean_diag) / np.sqrt(n)) * np.sqrt(n / (n - 1.))
W = np.ones(X.shape[1]) * choose_lambda(X) * 0.7
perturb = np.random.standard_normal(p) * randomizer_scale / np.sqrt(n)
conv = const(X,
Y,
W,
randomizer_scale=randomizer_scale / np.sqrt(n),
perturb=perturb,
ridge_term=ridge_term)
signs = conv.fit()
nonzero = signs != 0
# sanity check
if compare_to_lasso:
q_term = rr.identity_quadratic(ridge_term, 0, -perturb, 0)
soln2, sqrt_loss = solve_sqrt_lasso(X, Y, W, solve_args={'min_its':1000}, quadratic=q_term, force_fat=True)
soln = conv.initial_soln
denom = np.linalg.norm(Y - X.dot(soln))
new_weights = W * denom
loss = rr.glm.gaussian(X, Y)
pen = rr.weighted_l1norm(new_weights, lagrange=1.)
prob = rr.simple_problem(loss, pen)
rescaledQ = rr.identity_quadratic(ridge_term * denom,
0,
-perturb * denom,
0)
soln3 = prob.solve(quadratic=rescaledQ, min_its=1000, tol=1.e-12)
np.testing.assert_allclose(conv._initial_omega, perturb * denom)
np.testing.assert_allclose(soln, soln2)
np.testing.assert_allclose(soln, soln3)
if full:
(observed_target,
cov_target,
cov_target_score,
alternatives) = full_targets(conv.loglike,
conv._W,
nonzero)
else:
(observed_target,
cov_target,
cov_target_score,
alternatives) = selected_targets(conv.loglike,
conv._W,
nonzero)
_, pval, intervals = conv.summary(observed_target,
cov_target,
cov_target_score,
alternatives,
ndraw=ndraw,
burnin=burnin,
compute_intervals=False)
return pval[beta[nonzero] == 0], pval[beta[nonzero] != 0]
def test_weighted_l1():
a =rr.weighted_l1norm(2*np.ones(10), lagrange=0.5)
b= rr.l1norm(10, lagrange=1)
z = np.random.standard_normal(10)
npt.assert_equal(b.lagrange_prox(z), a.lagrange_prox(z))
npt.assert_equal(b.dual[1].bound_prox(z), a.dual[1].bound_prox(z))
def decompose_subgradient(self, condition=None, marginalize=None):
"""
ADD DOCSTRING
condition and marginalize should be disjoint
"""
p = self.penalty.shape[0]
condition_inactive = np.zeros(p, dtype=np.bool)
if condition is None:
condition = np.zeros(p, dtype=np.bool)
if marginalize is None:
marginalize = np.zeros(p, dtype=np.bool)
marginalize[self._overall] = 0
if np.any(condition * marginalize):
raise ValueError(
"cannot simultaneously condition and marginalize over a group's subgradient"
)
if not self._setup:
raise ValueError(
'setup_sampler should be called before using this function')
_inactive = self._inactive
limits_marginal = np.zeros_like(_inactive, np.float)
condition_inactive = _inactive * condition
moving_inactive = _inactive * ~(marginalize + condition)
margin_inactive = _inactive * marginalize
limits_marginal = self._lagrange
if np.asarray(self._lagrange).shape in [(), (1, )]:
limits_marginal = np.zeros_like(_inactive) * self._lagrange
opt_linear, opt_offset = self.opt_transform
new_linear = np.zeros((opt_linear.shape[0],
(self._active.sum() + self._unpenalized.sum() +
moving_inactive.sum())))
new_linear[:, self.scaling_slice] = opt_linear[:, self.scaling_slice]
new_linear[:,
self.unpenalized_slice] = opt_linear[:,
self.unpenalized_slice]
inactive_moving_idx = np.nonzero(moving_inactive)[0]
subgrad_idx = range(
self._active.sum() + self._unpenalized.sum(),
self._active.sum() + self._unpenalized.sum() +
moving_inactive.sum())
for _i, _s in zip(inactive_moving_idx, subgrad_idx):
new_linear[_i, _s] = 1.
observed_opt_state = self.observed_opt_state[:(
self._active.sum() + self._unpenalized.sum() +
moving_inactive.sum())]
observed_opt_state[subgrad_idx] = self.initial_subgrad[moving_inactive]
condition_linear = np.zeros(
(opt_linear.shape[0],
(self._active.sum() + self._unpenalized.sum() +
condition_inactive.sum())))
new_offset = opt_offset + 0.
new_offset[condition_inactive] += self.initial_subgrad[
condition_inactive]
new_opt_transform = (new_linear, new_offset)
if not hasattr(self.randomization, "cov_prec") or marginalize.sum(
): # use Langevin -- not gaussian
def _fraction(_cdf, _pdf, full_state_plus, full_state_minus,
margin_inactive):
return (np.divide(
_pdf(full_state_plus) - _pdf(full_state_minus),
_cdf(full_state_plus) -
_cdf(full_state_minus)))[margin_inactive]
def new_grad_log_density(query, limits_marginal, margin_inactive,
_cdf, _pdf, new_opt_transform,
deriv_log_dens, score_state, opt_state):
full_state = score_state + reconstruct_opt(
new_opt_transform, opt_state)
p = query.penalty.shape[0]
weights = np.zeros(p)
if margin_inactive.sum() > 0:
full_state_plus = full_state + limits_marginal * margin_inactive
full_state_minus = full_state - limits_marginal * margin_inactive
weights[margin_inactive] = _fraction(
_cdf, _pdf, full_state_plus, full_state_minus,
margin_inactive)
weights[~margin_inactive] = deriv_log_dens(
full_state)[~margin_inactive]
return -opt_linear.T.dot(weights)
new_grad_log_density = functools.partial(
new_grad_log_density, self, limits_marginal, margin_inactive,
self.randomization._cdf, self.randomization._pdf,
new_opt_transform, self.randomization._derivative_log_density)
def new_log_density(query, limits_marginal, margin_inactive, _cdf,
_pdf, new_opt_transform, log_dens, score_state,
opt_state):
full_state = score_state + reconstruct_opt(
new_opt_transform, opt_state)
full_state = np.atleast_2d(full_state)
p = query.penalty.shape[0]
logdens = np.zeros(full_state.shape[0])
if margin_inactive.sum() > 0:
full_state_plus = full_state + limits_marginal * margin_inactive
full_state_minus = full_state - limits_marginal * margin_inactive
logdens += np.sum(
np.log(_cdf(full_state_plus) -
_cdf(full_state_minus))[:, margin_inactive],
axis=1)
logdens += log_dens(full_state[:, ~margin_inactive])
return np.squeeze(
logdens
) # should this be negative to match the gradient log density?
new_log_density = functools.partial(
new_log_density, self, limits_marginal, margin_inactive,
self.randomization._cdf, self.randomization._pdf,
new_opt_transform, self.randomization._log_density)
new_lagrange = self.penalty.weights[moving_inactive]
new_dual = rr.weighted_l1norm(new_lagrange, lagrange=1.).conjugate
def new_projection(dual, noverall, opt_state):
new_state = opt_state.copy()
new_state[self.scaling_slice] = np.maximum(
opt_state[self.scaling_slice], 0)
new_state[noverall:] = dual.bound_prox(opt_state[noverall:])
return new_state
new_projection = functools.partial(new_projection, new_dual,
self._overall.sum())
new_selection_variable = copy(self.selection_variable)
new_selection_variable['subgradient'] = self.observed_opt_state[
condition_inactive]
self.sampler = langevin_sampler(
observed_opt_state,
self.observed_score_state,
self.score_transform,
new_opt_transform,
new_projection,
new_grad_log_density,
new_log_density,
selection_info=(self, new_selection_variable))
else:
cov, prec = self.randomization.cov_prec
prec_array = len(np.asarray(prec).shape) == 2
if prec_array:
cond_precision = new_linear.T.dot(prec.dot(new_linear))
cond_cov = np.linalg.inv(cond_precision)
logdens_linear = cond_cov.dot(new_linear.T.dot(prec))
else:
cond_precision = new_linear.T.dot(new_linear) * prec
cond_cov = np.linalg.inv(cond_precision)
logdens_linear = cond_cov.dot(new_linear.T) * prec
cond_mean = -logdens_linear.dot(self.observed_score_state +
new_offset)
def log_density(logdens_linear, offset, cond_prec, score, opt):
if score.ndim == 1:
mean_term = logdens_linear.dot(score.T + offset).T
else:
mean_term = logdens_linear.dot(score.T + offset[:, None]).T
arg = opt + mean_term
return -0.5 * np.sum(arg * cond_prec.dot(arg.T).T, 1)
log_density = functools.partial(log_density, logdens_linear,
new_offset, cond_precision)
# now make the constraints
# scaling constraints
# the scalings are first set of opt variables
# then unpenalized
# then the subgradients
I = np.identity(cond_cov.shape[0])
A_scaling = -I[self.scaling_slice]
b_scaling = np.zeros(A_scaling.shape[0])
A_subgrad = np.vstack(
[I[self._overall.sum():], -I[self._overall.sum():]])
inactive_lagrange = self.penalty.weights[moving_inactive]
b_subgrad = np.hstack([inactive_lagrange, inactive_lagrange])
linear_term = np.vstack([A_scaling, A_subgrad])
offset = np.hstack([b_scaling, b_subgrad])
affine_con = constraints(linear_term,
offset,
mean=cond_mean,
covariance=cond_cov)
logdens_transform = (logdens_linear, new_offset)
self._sampler = affine_gaussian_sampler(
affine_con,
observed_opt_state,
self.observed_score_state,
log_density,
logdens_transform,
selection_info=self.selection_variable
) # should be signs and the subgradients we've conditioned on
def form_penalty(self):
penalty = weighted_l1norm(self.weights, lagrange=1.)
penalty.quadratic = identity_quadratic(0, 0, self.random_linear_term, 0)
return penalty
def form_penalty(self):
penalty = weighted_l1norm(self.weights, lagrange=1.)
penalty.quadratic = identity_quadratic(0, 0, self.random_linear_term,
0)
return penalty
def fit(self, tol=1.e-12, min_its=50, **solve_args):
"""
Fit the lasso using `regreg`.
This sets the attributes `soln`, `onestep` and
forms the constraints necessary for post-selection inference
by calling `form_constraints()`.
Parameters
----------
solve_args : keyword args
Passed to `regreg.problems.simple_problem.solve`.
Returns
-------
soln : np.float
Solution to lasso.
"""
penalty = weighted_l1norm(self.feature_weights, lagrange=1.)
problem = simple_problem(self.loglike, penalty)
lasso_solution = problem.solve(tol=tol, min_its=min_its, **solve_args)
self.lasso_solution = lasso_solution
if not np.all(lasso_solution == 0):
self.active = np.nonzero(lasso_solution != 0)[0]
self.inactive = lasso_solution == 0
self.active_signs = np.sign(lasso_solution[self.active])
self._active_soln = lasso_solution[self.active]
H = self.loglike.hessian(self.lasso_solution)
H_AA = H[self.active][:,self.active]
H_AAinv = np.linalg.inv(H_AA)
Q = self.loglike.quadratic
G_Q = Q.objective(self.lasso_solution, 'grad')
G = self.loglike.gradient(self.lasso_solution) + G_Q
G_A = G[self.active]
G_I = self._G_I = G[self.inactive]
dbeta_A = H_AAinv.dot(G_A)
self.onestep_estimator = self._active_soln - dbeta_A
self.active_penalized = self.feature_weights[self.active] != 0
self._constraints = constraints(-np.diag(self.active_signs)[self.active_penalized],
(self.active_signs * dbeta_A)[self.active_penalized],
covariance=H_AAinv)
if self.inactive.sum():
# inactive constraints
H_IA = H[self.inactive][:,self.active]
H_II = H[self.inactive][:,self.inactive]
inactive_cov = H_II - H_IA.dot(H_AAinv).dot(H_IA.T)
irrepresentable = H_IA.dot(H_AAinv)
inactive_mean = irrepresentable.dot(-G_A)
self._inactive_constraints = constraints(np.vstack([np.identity(self.inactive.sum()),
-np.identity(self.inactive.sum())]),
np.hstack([self.feature_weights[self.inactive],
self.feature_weights[self.inactive]]),
covariance=inactive_cov,
mean=inactive_mean)
if not self._inactive_constraints(G_I):
warnings.warn('inactive constraint of KKT conditions not satisfied -- perhaps need to solve with more accuracy')
if self.covariance_estimator is not None:
# make full constraints
_cov_FA = self.covariance_estimator(self.onestep_estimator,
self.active,
self.inactive)
_cov_IA = _cov_FA[len(self.active):]
_cov_AA = _cov_FA[:len(self.active)]
# X_{-E}^T(y - X_E \bar{\beta}_E)
_inactive_score = - G_I - inactive_mean
_beta_bar = self.onestep_estimator
_indep_linear_part = _cov_IA.dot(np.linalg.inv(_cov_AA))
# we "fix" _nuisance, effectively conditioning on it
_nuisance = _inactive_score - _indep_linear_part.dot(_beta_bar)
_upper_lim = (self.feature_weights[self.inactive] -
_nuisance -
inactive_mean)
_lower_lim = (_nuisance +
self.feature_weights[self.inactive] +
inactive_mean)
_upper_linear = _indep_linear_part
_lower_linear = -_indep_linear_part
C = self._constraints
_full_linear = np.vstack([C.linear_part,
_upper_linear,
_lower_linear])
_full_offset = np.hstack([C.offset,
_upper_lim,
_lower_lim])
self._constraints = constraints(_full_linear,
_full_offset,
covariance=_cov_AA)
if not self._constraints(_beta_bar):
warnings.warn('constraints of KKT conditions on one-step estimator ' +
' not satisfied -- perhaps need to solve with more' +
'accuracy')
else:
self._inactive_constraints = None
else:
self.active = []
self.inactive = np.arange(lasso_solution.shape[0])
self._constraints = None
self._inactive_constraints = None
return self.lasso_solution
