449 lines
14 KiB
Python
449 lines
14 KiB
Python
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
|
|
# Fabian Pedregosa <fabian.pedregosa@inria.fr>
|
|
# Olivier Grisel <olivier.grisel@ensta.org>
|
|
#
|
|
# License: BSD Style.
|
|
|
|
import warnings
|
|
import numpy as np
|
|
|
|
from .base import LinearModel
|
|
from ..cross_val import KFold
|
|
from . import cd_fast
|
|
|
|
|
|
###############################################################################
|
|
# ElasticNet model
|
|
|
|
class ElasticNet(LinearModel):
|
|
"""Linear Model trained with L1 and L2 prior as regularizer
|
|
|
|
rho=1 is the lasso penalty. Currently, rho <= 0.01 is not
|
|
reliable, unless you supply your own sequence of alpha.
|
|
|
|
Parameters
|
|
----------
|
|
alpha : float
|
|
Constant that multiplies the L1 term. Defaults to 1.0
|
|
|
|
rho : float
|
|
The ElasticNet mixing parameter, with 0 < rho <= 1.
|
|
|
|
coef_: ndarray of shape n_features
|
|
The initial coeffients to warm-start the optimization
|
|
|
|
fit_intercept: bool
|
|
Whether the intercept should be estimated or not. If False, the
|
|
data is assumed to be already centered.
|
|
|
|
Notes
|
|
-----
|
|
To avoid unnecessary memory duplication the X argument of the fit method
|
|
should be directly passed as a fortran contiguous numpy array.
|
|
"""
|
|
|
|
def __init__(self, alpha=1.0, rho=0.5, fit_intercept=True):
|
|
self.alpha = alpha
|
|
self.rho = rho
|
|
self.coef_ = None
|
|
self.fit_intercept = fit_intercept
|
|
|
|
# @profile
|
|
def fit(self, X, y, precompute='auto', Xy=None, max_iter=1000, tol=1e-4,
|
|
coef_init=None, **params):
|
|
"""Fit Elastic Net model with coordinate descent
|
|
|
|
Parameters
|
|
-----------
|
|
X: ndarray, (n_samples, n_features)
|
|
Data
|
|
y: ndarray, (n_samples)
|
|
Target
|
|
precompute : True | False | 'auto' | array-like
|
|
Whether to use a precomputed Gram matrix to speed up
|
|
calculations. If set to 'auto' let us decide. The Gram
|
|
matrix can also be passed as argument.
|
|
Xy : array-like, optional
|
|
Xy = np.dot(X.T, y) that can be precomputed. It is useful
|
|
only when the Gram matrix is precomuted.
|
|
max_iter: int, optional
|
|
The maximum number of iterations
|
|
tol: float, optional
|
|
The tolerance for the optimization: if the updates are
|
|
smaller than 'tol', the optimization code checks the
|
|
dual gap for optimality and continues until it is smaller
|
|
than tol.
|
|
|
|
Notes
|
|
-----
|
|
|
|
Coordinate descent is an algorithm that considers each column of
|
|
data at a time hence it will automatically convert the X input
|
|
as a fortran contiguous numpy array if necessary.
|
|
|
|
To avoid memory re-allocation it is advised to allocate the
|
|
initial data in memory directly using that format.
|
|
"""
|
|
self._set_params(**params)
|
|
X = np.asanyarray(X, dtype=np.float64)
|
|
y = np.asanyarray(y, dtype=np.float64)
|
|
|
|
X, y, Xmean, ymean = LinearModel._center_data(X, y, self.fit_intercept)
|
|
|
|
if coef_init is None:
|
|
self.coef_ = np.zeros(X.shape[1], dtype=np.float64)
|
|
else:
|
|
self.coef_ = coef_init
|
|
|
|
n_samples = X.shape[0]
|
|
alpha = self.alpha * self.rho * n_samples
|
|
beta = self.alpha * (1.0 - self.rho) * n_samples
|
|
|
|
X = np.asfortranarray(X) # make data contiguous in memory
|
|
|
|
# precompute if n_samples > n_features
|
|
if hasattr(precompute, '__array__'):
|
|
Gram = precompute
|
|
elif precompute == True or \
|
|
(precompute == 'auto' and X.shape[0] > X.shape[1]):
|
|
Gram = np.dot(X.T, X)
|
|
else:
|
|
Gram = None
|
|
|
|
if Gram is None:
|
|
self.coef_, self.dual_gap_, self.eps_ = \
|
|
cd_fast.enet_coordinate_descent(self.coef_, alpha, beta,
|
|
X, y, max_iter, tol)
|
|
else:
|
|
if Xy is None:
|
|
Xy = np.dot(X.T, y)
|
|
self.coef_, self.dual_gap_, self.eps_ = \
|
|
cd_fast.enet_coordinate_descent_gram(self.coef_, alpha,
|
|
beta, Gram, Xy, y, max_iter, tol)
|
|
|
|
self._set_intercept(Xmean, ymean)
|
|
|
|
if self.dual_gap_ > self.eps_:
|
|
warnings.warn('Objective did not converge, you might want'
|
|
' to increase the number of interations')
|
|
|
|
# return self for chaining fit and predict calls
|
|
return self
|
|
|
|
|
|
###############################################################################
|
|
# Lasso model
|
|
|
|
class Lasso(ElasticNet):
|
|
"""Linear Model trained with L1 prior as regularizer (aka the Lasso)
|
|
|
|
Technically the Lasso model is optimizing the same objective function as
|
|
the Elastic Net with rho=1.0 (no L2 penalty).
|
|
|
|
Parameters
|
|
----------
|
|
alpha : float, optional
|
|
Constant that multiplies the L1 term. Defaults to 1.0
|
|
|
|
fit_intercept : boolean
|
|
whether to calculate the intercept for this model. If set
|
|
to false, no intercept will be used in calculations
|
|
(e.g. data is expected to be already centered).
|
|
|
|
Attributes
|
|
----------
|
|
`coef_` : array, shape = [n_features]
|
|
parameter vector (w in the fomulation formula)
|
|
|
|
`intercept_` : float
|
|
independent term in decision function.
|
|
|
|
Examples
|
|
--------
|
|
>>> from scikits.learn import linear_model
|
|
>>> clf = linear_model.Lasso(alpha=0.1)
|
|
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
|
|
Lasso(alpha=0.1, fit_intercept=True)
|
|
>>> print clf.coef_
|
|
[ 0.85 0. ]
|
|
>>> print clf.intercept_
|
|
0.15
|
|
|
|
See also
|
|
--------
|
|
LassoLARS
|
|
|
|
Notes
|
|
-----
|
|
The algorithm used to fit the model is coordinate descent.
|
|
|
|
To avoid unnecessary memory duplication the X argument of the fit method
|
|
should be directly passed as a fortran contiguous numpy array.
|
|
"""
|
|
|
|
def __init__(self, alpha=1.0, fit_intercept=True):
|
|
super(Lasso, self).__init__(alpha=alpha, rho=1.0,
|
|
fit_intercept=fit_intercept)
|
|
|
|
###############################################################################
|
|
# Classes to store linear models along a regularization path
|
|
|
|
def lasso_path(X, y, eps=1e-3, n_alphas=100, alphas=None, fit_intercept=True,
|
|
verbose=False, **fit_params):
|
|
"""Compute Lasso path with coordinate descent
|
|
|
|
Parameters
|
|
----------
|
|
X : numpy array of shape [n_samples,n_features]
|
|
Training data. Pass directly as fortran contiguous data to avoid
|
|
unnecessary memory duplication
|
|
|
|
y : numpy array of shape [n_samples]
|
|
Target values
|
|
|
|
eps : float, optional
|
|
Length of the path. eps=1e-3 means that
|
|
alpha_min / alpha_max = 1e-3
|
|
|
|
n_alphas : int, optional
|
|
Number of alphas along the regularization path
|
|
|
|
alphas : numpy array, optional
|
|
List of alphas where to compute the models.
|
|
If None alphas are set automatically
|
|
|
|
fit_params : kwargs
|
|
keyword arguments passed to the Lasso fit method
|
|
|
|
Returns
|
|
-------
|
|
models : a list of models along the regularization path
|
|
|
|
Notes
|
|
-----
|
|
See examples/plot_lasso_coordinate_descent_path.py for an example.
|
|
|
|
To avoid unnecessary memory duplication the X argument of the fit method
|
|
should be directly passed as a fortran contiguous numpy array.
|
|
"""
|
|
return enet_path(X, y, rho=1., eps=eps, n_alphas=n_alphas, alphas=alphas,
|
|
fit_intercept=fit_intercept, verbose=verbose, **fit_params)
|
|
|
|
|
|
def enet_path(X, y, rho=0.5, eps=1e-3, n_alphas=100, alphas=None,
|
|
fit_intercept=True, verbose=False, **fit_params):
|
|
"""Compute Elastic-Net path with coordinate descent
|
|
|
|
Parameters
|
|
----------
|
|
X : numpy array of shape [n_samples, n_features]
|
|
Training data. Pass directly as fortran contiguous data to avoid
|
|
unnecessary memory duplication
|
|
|
|
y : numpy array of shape [n_samples]
|
|
Target values
|
|
|
|
rho : float, optional
|
|
float between 0 and 1 passed to ElasticNet (scaling between
|
|
l1 and l2 penalties). rho=1 corresponds to the Lasso
|
|
|
|
eps : float
|
|
Length of the path. eps=1e-3 means that
|
|
alpha_min / alpha_max = 1e-3
|
|
|
|
n_alphas : int, optional
|
|
Number of alphas along the regularization path
|
|
|
|
alphas : numpy array, optional
|
|
List of alphas where to compute the models.
|
|
If None alphas are set automatically
|
|
|
|
fit_params : kwargs
|
|
keyword arguments passed to the Lasso fit method
|
|
|
|
Returns
|
|
-------
|
|
models : a list of models along the regularization path
|
|
|
|
Notes
|
|
-----
|
|
See examples/plot_lasso_coordinate_descent_path.py for an example.
|
|
"""
|
|
X, y, Xmean, ymean = LinearModel._center_data(X, y, fit_intercept)
|
|
X = np.asfortranarray(X) # make data contiguous in memory
|
|
|
|
n_samples = X.shape[0]
|
|
if alphas is None:
|
|
alpha_max = np.abs(np.dot(X.T, y)).max() / (n_samples * rho)
|
|
alphas = np.logspace(np.log10(alpha_max*eps), np.log10(alpha_max),
|
|
num=n_alphas)[::-1]
|
|
else:
|
|
alphas = np.sort(alphas)[::-1] # make sure alphas are properly ordered
|
|
coef_ = None # init coef_
|
|
models = []
|
|
|
|
if not 'precompute' in fit_params \
|
|
or fit_params['precompute'] is True \
|
|
or (fit_intercept and hasattr(fit_params['precompute'], '__array__')):
|
|
fit_params['precompute'] = np.dot(X.T, X)
|
|
if not 'Xy' in fit_params or fit_params['Xy'] is None:
|
|
fit_params['Xy'] = np.dot(X.T, y)
|
|
|
|
for alpha in alphas:
|
|
model = ElasticNet(alpha=alpha, rho=rho, fit_intercept=False)
|
|
model.fit(X, y, coef_init=coef_, **fit_params)
|
|
if fit_intercept:
|
|
model.fit_intercept = True
|
|
model._set_intercept(Xmean, ymean)
|
|
if verbose:
|
|
print model
|
|
coef_ = model.coef_.copy()
|
|
models.append(model)
|
|
return models
|
|
|
|
|
|
class LinearModelCV(LinearModel):
|
|
"""Base class for iterative model fitting along a regularization path"""
|
|
|
|
def __init__(self, eps=1e-3, n_alphas=100, alphas=None,
|
|
fit_intercept=True):
|
|
self.eps = eps
|
|
self.n_alphas = n_alphas
|
|
self.alphas = alphas
|
|
self.fit_intercept = fit_intercept
|
|
|
|
def fit(self, X, y, cv=None, **fit_params):
|
|
"""Fit linear model with coordinate descent along decreasing alphas
|
|
using cross-validation
|
|
|
|
Parameters
|
|
----------
|
|
|
|
X : numpy array of shape [n_samples,n_features]
|
|
Training data. Pass directly as fortran contiguous data to avoid
|
|
unnecessary memory duplication
|
|
|
|
y : numpy array of shape [n_samples]
|
|
Target values
|
|
|
|
cv : cross-validation generator, optional
|
|
If None, KFold will be used.
|
|
|
|
fit_params : kwargs
|
|
keyword arguments passed to the Lasso fit method
|
|
|
|
"""
|
|
|
|
X = np.asfortranarray(X, dtype=np.float64)
|
|
y = np.asanyarray(y, dtype=np.float64)
|
|
|
|
n_samples = X.shape[0]
|
|
|
|
# Start to compute path on full data
|
|
path_params = fit_params.copy()
|
|
path_params.update(self._get_params())
|
|
models = self.path(X, y, **path_params)
|
|
|
|
alphas = [model.alpha for model in models]
|
|
n_alphas = len(alphas)
|
|
|
|
# init cross-validation generator
|
|
cv = cv if cv else KFold(n_samples, 5)
|
|
|
|
params = self._get_params()
|
|
params['alphas'] = alphas
|
|
params['n_alphas'] = n_alphas
|
|
|
|
# Compute path for all folds and compute MSE to get the best alpha
|
|
folds = list(cv)
|
|
mse_alphas = np.zeros((len(folds), n_alphas))
|
|
fit_params.update(params)
|
|
for i, (train, test) in enumerate(folds):
|
|
models_train = self.path(X[train], y[train], **fit_params)
|
|
for i_alpha, model in enumerate(models_train):
|
|
y_ = model.predict(X[test])
|
|
mse_alphas[i, i_alpha] += ((y_ - y[test]) ** 2).mean()
|
|
|
|
i_best_alpha = np.argmin(np.mean(mse_alphas, axis=0))
|
|
model = models[i_best_alpha]
|
|
|
|
self.coef_ = model.coef_
|
|
self.intercept_ = model.intercept_
|
|
self.alpha = model.alpha
|
|
self.alphas = np.asarray(alphas)
|
|
self.coef_path_ = np.asarray([model.coef_ for model in models])
|
|
self.mse_path_ = mse_alphas.T
|
|
return self
|
|
|
|
|
|
class LassoCV(LinearModelCV):
|
|
"""Lasso linear model with iterative fitting along a regularization path
|
|
|
|
The best model is selected by cross-validation.
|
|
|
|
Parameters
|
|
----------
|
|
eps : float, optional
|
|
Length of the path. eps=1e-3 means that
|
|
alpha_min / alpha_max = 1e-3.
|
|
|
|
n_alphas : int, optional
|
|
Number of alphas along the regularization path
|
|
|
|
alphas : numpy array, optional
|
|
List of alphas where to compute the models.
|
|
If None alphas are set automatically
|
|
|
|
Notes
|
|
-----
|
|
See examples/linear_model/lasso_path_with_crossvalidation.py
|
|
for an example.
|
|
|
|
To avoid unnecessary memory duplication the X argument of the fit method
|
|
should be directly passed as a fortran contiguous numpy array.
|
|
"""
|
|
|
|
path = staticmethod(lasso_path)
|
|
|
|
|
|
class ElasticNetCV(LinearModelCV):
|
|
"""Elastic Net model with iterative fitting along a regularization path
|
|
|
|
The best model is selected by cross-validation.
|
|
|
|
Parameters
|
|
----------
|
|
rho : float, optional
|
|
float between 0 and 1 passed to ElasticNet (scaling between
|
|
l1 and l2 penalties)
|
|
|
|
eps : float, optional
|
|
Length of the path. eps=1e-3 means that
|
|
alpha_min / alpha_max = 1e-3.
|
|
|
|
n_alphas : int, optional
|
|
Number of alphas along the regularization path
|
|
|
|
alphas : numpy array, optional
|
|
List of alphas where to compute the models.
|
|
If None alphas are set automatically
|
|
|
|
Notes
|
|
-----
|
|
See examples/linear_model/lasso_path_with_crossvalidation.py
|
|
for an example.
|
|
|
|
To avoid unnecessary memory duplication the X argument of the fit method
|
|
should be directly passed as a fortran contiguous numpy array.
|
|
"""
|
|
|
|
path = staticmethod(enet_path)
|
|
|
|
def __init__(self, rho=0.5, eps=1e-3, n_alphas=100, alphas=None,
|
|
fit_intercept=True):
|
|
self.rho = rho
|
|
self.eps = eps
|
|
self.n_alphas = n_alphas
|
|
self.alphas = alphas
|
|
self.fit_intercept = fit_intercept
|