421 lines
14 KiB
Python
421 lines
14 KiB
Python
"""
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Generalized Linear models.
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"""
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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Fabian Pedregosa <fabian.pedregosa@inria.fr>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# Vincent Michel <vincent.michel@inria.fr>
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# Peter Prettenhofer <peter.prettenhofer@gmail.com>
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# Mathieu Blondel <mathieu@mblondel.org>
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# Lars Buitinck <L.J.Buitinck@uva.nl>
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#
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# License: BSD 3 clause
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from abc import ABCMeta, abstractmethod
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import numbers
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import numpy as np
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import scipy.sparse as sp
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from scipy import linalg
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from scipy import sparse
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from ..externals import six
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from ..externals.joblib import Parallel, delayed
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from ..base import BaseEstimator, ClassifierMixin, RegressorMixin
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from ..utils import as_float_array, atleast2d_or_csr, safe_asarray
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from ..utils.extmath import safe_sparse_dot
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from ..utils.fixes import lsqr
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from ..utils.sparsefuncs import (csc_mean_variance_axis0,
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inplace_csc_column_scale)
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from .cd_fast import sparse_std
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###
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### TODO: intercept for all models
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### We should define a common function to center data instead of
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### repeating the same code inside each fit method.
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### TODO: bayesian_ridge_regression and bayesian_regression_ard
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### should be squashed into its respective objects.
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def sparse_center_data(X, y, fit_intercept, normalize=False):
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"""
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Compute information needed to center data to have mean zero along
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axis 0. Be aware that X will not be centered since it would break
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the sparsity, but will be normalized if asked so.
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"""
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X = safe_asarray(X, dtype=np.float64)
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if fit_intercept:
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X_data = X.data
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# copy if 'normalize' is True or X is not a csc matrix
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X = sp.csc_matrix(X, copy=normalize)
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X_mean, X_std = csc_mean_variance_axis0(X)
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if normalize:
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X_std = sparse_std(
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X.shape[0], X.shape[1],
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X_data, X.indices, X.indptr, X_mean)
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X_std[X_std == 0] = 1
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inplace_csc_column_scale(X, X_std)
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else:
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X_std = np.ones(X.shape[1])
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y_mean = y.mean(axis=0)
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y = y - y_mean
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else:
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X_mean = np.zeros(X.shape[1])
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X_std = np.ones(X.shape[1])
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y_mean = 0. if y.ndim == 1 else np.zeros(y.shape[1], dtype=X.dtype)
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return X, y, X_mean, y_mean, X_std
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def center_data(X, y, fit_intercept, normalize=False, copy=True,
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sample_weight=None):
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"""
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Centers data to have mean zero along axis 0. This is here because
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nearly all linear models will want their data to be centered.
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If sample_weight is not None, then the weighted mean of X and y
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is zero, and not the mean itself
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"""
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X = as_float_array(X, copy)
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no_sample_weight = (sample_weight is None
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or isinstance(sample_weight, numbers.Number))
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if fit_intercept:
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if sp.issparse(X):
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X_mean = np.zeros(X.shape[1])
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X_std = np.ones(X.shape[1])
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else:
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if no_sample_weight:
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X_mean = X.mean(axis=0)
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else:
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X_mean = (np.sum(X * sample_weight[:, np.newaxis], axis=0)
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/ np.sum(sample_weight))
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X -= X_mean
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if normalize:
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X_std = np.sqrt(np.sum(X ** 2, axis=0))
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X_std[X_std == 0] = 1
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X /= X_std
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else:
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X_std = np.ones(X.shape[1])
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if no_sample_weight:
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y_mean = y.mean(axis=0)
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else:
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if y.ndim <= 1:
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y_mean = (np.sum(y * sample_weight, axis=0)
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/ np.sum(sample_weight))
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else:
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# cater for multi-output problems
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y_mean = (np.sum(y * sample_weight[:, np.newaxis], axis=0)
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/ np.sum(sample_weight))
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y = y - y_mean
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else:
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X_mean = np.zeros(X.shape[1])
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X_std = np.ones(X.shape[1])
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y_mean = 0. if y.ndim == 1 else np.zeros(y.shape[1], dtype=X.dtype)
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return X, y, X_mean, y_mean, X_std
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class LinearModel(six.with_metaclass(ABCMeta, BaseEstimator)):
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"""Base class for Linear Models"""
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@abstractmethod
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def fit(self, X, y):
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"""Fit model."""
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def decision_function(self, X):
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"""Decision function of the linear model.
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = (n_samples, n_features)
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Samples.
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Returns
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-------
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C : array, shape = (n_samples,)
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Returns predicted values.
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"""
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X = safe_asarray(X)
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return safe_sparse_dot(X, self.coef_.T,
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dense_output=True) + self.intercept_
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def predict(self, X):
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"""Predict using the linear model
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = (n_samples, n_features)
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Samples.
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Returns
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-------
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C : array, shape = (n_samples,)
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Returns predicted values.
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"""
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return self.decision_function(X)
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_center_data = staticmethod(center_data)
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def _set_intercept(self, X_mean, y_mean, X_std):
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"""Set the intercept_
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"""
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if self.fit_intercept:
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self.coef_ = self.coef_ / X_std
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self.intercept_ = y_mean - np.dot(X_mean, self.coef_.T)
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else:
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self.intercept_ = 0.
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# XXX Should this derive from LinearModel? It should be a mixin, not an ABC.
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# Maybe the n_features checking can be moved to LinearModel.
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class LinearClassifierMixin(ClassifierMixin):
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"""Mixin for linear classifiers.
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Handles prediction for sparse and dense X.
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"""
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def decision_function(self, X):
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"""Predict confidence scores for samples.
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The confidence score for a sample is the signed distance of that
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sample to the hyperplane.
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = (n_samples, n_features)
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Samples.
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Returns
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-------
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array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)
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Confidence scores per (sample, class) combination. In the binary
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case, confidence score for self.classes_[1] where >0 means this
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class would be predicted.
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"""
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X = atleast2d_or_csr(X)
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n_features = self.coef_.shape[1]
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if X.shape[1] != n_features:
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raise ValueError("X has %d features per sample; expecting %d"
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% (X.shape[1], n_features))
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scores = safe_sparse_dot(X, self.coef_.T,
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dense_output=True) + self.intercept_
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return scores.ravel() if scores.shape[1] == 1 else scores
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def predict(self, X):
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"""Predict class labels for samples in X.
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Parameters
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----------
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X : {array-like, sparse matrix}, shape = [n_samples, n_features]
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Samples.
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Returns
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-------
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C : array, shape = [n_samples]
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Predicted class label per sample.
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"""
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scores = self.decision_function(X)
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if len(scores.shape) == 1:
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indices = (scores > 0).astype(np.int)
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else:
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indices = scores.argmax(axis=1)
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return self.classes_[indices]
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def _predict_proba_lr(self, X):
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"""Probability estimation for OvR logistic regression.
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Positive class probabilities are computed as
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1. / (1. + np.exp(-self.decision_function(X)));
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multiclass is handled by normalizing that over all classes.
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"""
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prob = self.decision_function(X)
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prob *= -1
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np.exp(prob, prob)
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prob += 1
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np.reciprocal(prob, prob)
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if len(prob.shape) == 1:
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return np.vstack([1 - prob, prob]).T
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else:
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# OvR normalization, like LibLinear's predict_probability
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prob /= prob.sum(axis=1).reshape((prob.shape[0], -1))
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return prob
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class SparseCoefMixin(object):
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"""Mixin for converting coef_ to and from CSR format.
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L1-regularizing estimators should inherit this.
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"""
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def densify(self):
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"""Convert coefficient matrix to dense array format.
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Converts the ``coef_`` member (back) to a numpy.ndarray. This is the
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default format of ``coef_`` and is required for fitting, so calling
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this method is only required on models that have previously been
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sparsified; otherwise, it is a no-op.
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Returns
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-------
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self: estimator
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"""
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if not hasattr(self, "coef_"):
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raise ValueError("Estimator must be fitted before densifying.")
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if sp.issparse(self.coef_):
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self.coef_ = self.coef_.toarray()
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return self
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def sparsify(self):
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"""Convert coefficient matrix to sparse format.
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Converts the ``coef_`` member to a scipy.sparse matrix, which for
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L1-regularized models can be much more memory- and storage-efficient
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than the usual numpy.ndarray representation.
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The ``intercept_`` member is not converted.
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Notes
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-----
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For non-sparse models, i.e. when there are not many zeros in ``coef_``,
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this may actually *increase* memory usage, so use this method with
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care. A rule of thumb is that the number of zero elements, which can
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be computed with ``(coef_ == 0).sum()``, must be more than 50% for this
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to provide significant benefits.
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After calling this method, further fitting with the partial_fit
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method (if any) will not work until you call densify.
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Returns
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-------
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self: estimator
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"""
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if not hasattr(self, "coef_"):
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raise ValueError("Estimator must be fitted before sparsifying.")
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self.coef_ = sp.csr_matrix(self.coef_)
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return self
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class LinearRegression(LinearModel, RegressorMixin):
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"""
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Ordinary least squares Linear Regression.
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Parameters
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----------
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fit_intercept : boolean, optional
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whether to calculate the intercept for this model. If set
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to false, no intercept will be used in calculations
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(e.g. data is expected to be already centered).
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normalize : boolean, optional, default False
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If True, the regressors X will be normalized before regression.
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Attributes
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----------
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`coef_` : array, shape (n_features, ) or (n_targets, n_features)
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Estimated coefficients for the linear regression problem.
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If multiple targets are passed during the fit (y 2D), this
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is a 2D array of shape (n_targets, n_features), while if only
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one target is passed, this is a 1D array of length n_features.
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`intercept_` : array
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Independent term in the linear model.
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Notes
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-----
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From the implementation point of view, this is just plain Ordinary
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Least Squares (scipy.linalg.lstsq) wrapped as a predictor object.
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"""
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def __init__(self, fit_intercept=True, normalize=False, copy_X=True):
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self.fit_intercept = fit_intercept
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self.normalize = normalize
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self.copy_X = copy_X
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def fit(self, X, y, n_jobs=1):
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"""
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Fit linear model.
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Parameters
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----------
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X : numpy array or sparse matrix of shape [n_samples,n_features]
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Training data
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y : numpy array of shape [n_samples, n_targets]
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Target values
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n_jobs : The number of jobs to use for the computation.
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If -1 all CPUs are used. This will only provide speedup for
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n_targets > 1 and sufficient large problems
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Returns
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-------
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self : returns an instance of self.
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"""
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X = safe_asarray(X)
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y = np.asarray(y)
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X, y, X_mean, y_mean, X_std = self._center_data(
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X, y, self.fit_intercept, self.normalize, self.copy_X)
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if sp.issparse(X):
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if y.ndim < 2:
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out = lsqr(X, y)
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self.coef_ = out[0]
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self.residues_ = out[3]
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else:
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# sparse_lstsq cannot handle y with shape (M, K)
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outs = Parallel(n_jobs=n_jobs)(
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delayed(lsqr)(X, y[:, j].ravel())
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for j in range(y.shape[1]))
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self.coef_ = np.vstack(out[0] for out in outs)
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self.residues_ = np.vstack(out[3] for out in outs)
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else:
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self.coef_, self.residues_, self.rank_, self.singular_ = \
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linalg.lstsq(X, y)
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self.coef_ = self.coef_.T
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if y.ndim == 1:
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self.coef_ = np.ravel(self.coef_)
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self._set_intercept(X_mean, y_mean, X_std)
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return self
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def _pre_fit(X, y, Xy, precompute, normalize, fit_intercept, copy):
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"""Aux function used at beginning of fit in linear models"""
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n_samples, n_features = X.shape
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if sparse.isspmatrix(X):
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precompute = False
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X, y, X_mean, y_mean, X_std = sparse_center_data(
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X, y, fit_intercept, normalize)
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else:
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# copy was done in fit if necessary
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X, y, X_mean, y_mean, X_std = center_data(
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X, y, fit_intercept, normalize, copy=copy)
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if hasattr(precompute, '__array__') \
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and not np.allclose(X_mean, np.zeros(n_features)) \
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and not np.allclose(X_std, np.ones(n_features)):
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# recompute Gram
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precompute = 'auto'
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Xy = None
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# precompute if n_samples > n_features
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if precompute == 'auto':
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precompute = (n_samples > n_features)
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if precompute is True:
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precompute = np.dot(X.T, X)
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if not hasattr(precompute, '__array__'):
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Xy = None # cannot use Xy if precompute is not Gram
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if hasattr(precompute, '__array__') and Xy is None:
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Xy = np.dot(X.T, y)
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return X, y, X_mean, y_mean, X_std, precompute, Xy
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