def gaussian(klass,
X,
Y,
feature_weights,
split_frac=0.9,
sigma=1.,
stage_one=None):
n, p = X.shape
if stage_one is None:
splitn = int(n*split_frac)
indices = np.arange(n)
np.random.shuffle(indices)
stage_one = indices[:splitn]
stage_two = indices[splitn:]
else:
stage_two = [i for i in np.arange(n) if i not in stage_one]
Y1, X1 = Y[stage_one], X[stage_one]
Y2, X2 = Y[stage_two], X[stage_two]
loglike = glm.gaussian(X, Y, coef=1. / sigma**2)
loglike1 = glm.gaussian(X1, Y1, coef=1. / sigma**2)
loglike2 = glm.gaussian(X2, Y2, coef=1. / sigma**2)
return klass(loglike1, loglike2, loglike, np.sqrt(split_frac) * feature_weights / sigma**2)
def __init__(self, X, Y, epsilon, penalty, randomization, solve_args={'min_its':50, 'tol':1.e-10}):
loss = glm.gaussian(X, Y)
M_estimator.__init__(self,
loss,
epsilon,
penalty,
randomization, solve_args=solve_args)
def gaussian(X, Y, feature_weights, sigma, quadratic=None):
loglike = glm.gaussian(X, Y, coef=1. / sigma**2, quadratic=quadratic)
return lasso(loglike, feature_weights)
def gaussian(X,
Y,
feature_weights,
sigma=1.,
covariance_estimator=None,
quadratic=None):
r"""
Squared-error LASSO with feature weights.
Objective function is
$$
\beta \mapsto \frac{1}{2} \|Y-X\beta\|^2_2 + \sum_{i=1}^p \lambda_i |\beta_i|
$$
where $\lambda$ is `feature_weights`.
Parameters
----------
X : ndarray
Shape (n,p) -- the design matrix.
Y : ndarray
Shape (n,) -- the response.
feature_weights: [float, sequence]
Penalty weights. An intercept, or other unpenalized
features are handled by setting those entries of
`feature_weights` to 0. If `feature_weights` is
a float, then all parameters are penalized equally.
sigma : float (optional)
Noise variance. Set to 1 if `covariance_estimator` is not None.
This scales the loglikelihood by `sigma**(-2)`.
covariance_estimator : callable (optional)
If None, use the parameteric
covariance estimate of the selected model.
quadratic : `regreg.identity_quadratic.identity_quadratic` (optional)
An optional quadratic term to be added to the objective.
Can also be a linear term by setting quadratic
coefficient to 0.
Returns
-------
L : `selection.algorithms.lasso.lasso`
Notes
-----
If not None, `covariance_estimator` should
take arguments (beta, active, inactive)
and return an estimate of some of the
rows and columns of the covariance of
$(\bar{\beta}_E, \nabla \ell(\bar{\beta}_E)_{-E})$,
the unpenalized estimator and the inactive
coordinates of the gradient of the likelihood at
the unpenalized estimator.
"""
if covariance_estimator is not None:
sigma = 1.
# TODO should we scale the quadratic here when sigma is not 1?
loglike = glm.gaussian(X, Y, coef=1. / sigma**2, quadratic=quadratic)
return lasso(loglike, np.asarray(feature_weights) / sigma**2,
covariance_estimator=covariance_estimator)