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base.py
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"""
Generalized Linear models.
"""
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Fabian Pedregosa <fabian.pedregosa@inria.fr>
# Olivier Grisel <olivier.grisel@ensta.org>
# Vincent Michel <vincent.michel@inria.fr>
# Peter Prettenhofer <peter.prettenhofer@gmail.com>
# Mathieu Blondel <mathieu@mblondel.org>
#
# License: BSD Style.
from abc import ABCMeta, abstractmethod
import numpy as np
import scipy.sparse as sp
from scipy import linalg
import scipy.sparse.linalg as sp_linalg
from ..base import BaseEstimator
from ..base import RegressorMixin
from ..base import ClassifierMixin
from ..base import TransformerMixin
from ..utils.extmath import safe_sparse_dot
from ..utils import array2d, as_float_array, safe_asarray
from ..utils import atleast2d_or_csr, check_arrays
from .sgd_fast import Hinge, Log, ModifiedHuber, SquaredLoss, Huber
###
### TODO: intercept for all models
### We should define a common function to center data instead of
### repeating the same code inside each fit method.
###
### Also, bayesian_ridge_regression and bayesian_regression_ard
### should be squashed into its respective objects.
###
class LinearModel(BaseEstimator, RegressorMixin):
"""Base class for Linear Models"""
def predict(self, X):
"""Predict using the linear model
Parameters
----------
X : numpy array of shape [n_samples, n_features]
Returns
-------
C : array, shape = [n_samples]
Returns predicted values.
"""
X = safe_asarray(X)
return safe_sparse_dot(X, self.coef_.T) + self.intercept_
@staticmethod
def _center_data(X, y, fit_intercept, normalize=False, copy=True):
"""
Centers data to have mean zero along axis 0. This is here because
nearly all linear models will want their data to be centered.
If copy is False, modifies X in-place.
"""
X = as_float_array(X, copy)
if fit_intercept:
if sp.issparse(X):
X_mean = np.zeros(X.shape[1])
X_std = np.ones(X.shape[1])
else:
X_mean = X.mean(axis=0)
X -= X_mean
if normalize:
X_std = np.sqrt(np.sum(X ** 2, axis=0))
X_std[X_std == 0] = 1
X /= X_std
else:
X_std = np.ones(X.shape[1])
y_mean = y.mean()
y = y - y_mean
else:
X_mean = np.zeros(X.shape[1])
X_std = np.ones(X.shape[1])
y_mean = 0.
return X, y, X_mean, y_mean, X_std
def _set_intercept(self, X_mean, y_mean, X_std):
"""Set the intercept_
"""
if self.fit_intercept:
self.coef_ = self.coef_ / X_std
self.intercept_ = y_mean - np.dot(X_mean, self.coef_.T)
else:
self.intercept_ = 0
class LinearRegression(LinearModel):
"""
Ordinary least squares Linear Regression.
Attributes
----------
`coef_` : array
Estimated coefficients for the linear regression problem.
`intercept_` : array
Independent term in the linear model.
Parameters
----------
fit_intercept : boolean, optional
wether 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).
normalize : boolean, optional
If True, the regressors X are normalized
Notes
-----
From the implementation point of view, this is just plain Ordinary
Least Squares (numpy.linalg.lstsq) wrapped as a predictor object.
"""
def __init__(self, fit_intercept=True, normalize=False, copy_X=True):
self.fit_intercept = fit_intercept
self.normalize = normalize
self.copy_X = copy_X
def fit(self, X, y):
"""
Fit linear model.
Parameters
----------
X : numpy array or sparse matrix of shape [n_samples,n_features]
Training data
y : numpy array of shape [n_samples]
Target values
Returns
-------
self : returns an instance of self.
"""
X = safe_asarray(X)
y = np.asarray(y)
X, y, X_mean, y_mean, X_std = self._center_data(X, y,
self.fit_intercept, self.normalize, self.copy_X)
if sp.issparse(X):
if hasattr(sp_linalg, 'lsqr'):
out = sp_linalg.lsqr(X, y)
self.coef_ = out[0]
self.residues_ = out[3]
else:
# DEPENDENCY: scipy 0.7
self.coef_ = sp_linalg.spsolve(X, y)
self.residues_ = y - safe_sparse_dot(X, self.coef_)
else:
self.coef_, self.residues_, self.rank_, self.singular_ = \
linalg.lstsq(X, y)
self._set_intercept(X_mean, y_mean, X_std)
return self
##
## Stochastic Gradient Descent (SGD) abstract base classes
##
class BaseSGD(BaseEstimator):
"""Base class for dense and sparse SGD."""
__metaclass__ = ABCMeta
def __init__(self, loss, penalty='l2', alpha=0.0001,
rho=0.85, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, seed=0, learning_rate="optimal", eta0=0.0,
power_t=0.5, class_weight=None):
self.loss = str(loss)
self.penalty = str(penalty)
self._set_loss_function(self.loss)
self._set_penalty_type(self.penalty)
self.alpha = float(alpha)
if self.alpha < 0.0:
raise ValueError("alpha must be greater than zero")
self.rho = float(rho)
if self.rho < 0.0 or self.rho > 1.0:
raise ValueError("rho must be in [0, 1]")
self.fit_intercept = bool(fit_intercept)
self.n_iter = int(n_iter)
if self.n_iter <= 0:
raise ValueError("n_iter must be greater than zero")
if not isinstance(shuffle, bool):
raise ValueError("shuffle must be either True or False")
self.shuffle = bool(shuffle)
self.seed = seed
self.verbose = int(verbose)
self.learning_rate = str(learning_rate)
self._set_learning_rate(self.learning_rate)
self.eta0 = float(eta0)
self.power_t = float(power_t)
if self.learning_rate != "optimal":
if eta0 <= 0.0:
raise ValueError("eta0 must be greater than 0.0")
self.class_weight = class_weight
@abstractmethod
def fit(self, X, y):
"""Fit model."""
@abstractmethod
def predict(self, X):
"""Predict using model."""
def _set_learning_rate(self, learning_rate):
learning_rate_codes = {"constant": 1, "optimal": 2, "invscaling": 3}
try:
self.learning_rate_code = learning_rate_codes[learning_rate]
except KeyError:
raise ValueError("learning rate %s"
"is not supported. " % learning_rate)
def _set_loss_function(self, loss):
"""Get concrete LossFunction"""
raise NotImplementedError("BaseSGD is an abstract class.")
def _set_penalty_type(self, penalty):
penalty_types = {"l2": 2, "l1": 1, "elasticnet": 3}
try:
self.penalty_type = penalty_types[penalty]
except KeyError:
raise ValueError("Penalty %s is not supported. " % penalty)
def _validate_sample_weight(self, sample_weight, n_samples):
"""Set the sample weight array."""
if sample_weight == None:
sample_weight = np.ones(n_samples, dtype=np.float64, order='C')
else:
sample_weight = np.asarray(sample_weight, dtype=np.float64,
order="C")
if sample_weight.shape[0] != n_samples:
raise ValueError("Shapes of X and sample_weight do not match.")
return sample_weight
def _set_coef(self, coef_):
"""Make sure that coef_ is fortran-style and 2d. """
self.coef_ = np.asfortranarray(array2d(coef_))
def _allocate_parameter_mem(self, n_classes, n_features, coef_init=None,
intercept_init=None):
"""Allocate mem for parameters; initialize if provided."""
if n_classes > 2:
# allocate coef_ for multi-class
if coef_init is not None:
coef_init = np.asarray(coef_init)
if coef_init.shape != (n_classes, n_features):
raise ValueError("Provided coef_ does not match dataset. ")
self.coef_ = coef_init
else:
self.coef_ = np.zeros((n_classes, n_features),
dtype=np.float64, order="C")
# allocate intercept_ for multi-class
if intercept_init is not None:
intercept_init = np.asarray(intercept_init)
if intercept_init.shape != (n_classes, ):
raise ValueError("Provided intercept_init " \
"does not match dataset.")
self.intercept_ = intercept_init
else:
self.intercept_ = np.zeros(n_classes, dtype=np.float64,
order="C")
else:
# allocate coef_ for binary problem
if coef_init is not None:
coef_init = np.asarray(coef_init, dtype=np.float64,
order="C")
coef_init = coef_init.ravel()
if coef_init.shape != (n_features,):
raise ValueError("Provided coef_init does not " \
"match dataset.")
self.coef_ = coef_init
else:
self.coef_ = np.zeros(n_features, dtype=np.float64, order="C")
# allocate intercept_ for binary problem
if intercept_init is not None:
intercept_init = np.asarray(intercept_init, dtype=np.float64)
if intercept_init.shape != (1,) and intercept_init.shape != ():
raise ValueError("Provided intercept_init " \
"does not match dataset.")
self.intercept_ = intercept_init.reshape(1,)
else:
self.intercept_ = np.zeros(1, dtype=np.float64, order="C")
class BaseSGDClassifier(BaseSGD, ClassifierMixin):
"""Base class for dense and sparse classification using SGD."""
__metaclass__ = ABCMeta
def __init__(self, loss="hinge", penalty='l2', alpha=0.0001,
rho=0.85, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, n_jobs=1, seed=0, learning_rate="optimal",
eta0=0.0, power_t=0.5, class_weight=None):
super(BaseSGDClassifier, self).__init__(loss=loss, penalty=penalty,
alpha=alpha, rho=rho,
fit_intercept=fit_intercept,
n_iter=n_iter, shuffle=shuffle,
verbose=verbose, seed=seed,
learning_rate=learning_rate,
eta0=eta0, power_t=power_t,
class_weight=class_weight)
self.n_jobs = int(n_jobs)
def _set_loss_function(self, loss):
"""Set concrete LossFunction."""
loss_functions = {
"hinge": Hinge(),
"log": Log(),
"modified_huber": ModifiedHuber(),
}
try:
self.loss_function = loss_functions[loss]
except KeyError:
raise ValueError("The loss %s is not supported. " % loss)
def _set_class_weight(self, class_weight, classes, y):
"""Estimate class weights for unbalanced datasets."""
if class_weight is None:
class_weight = self.class_weight
if class_weight is None or len(class_weight) == 0:
weight = np.ones(classes.shape[0], dtype=np.float64, order='C')
elif class_weight == 'auto':
weight = np.array([1.0 / np.sum(y == i) for i in classes],
dtype=np.float64, order='C')
weight *= classes.shape[0] / np.sum(weight)
else:
weight = np.ones(classes.shape[0], dtype=np.float64, order='C')
if not isinstance(class_weight, dict):
raise ValueError("class_weight must be dict, 'auto', or None,"
" got: %r" % class_weight)
for c in class_weight:
i = np.searchsorted(classes, c)
if classes[i] != c:
raise ValueError("Class label %d not present." % c)
else:
weight[i] = class_weight[c]
self._expanded_class_weight = weight
def fit(self, X, y, coef_init=None, intercept_init=None,
class_weight=None, sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : numpy array of shape [n_samples,n_features]
Training data
y : numpy array of shape [n_samples]
Target values
coef_init : array, shape = [n_classes,n_features]
The initial coeffients to warm-start the optimization.
intercept_init : array, shape = [n_classes]
The initial intercept to warm-start the optimization.
class_weight : dict, {class_label : weight} or "auto"
Weights associated with classes. If not given, all classes
are supposed to have weight one.
The "auto" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies.
sample_weight : array-like, shape = [n_samples], optional
Weights applied to individual samples (1. for unweighted).
Returns
-------
self : returns an instance of self.
"""
X = safe_asarray(X)
y = np.asarray(y)
n_samples, n_features = X.shape
if n_samples != y.shape[0]:
raise ValueError("Shapes of X and y do not match.")
# sort in asc order; largest class id is positive class
self.classes = np.unique(y)
n_classes = self.classes.shape[0]
# Allocate datastructures from input arguments
self._set_class_weight(class_weight, self.classes, y)
sample_weight = self._validate_sample_weight(sample_weight, n_samples)
self._allocate_parameter_mem(n_classes, n_features,
coef_init, intercept_init)
# delegate to concrete training procedure
if n_classes > 2:
self._fit_multiclass(X, y, sample_weight)
elif n_classes == 2:
self._fit_binary(X, y, sample_weight)
else:
raise ValueError("The number of class labels must be "
"greater than one.")
# return self for chaining fit and predict calls
return self
@abstractmethod
def _fit_binary(self, X, y, sample_weight):
"""Fit binary classifier."""
@abstractmethod
def _fit_multiclass(self, X, y, sample_weight):
"""Fit multiclass classifier."""
def decision_function(self, X):
"""Predict signed 'distance' to the hyperplane (aka confidence score)
Parameters
----------
X : array, shape [n_samples, n_features]
Returns
-------
array, shape = [n_samples] if n_classes == 2 else [n_samples,n_classes]
The signed 'distances' to the hyperplane(s).
"""
X = atleast2d_or_csr(X)
scores = safe_sparse_dot(X, self.coef_.T) + self.intercept_
if self.classes.shape[0] == 2:
return np.ravel(scores)
else:
return scores
def predict(self, X):
"""Predict using the linear model
Parameters
----------
X : array or scipy.sparse matrix of shape [n_samples, n_features]
Whether the numpy.array or scipy.sparse matrix is accepted depends
on the actual implementation
Returns
-------
array, shape = [n_samples]
Array containing the predicted class labels.
"""
scores = self.decision_function(X)
if self.classes.shape[0] == 2:
indices = np.array(scores > 0, dtype=np.int)
else:
indices = scores.argmax(axis=1)
return self.classes[np.ravel(indices)]
def predict_proba(self, X):
"""Predict class membership probability
Parameters
----------
X : array or scipy.sparse matrix of shape [n_samples, n_features]
Returns
-------
array, shape = [n_samples] if n_classes == 2 else [n_samples,
n_classes]
Contains the membership probabilities of the positive class.
"""
if len(self.classes) != 2:
raise NotImplementedError("predict_(log_)proba only supported"
" for binary classification")
elif not isinstance(self.loss_function, Log):
raise NotImplementedError("predict_(log_)proba only supported when"
" loss='log' (%s given)" % self.loss)
return 1.0 / (1.0 + np.exp(-self.decision_function(X)))
class BaseSGDRegressor(BaseSGD, RegressorMixin):
"""Base class for dense and sparse regression using SGD."""
__metaclass__ = ABCMeta
def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001,
rho=0.85, fit_intercept=True, n_iter=5, shuffle=False,
verbose=0, p=0.1, seed=0, learning_rate="invscaling",
eta0=0.01, power_t=0.25):
self.p = float(p)
super(BaseSGDRegressor, self).__init__(loss=loss, penalty=penalty,
alpha=alpha, rho=rho,
fit_intercept=fit_intercept,
n_iter=n_iter, shuffle=shuffle,
verbose=verbose, seed=seed,
learning_rate=learning_rate,
eta0=eta0, power_t=power_t)
def _set_loss_function(self, loss):
"""Get concrete LossFunction"""
loss_functions = {
"squared_loss": SquaredLoss(),
"huber": Huber(self.p),
}
try:
self.loss_function = loss_functions[loss]
except KeyError:
raise ValueError("The loss %s is not supported. " % loss)
def fit(self, X, y, coef_init=None, intercept_init=None,
sample_weight=None):
"""Fit linear model with Stochastic Gradient Descent.
Parameters
----------
X : numpy array of shape [n_samples,n_features]
Training data
y : numpy array of shape [n_samples]
Target values
coef_init : array, shape = [n_features]
The initial coeffients to warm-start the optimization.
intercept_init : array, shape = [1]
The initial intercept to warm-start the optimization.
sample_weight : array-like, shape = [n_samples], optional
Weights applied to individual samples (1. for unweighted).
Returns
-------
self : returns an instance of self.
"""
X, y = check_arrays(X, y, sparse_format="csr", copy=False)
y = np.asarray(y, dtype=np.float64, order="C")
n_samples, n_features = X.shape
# Allocate datastructures from input arguments
sample_weight = self._validate_sample_weight(sample_weight, n_samples)
self._allocate_parameter_mem(1, n_features,
coef_init, intercept_init)
self._fit_regressor(X, y, sample_weight)
return self
@abstractmethod
def _fit_regressor(self, X, y, sample_weight):
"""Fit regression model."""
def predict(self, X):
"""Predict using the linear model
Parameters
----------
X : array or scipy.sparse matrix of shape [n_samples, n_features]
Whether the numpy.array or scipy.sparse matrix is accepted depends
on the actual implementation.
Returns
-------
array, shape = [n_samples]
Array containing the predicted class labels.
"""
X = atleast2d_or_csr(X)
scores = safe_sparse_dot(X, self.coef_) + self.intercept_
return scores.ravel()
class CoefSelectTransformerMixin(TransformerMixin):
"""Mixin for linear models that can find sparse solutions."""
def transform(self, X, threshold=1e-10):
if len(self.coef_.shape) == 1 or self.coef_.shape[1] == 1:
# 2-class case
coef = np.ravel(self.coef_)
else:
# multi-class case
coef = np.mean(self.coef_, axis=0)
return X[:, coef > threshold]