base.py

"""
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>
#         Lars Buitinck
#         Maryan Morel <maryan.morel@polytechnique.edu>
#         Giorgio Patrini <giorgio.patrini@anu.edu.au>
# License: BSD 3 clause

from __future__ import division
from abc import ABCMeta, abstractmethod
import numbers
import warnings

import numpy as np
import scipy.sparse as sp
from scipy import linalg
from scipy import sparse

from ..externals import six
from ..externals.joblib import Parallel, delayed
from ..base import BaseEstimator, ClassifierMixin, RegressorMixin
from ..utils import check_array, check_X_y, deprecated, as_float_array
from ..utils.validation import FLOAT_DTYPES
from ..utils import check_random_state
from ..utils.extmath import safe_sparse_dot
from ..utils.sparsefuncs import mean_variance_axis, inplace_column_scale
from ..utils.fixes import sparse_lsqr
from ..utils.seq_dataset import ArrayDataset, CSRDataset
from ..utils.validation import check_is_fitted
from ..exceptions import NotFittedError
from ..preprocessing.data import normalize as f_normalize

# TODO: bayesian_ridge_regression and bayesian_regression_ard
# should be squashed into its respective objects.

SPARSE_INTERCEPT_DECAY = 0.01
# For sparse data intercept updates are scaled by this decay factor to avoid
# intercept oscillation.


def make_dataset(X, y, sample_weight, random_state=None):
    """Create ``Dataset`` abstraction for sparse and dense inputs.

    This also returns the ``intercept_decay`` which is different
    for sparse datasets.
    """

    rng = check_random_state(random_state)
    # seed should never be 0 in SequentialDataset
    seed = rng.randint(1, np.iinfo(np.int32).max)

    if sp.issparse(X):
        dataset = CSRDataset(X.data, X.indptr, X.indices, y, sample_weight,
                             seed=seed)
        intercept_decay = SPARSE_INTERCEPT_DECAY
    else:
        dataset = ArrayDataset(X, y, sample_weight, seed=seed)
        intercept_decay = 1.0

    return dataset, intercept_decay


@deprecated("sparse_center_data was deprecated in version 0.18 and will be "
            "removed in 0.20. Use utilities in preprocessing.data instead")
def sparse_center_data(X, y, fit_intercept, normalize=False):
    """
    Compute information needed to center data to have mean zero along
    axis 0. Be aware that X will not be centered since it would break
    the sparsity, but will be normalized if asked so.
    """
    if fit_intercept:
        # we might require not to change the csr matrix sometimes
        # store a copy if normalize is True.
        # Change dtype to float64 since mean_variance_axis accepts
        # it that way.
        if sp.isspmatrix(X) and X.getformat() == 'csr':
            X = sp.csr_matrix(X, copy=normalize, dtype=np.float64)
        else:
            X = sp.csc_matrix(X, copy=normalize, dtype=np.float64)

        X_offset, X_var = mean_variance_axis(X, axis=0)
        if normalize:
            # transform variance to std in-place
            X_var *= X.shape[0]
            X_std = np.sqrt(X_var, X_var)
            del X_var
            X_std[X_std == 0] = 1
            inplace_column_scale(X, 1. / X_std)
        else:
            X_std = np.ones(X.shape[1])
        y_offset = y.mean(axis=0)
        y = y - y_offset
    else:
        X_offset = np.zeros(X.shape[1])
        X_std = np.ones(X.shape[1])
        y_offset = 0. if y.ndim == 1 else np.zeros(y.shape[1], dtype=X.dtype)

    return X, y, X_offset, y_offset, X_std


@deprecated("center_data was deprecated in version 0.18 and will be removed "
            "in 0.20. Use utilities in preprocessing.data instead")
def center_data(X, y, fit_intercept, normalize=False, copy=True,
                sample_weight=None):
    """
    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 sample_weight is not None, then the weighted mean of X and y
    is zero, and not the mean itself
    """
    X = as_float_array(X, copy)
    if fit_intercept:
        if isinstance(sample_weight, numbers.Number):
            sample_weight = None
        if sp.issparse(X):
            X_offset = np.zeros(X.shape[1])
            X_std = np.ones(X.shape[1])
        else:
            X_offset = np.average(X, axis=0, weights=sample_weight)
            X -= X_offset
            # XXX: currently scaled to variance=n_samples
            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_offset = np.average(y, axis=0, weights=sample_weight)
        y = y - y_offset
    else:
        X_offset = np.zeros(X.shape[1])
        X_std = np.ones(X.shape[1])
        y_offset = 0. if y.ndim == 1 else np.zeros(y.shape[1], dtype=X.dtype)
    return X, y, X_offset, y_offset, X_std


def _preprocess_data(X, y, fit_intercept, normalize=False, copy=True,
                     sample_weight=None, return_mean=False):
    """
    Centers data to have mean zero along axis 0. If fit_intercept=False or if
    the X is a sparse matrix, no centering is done, but normalization can still
    be applied. The function returns the statistics necessary to reconstruct
    the input data, which are X_offset, y_offset, X_scale, such that the output

        X = (X - X_offset) / X_scale

    X_scale is the L2 norm of X - X_offset. If sample_weight is not None,
    then the weighted mean of X and y is zero, and not the mean itself. If
    return_mean=True, the mean, eventually weighted, is returned, independently
    of whether X was centered (option used for optimization with sparse data in
    coordinate_descend).

    This is here because nearly all linear models will want their data to be
    centered. This function also systematically makes y consistent with X.dtype
    """

    if isinstance(sample_weight, numbers.Number):
        sample_weight = None

    X = check_array(X, copy=copy, accept_sparse=['csr', 'csc'],
                    dtype=FLOAT_DTYPES)
    y = np.asarray(y, dtype=X.dtype)

    if fit_intercept:
        if sp.issparse(X):
            X_offset, X_var = mean_variance_axis(X, axis=0)
            if not return_mean:
                X_offset[:] = X.dtype.type(0)

            if normalize:

                # TODO: f_normalize could be used here as well but the function
                # inplace_csr_row_normalize_l2 must be changed such that it
                # can return also the norms computed internally

                # transform variance to norm in-place
                X_var *= X.shape[0]
                X_scale = np.sqrt(X_var, X_var)
                del X_var
                X_scale[X_scale == 0] = 1
                inplace_column_scale(X, 1. / X_scale)
            else:
                X_scale = np.ones(X.shape[1], dtype=X.dtype)

        else:
            X_offset = np.average(X, axis=0, weights=sample_weight)
            X -= X_offset
            if normalize:
                X, X_scale = f_normalize(X, axis=0, copy=False,
                                         return_norm=True)
            else:
                X_scale = np.ones(X.shape[1], dtype=X.dtype)
        y_offset = np.average(y, axis=0, weights=sample_weight)
        y = y - y_offset
    else:
        X_offset = np.zeros(X.shape[1], dtype=X.dtype)
        X_scale = np.ones(X.shape[1], dtype=X.dtype)
        if y.ndim == 1:
            y_offset = X.dtype.type(0)
        else:
            y_offset = np.zeros(y.shape[1], dtype=X.dtype)

    return X, y, X_offset, y_offset, X_scale


# TODO: _rescale_data should be factored into _preprocess_data.
# Currently, the fact that sag implements its own way to deal with
# sample_weight makes the refactoring tricky.

def _rescale_data(X, y, sample_weight):
    """Rescale data so as to support sample_weight"""
    n_samples = X.shape[0]
    sample_weight = sample_weight * np.ones(n_samples)
    sample_weight = np.sqrt(sample_weight)
    sw_matrix = sparse.dia_matrix((sample_weight, 0),
                                  shape=(n_samples, n_samples))
    X = safe_sparse_dot(sw_matrix, X)
    y = safe_sparse_dot(sw_matrix, y)
    return X, y


class LinearModel(six.with_metaclass(ABCMeta, BaseEstimator)):
    """Base class for Linear Models"""

    @abstractmethod
    def fit(self, X, y):
        """Fit model."""

    def _decision_function(self, X):
        check_is_fitted(self, "coef_")

        X = check_array(X, accept_sparse=['csr', 'csc', 'coo'])
        return safe_sparse_dot(X, self.coef_.T,
                               dense_output=True) + self.intercept_

    def predict(self, X):
        """Predict using the linear model

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape = (n_samples, n_features)
            Samples.

        Returns
        -------
        C : array, shape = (n_samples,)
            Returns predicted values.
        """
        return self._decision_function(X)

    _preprocess_data = staticmethod(_preprocess_data)

    def _set_intercept(self, X_offset, y_offset, X_scale):
        """Set the intercept_
        """
        if self.fit_intercept:
            self.coef_ = self.coef_ / X_scale
            self.intercept_ = y_offset - np.dot(X_offset, self.coef_.T)
        else:
            self.intercept_ = 0.


# XXX Should this derive from LinearModel? It should be a mixin, not an ABC.
# Maybe the n_features checking can be moved to LinearModel.
class LinearClassifierMixin(ClassifierMixin):
    """Mixin for linear classifiers.

    Handles prediction for sparse and dense X.
    """

    def decision_function(self, X):
        """Predict confidence scores for samples.

        The confidence score for a sample is the signed distance of that
        sample to the hyperplane.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape = (n_samples, n_features)
            Samples.

        Returns
        -------
        array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)
            Confidence scores per (sample, class) combination. In the binary
            case, confidence score for self.classes_[1] where >0 means this
            class would be predicted.
        """
        if not hasattr(self, 'coef_') or self.coef_ is None:
            raise NotFittedError("This %(name)s instance is not fitted "
                                 "yet" % {'name': type(self).__name__})

        X = check_array(X, accept_sparse='csr')

        n_features = self.coef_.shape[1]
        if X.shape[1] != n_features:
            raise ValueError("X has %d features per sample; expecting %d"
                             % (X.shape[1], n_features))

        scores = safe_sparse_dot(X, self.coef_.T,
                                 dense_output=True) + self.intercept_
        return scores.ravel() if scores.shape[1] == 1 else scores

    def predict(self, X):
        """Predict class labels for samples in X.

        Parameters
        ----------
        X : {array-like, sparse matrix}, shape = [n_samples, n_features]
            Samples.

        Returns
        -------
        C : array, shape = [n_samples]
            Predicted class label per sample.
        """
        scores = self.decision_function(X)
        if len(scores.shape) == 1:
            indices = (scores > 0).astype(np.int)
        else:
            indices = scores.argmax(axis=1)
        return self.classes_[indices]

    def _predict_proba_lr(self, X):
        """Probability estimation for OvR logistic regression.

        Positive class probabilities are computed as
        1. / (1. + np.exp(-self.decision_function(X)));
        multiclass is handled by normalizing that over all classes.
        """
        prob = self.decision_function(X)
        prob *= -1
        np.exp(prob, prob)
        prob += 1
        np.reciprocal(prob, prob)
        if prob.ndim == 1:
            return np.vstack([1 - prob, prob]).T
        else:
            # OvR normalization, like LibLinear's predict_probability
            prob /= prob.sum(axis=1).reshape((prob.shape[0], -1))
            return prob


class SparseCoefMixin(object):
    """Mixin for converting coef_ to and from CSR format.

    L1-regularizing estimators should inherit this.
    """

    def densify(self):
        """Convert coefficient matrix to dense array format.

        Converts the ``coef_`` member (back) to a numpy.ndarray. This is the
        default format of ``coef_`` and is required for fitting, so calling
        this method is only required on models that have previously been
        sparsified; otherwise, it is a no-op.

        Returns
        -------
        self : estimator
        """
        msg = "Estimator, %(name)s, must be fitted before densifying."
        check_is_fitted(self, "coef_", msg=msg)
        if sp.issparse(self.coef_):
            self.coef_ = self.coef_.toarray()
        return self

    def sparsify(self):
        """Convert coefficient matrix to sparse format.

        Converts the ``coef_`` member to a scipy.sparse matrix, which for
        L1-regularized models can be much more memory- and storage-efficient
        than the usual numpy.ndarray representation.

        The ``intercept_`` member is not converted.

        Notes
        -----
        For non-sparse models, i.e. when there are not many zeros in ``coef_``,
        this may actually *increase* memory usage, so use this method with
        care. A rule of thumb is that the number of zero elements, which can
        be computed with ``(coef_ == 0).sum()``, must be more than 50% for this
        to provide significant benefits.

        After calling this method, further fitting with the partial_fit
        method (if any) will not work until you call densify.

        Returns
        -------
        self : estimator
        """
        msg = "Estimator, %(name)s, must be fitted before sparsifying."
        check_is_fitted(self, "coef_", msg=msg)
        self.coef_ = sp.csr_matrix(self.coef_)
        return self


class LinearRegression(LinearModel, RegressorMixin):
    """
    Ordinary least squares Linear Regression.

    Parameters
    ----------
    fit_intercept : boolean, optional, default True
        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).

    normalize : boolean, optional, default False
        This parameter is ignored when ``fit_intercept`` is set to False.
        If True, the regressors X will be normalized before regression by
        subtracting the mean and dividing by the l2-norm.
        If you wish to standardize, please use
        :class:`sklearn.preprocessing.StandardScaler` before calling ``fit`` on
        an estimator with ``normalize=False``.

    copy_X : boolean, optional, default True
        If True, X will be copied; else, it may be overwritten.

    n_jobs : int, optional, default 1
        The number of jobs to use for the computation.
        If -1 all CPUs are used. This will only provide speedup for
        n_targets > 1 and sufficient large problems.

    Attributes
    ----------
    coef_ : array, shape (n_features, ) or (n_targets, n_features)
        Estimated coefficients for the linear regression problem.
        If multiple targets are passed during the fit (y 2D), this
        is a 2D array of shape (n_targets, n_features), while if only
        one target is passed, this is a 1D array of length n_features.

    intercept_ : array
        Independent term in the linear model.

    Notes
    -----
    From the implementation point of view, this is just plain Ordinary
    Least Squares (scipy.linalg.lstsq) wrapped as a predictor object.

    """

    def __init__(self, fit_intercept=True, normalize=False, copy_X=True,
                 n_jobs=1):
        self.fit_intercept = fit_intercept
        self.normalize = normalize
        self.copy_X = copy_X
        self.n_jobs = n_jobs

    def fit(self, X, y, sample_weight=None):
        """
        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, n_targets]
            Target values. Will be cast to X's dtype if necessary

        sample_weight : numpy array of shape [n_samples]
            Individual weights for each sample

            .. versionadded:: 0.17
               parameter *sample_weight* support to LinearRegression.

        Returns
        -------
        self : returns an instance of self.
        """

        n_jobs_ = self.n_jobs
        X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'],
                         y_numeric=True, multi_output=True)

        if sample_weight is not None and np.atleast_1d(sample_weight).ndim > 1:
            raise ValueError("Sample weights must be 1D array or scalar")

        X, y, X_offset, y_offset, X_scale = self._preprocess_data(
            X, y, fit_intercept=self.fit_intercept, normalize=self.normalize,
            copy=self.copy_X, sample_weight=sample_weight)

        if sample_weight is not None:
            # Sample weight can be implemented via a simple rescaling.
            X, y = _rescale_data(X, y, sample_weight)

        if sp.issparse(X):
            if y.ndim < 2:
                out = sparse_lsqr(X, y)
                self.coef_ = out[0]
                self._residues = out[3]
            else:
                # sparse_lstsq cannot handle y with shape (M, K)
                outs = Parallel(n_jobs=n_jobs_)(
                    delayed(sparse_lsqr)(X, y[:, j].ravel())
                    for j in range(y.shape[1]))
                self.coef_ = np.vstack(out[0] for out in outs)
                self._residues = np.vstack(out[3] for out in outs)
        else:
            self.coef_, self._residues, self.rank_, self.singular_ = \
                linalg.lstsq(X, y)
            self.coef_ = self.coef_.T

        if y.ndim == 1:
            self.coef_ = np.ravel(self.coef_)
        self._set_intercept(X_offset, y_offset, X_scale)
        return self


def _pre_fit(X, y, Xy, precompute, normalize, fit_intercept, copy):
    """Aux function used at beginning of fit in linear models"""
    n_samples, n_features = X.shape

    if sparse.isspmatrix(X):
        # copy is not needed here as X is not modified inplace when X is sparse
        precompute = False
        X, y, X_offset, y_offset, X_scale = _preprocess_data(
            X, y, fit_intercept=fit_intercept, normalize=normalize,
            copy=False, return_mean=True)
    else:
        # copy was done in fit if necessary
        X, y, X_offset, y_offset, X_scale = _preprocess_data(
            X, y, fit_intercept=fit_intercept, normalize=normalize, copy=copy)
    if hasattr(precompute, '__array__') and (
            fit_intercept and not np.allclose(X_offset, np.zeros(n_features)) or
            normalize and not np.allclose(X_scale, np.ones(n_features))):
        warnings.warn("Gram matrix was provided but X was centered"
                      " to fit intercept, "
                      "or X was normalized : recomputing Gram matrix.",
                      UserWarning)
        # recompute Gram
        precompute = 'auto'
        Xy = None

    # precompute if n_samples > n_features
    if isinstance(precompute, six.string_types) and precompute == 'auto':
        precompute = (n_samples > n_features)

    if precompute is True:
        # make sure that the 'precompute' array is contiguous.
        precompute = np.empty(shape=(n_features, n_features), dtype=X.dtype,
                              order='C')
        np.dot(X.T, X, out=precompute)

    if not hasattr(precompute, '__array__'):
        Xy = None  # cannot use Xy if precompute is not Gram

    if hasattr(precompute, '__array__') and Xy is None:
        common_dtype = np.find_common_type([X.dtype, y.dtype], [])
        if y.ndim == 1:
            # Xy is 1d, make sure it is contiguous.
            Xy = np.empty(shape=n_features, dtype=common_dtype, order='C')
            np.dot(X.T, y, out=Xy)
        else:
            # Make sure that Xy is always F contiguous even if X or y are not
            # contiguous: the goal is to make it fast to extract the data for a
            # specific target.
            n_targets = y.shape[1]
            Xy = np.empty(shape=(n_features, n_targets), dtype=common_dtype,
                          order='F')
            np.dot(y.T, X, out=Xy.T)

    return X, y, X_offset, y_offset, X_scale, precompute, Xy