846 lines
27 KiB
Python
846 lines
27 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
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# Maryan Morel <maryan.morel@polytechnique.edu>
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# Giorgio Patrini <giorgio.patrini@anu.edu.au>
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# Maria Telenczuk <https://github.com/maikia>
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# License: BSD 3 clause
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import numbers
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import warnings
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from abc import ABCMeta, abstractmethod
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from numbers import Integral
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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, optimize, sparse
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from scipy.sparse.linalg import lsqr
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from scipy.special import expit
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from ..base import (
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BaseEstimator,
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ClassifierMixin,
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MultiOutputMixin,
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RegressorMixin,
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_fit_context,
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)
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from ..utils import check_array, check_random_state
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from ..utils._array_api import (
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_asarray_with_order,
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_average,
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get_namespace,
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get_namespace_and_device,
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indexing_dtype,
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supported_float_dtypes,
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)
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from ..utils._seq_dataset import (
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ArrayDataset32,
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ArrayDataset64,
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CSRDataset32,
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CSRDataset64,
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)
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from ..utils.extmath import safe_sparse_dot
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from ..utils.parallel import Parallel, delayed
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from ..utils.sparsefuncs import mean_variance_axis
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from ..utils.validation import _check_sample_weight, check_is_fitted
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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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SPARSE_INTERCEPT_DECAY = 0.01
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# For sparse data intercept updates are scaled by this decay factor to avoid
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# intercept oscillation.
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def make_dataset(X, y, sample_weight, random_state=None):
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"""Create ``Dataset`` abstraction for sparse and dense inputs.
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This also returns the ``intercept_decay`` which is different
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for sparse datasets.
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Parameters
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----------
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X : array-like, shape (n_samples, n_features)
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Training data
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y : array-like, shape (n_samples, )
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Target values.
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sample_weight : numpy array of shape (n_samples,)
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The weight of each sample
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random_state : int, RandomState instance or None (default)
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Determines random number generation for dataset random sampling. It is not
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used for dataset shuffling.
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Pass an int for reproducible output across multiple function calls.
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See :term:`Glossary <random_state>`.
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Returns
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-------
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dataset
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The ``Dataset`` abstraction
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intercept_decay
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The intercept decay
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"""
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rng = check_random_state(random_state)
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# seed should never be 0 in SequentialDataset64
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seed = rng.randint(1, np.iinfo(np.int32).max)
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if X.dtype == np.float32:
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CSRData = CSRDataset32
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ArrayData = ArrayDataset32
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else:
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CSRData = CSRDataset64
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ArrayData = ArrayDataset64
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if sp.issparse(X):
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dataset = CSRData(X.data, X.indptr, X.indices, y, sample_weight, seed=seed)
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intercept_decay = SPARSE_INTERCEPT_DECAY
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else:
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X = np.ascontiguousarray(X)
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dataset = ArrayData(X, y, sample_weight, seed=seed)
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intercept_decay = 1.0
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return dataset, intercept_decay
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def _preprocess_data(
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X,
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y,
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*,
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fit_intercept,
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copy=True,
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copy_y=True,
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sample_weight=None,
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check_input=True,
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):
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"""Common data preprocessing for fitting linear models.
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This helper is in charge of the following steps:
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- Ensure that `sample_weight` is an array or `None`.
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- If `check_input=True`, perform standard input validation of `X`, `y`.
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- Perform copies if requested to avoid side-effects in case of inplace
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modifications of the input.
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Then, if `fit_intercept=True` this preprocessing centers both `X` and `y` as
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follows:
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- if `X` is dense, center the data and
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store the mean vector in `X_offset`.
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- if `X` is sparse, store the mean in `X_offset`
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without centering `X`. The centering is expected to be handled by the
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linear solver where appropriate.
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- in either case, always center `y` and store the mean in `y_offset`.
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- both `X_offset` and `y_offset` are always weighted by `sample_weight`
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if not set to `None`.
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If `fit_intercept=False`, no centering is performed and `X_offset`, `y_offset`
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are set to zero.
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Returns
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-------
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X_out : {ndarray, sparse matrix} of shape (n_samples, n_features)
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If copy=True a copy of the input X is triggered, otherwise operations are
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inplace.
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If input X is dense, then X_out is centered.
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y_out : {ndarray, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)
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Centered version of y. Possibly performed inplace on input y depending
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on the copy_y parameter.
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X_offset : ndarray of shape (n_features,)
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The mean per column of input X.
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y_offset : float or ndarray of shape (n_features,)
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X_scale : ndarray of shape (n_features,)
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Always an array of ones. TODO: refactor the code base to make it
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possible to remove this unused variable.
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"""
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xp, _, device_ = get_namespace_and_device(X, y, sample_weight)
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n_samples, n_features = X.shape
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X_is_sparse = sp.issparse(X)
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if isinstance(sample_weight, numbers.Number):
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sample_weight = None
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if sample_weight is not None:
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sample_weight = xp.asarray(sample_weight)
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if check_input:
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X = check_array(
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X, copy=copy, accept_sparse=["csr", "csc"], dtype=supported_float_dtypes(xp)
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)
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y = check_array(y, dtype=X.dtype, copy=copy_y, ensure_2d=False)
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else:
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y = xp.astype(y, X.dtype, copy=copy_y)
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if copy:
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if X_is_sparse:
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X = X.copy()
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else:
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X = _asarray_with_order(X, order="K", copy=True, xp=xp)
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dtype_ = X.dtype
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if fit_intercept:
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if X_is_sparse:
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X_offset, X_var = mean_variance_axis(X, axis=0, weights=sample_weight)
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else:
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X_offset = _average(X, axis=0, weights=sample_weight, xp=xp)
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X_offset = xp.astype(X_offset, X.dtype, copy=False)
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X -= X_offset
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y_offset = _average(y, axis=0, weights=sample_weight, xp=xp)
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y -= y_offset
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else:
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X_offset = xp.zeros(n_features, dtype=X.dtype, device=device_)
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if y.ndim == 1:
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y_offset = xp.asarray(0.0, dtype=dtype_, device=device_)
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else:
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y_offset = xp.zeros(y.shape[1], dtype=dtype_, device=device_)
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# XXX: X_scale is no longer needed. It is an historic artifact from the
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# time where linear model exposed the normalize parameter.
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X_scale = xp.ones(n_features, dtype=X.dtype, device=device_)
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return X, y, X_offset, y_offset, X_scale
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# TODO: _rescale_data should be factored into _preprocess_data.
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# Currently, the fact that sag implements its own way to deal with
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# sample_weight makes the refactoring tricky.
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def _rescale_data(X, y, sample_weight, inplace=False):
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"""Rescale data sample-wise by square root of sample_weight.
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For many linear models, this enables easy support for sample_weight because
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(y - X w)' S (y - X w)
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with S = diag(sample_weight) becomes
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||y_rescaled - X_rescaled w||_2^2
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when setting
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y_rescaled = sqrt(S) y
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X_rescaled = sqrt(S) X
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Returns
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-------
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X_rescaled : {array-like, sparse matrix}
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y_rescaled : {array-like, sparse matrix}
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"""
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# Assume that _validate_data and _check_sample_weight have been called by
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# the caller.
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xp, _ = get_namespace(X, y, sample_weight)
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n_samples = X.shape[0]
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sample_weight_sqrt = xp.sqrt(sample_weight)
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if sp.issparse(X) or sp.issparse(y):
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sw_matrix = sparse.dia_matrix(
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(sample_weight_sqrt, 0), shape=(n_samples, n_samples)
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)
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if sp.issparse(X):
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X = safe_sparse_dot(sw_matrix, X)
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else:
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if inplace:
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X *= sample_weight_sqrt[:, None]
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else:
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X = X * sample_weight_sqrt[:, None]
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if sp.issparse(y):
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y = safe_sparse_dot(sw_matrix, y)
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else:
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if inplace:
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if y.ndim == 1:
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y *= sample_weight_sqrt
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else:
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y *= sample_weight_sqrt[:, None]
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else:
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if y.ndim == 1:
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y = y * sample_weight_sqrt
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else:
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y = y * sample_weight_sqrt[:, None]
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return X, y, sample_weight_sqrt
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class LinearModel(BaseEstimator, metaclass=ABCMeta):
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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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check_is_fitted(self)
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X = self._validate_data(X, accept_sparse=["csr", "csc", "coo"], reset=False)
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coef_ = self.coef_
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if coef_.ndim == 1:
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return X @ coef_ + self.intercept_
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else:
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return X @ coef_.T + self.intercept_
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def predict(self, X):
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"""
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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 or 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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def _set_intercept(self, X_offset, y_offset, X_scale):
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"""Set the intercept_"""
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xp, _ = get_namespace(X_offset, y_offset, X_scale)
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if self.fit_intercept:
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# We always want coef_.dtype=X.dtype. For instance, X.dtype can differ from
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# coef_.dtype if warm_start=True.
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coef_ = xp.astype(self.coef_, X_scale.dtype, copy=False)
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coef_ = self.coef_ = xp.divide(coef_, X_scale)
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if coef_.ndim == 1:
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intercept_ = y_offset - X_offset @ coef_
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else:
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intercept_ = y_offset - X_offset @ coef_.T
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self.intercept_ = intercept_
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else:
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self.intercept_ = 0.0
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def _more_tags(self):
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return {"requires_y": True}
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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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"""
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Predict confidence scores for samples.
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The confidence score for a sample is proportional to the signed
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distance of that sample to the hyperplane.
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Parameters
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----------
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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The data matrix for which we want to get the confidence scores.
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Returns
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-------
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scores : ndarray of shape (n_samples,) or (n_samples, n_classes)
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Confidence scores per `(n_samples, n_classes)` combination. In the
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binary case, confidence score for `self.classes_[1]` where >0 means
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this class would be predicted.
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"""
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check_is_fitted(self)
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xp, _ = get_namespace(X)
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X = self._validate_data(X, accept_sparse="csr", reset=False)
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scores = safe_sparse_dot(X, self.coef_.T, dense_output=True) + self.intercept_
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return xp.reshape(scores, (-1,)) if scores.shape[1] == 1 else scores
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def predict(self, X):
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"""
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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} of shape (n_samples, n_features)
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The data matrix for which we want to get the predictions.
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Returns
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-------
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y_pred : ndarray of shape (n_samples,)
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Vector containing the class labels for each sample.
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"""
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xp, _ = get_namespace(X)
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scores = self.decision_function(X)
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if len(scores.shape) == 1:
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indices = xp.astype(scores > 0, indexing_dtype(xp))
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else:
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indices = xp.argmax(scores, axis=1)
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return xp.take(self.classes_, indices, axis=0)
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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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expit(prob, out=prob)
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if prob.ndim == 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:
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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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"""
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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
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Fitted estimator.
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"""
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msg = "Estimator, %(name)s, must be fitted before densifying."
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check_is_fitted(self, msg=msg)
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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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"""
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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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Returns
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-------
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self
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Fitted estimator.
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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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"""
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msg = "Estimator, %(name)s, must be fitted before sparsifying."
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check_is_fitted(self, msg=msg)
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self.coef_ = sp.csr_matrix(self.coef_)
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return self
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class LinearRegression(MultiOutputMixin, RegressorMixin, LinearModel):
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"""
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Ordinary least squares Linear Regression.
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LinearRegression fits a linear model with coefficients w = (w1, ..., wp)
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to minimize the residual sum of squares between the observed targets in
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the dataset, and the targets predicted by the linear approximation.
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Parameters
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----------
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fit_intercept : bool, default=True
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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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(i.e. data is expected to be centered).
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copy_X : bool, default=True
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If True, X will be copied; else, it may be overwritten.
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n_jobs : int, default=None
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The number of jobs to use for the computation. This will only provide
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speedup in case of sufficiently large problems, that is if firstly
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`n_targets > 1` and secondly `X` is sparse or if `positive` is set
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to `True`. ``None`` means 1 unless in a
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:obj:`joblib.parallel_backend` context. ``-1`` means using all
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processors. See :term:`Glossary <n_jobs>` for more details.
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positive : bool, default=False
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When set to ``True``, forces the coefficients to be positive. This
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option is only supported for dense arrays.
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.. versionadded:: 0.24
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Attributes
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----------
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coef_ : array of 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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rank_ : int
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Rank of matrix `X`. Only available when `X` is dense.
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singular_ : array of shape (min(X, y),)
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Singular values of `X`. Only available when `X` is dense.
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intercept_ : float or array of shape (n_targets,)
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Independent term in the linear model. Set to 0.0 if
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`fit_intercept = False`.
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
|
has feature names that are all strings.
|
|
|
|
.. versionadded:: 1.0
|
|
|
|
See Also
|
|
--------
|
|
Ridge : Ridge regression addresses some of the
|
|
problems of Ordinary Least Squares by imposing a penalty on the
|
|
size of the coefficients with l2 regularization.
|
|
Lasso : The Lasso is a linear model that estimates
|
|
sparse coefficients with l1 regularization.
|
|
ElasticNet : Elastic-Net is a linear regression
|
|
model trained with both l1 and l2 -norm regularization of the
|
|
coefficients.
|
|
|
|
Notes
|
|
-----
|
|
From the implementation point of view, this is just plain Ordinary
|
|
Least Squares (scipy.linalg.lstsq) or Non Negative Least Squares
|
|
(scipy.optimize.nnls) wrapped as a predictor object.
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> from sklearn.linear_model import LinearRegression
|
|
>>> X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
|
|
>>> # y = 1 * x_0 + 2 * x_1 + 3
|
|
>>> y = np.dot(X, np.array([1, 2])) + 3
|
|
>>> reg = LinearRegression().fit(X, y)
|
|
>>> reg.score(X, y)
|
|
1.0
|
|
>>> reg.coef_
|
|
array([1., 2.])
|
|
>>> reg.intercept_
|
|
3.0...
|
|
>>> reg.predict(np.array([[3, 5]]))
|
|
array([16.])
|
|
"""
|
|
|
|
_parameter_constraints: dict = {
|
|
"fit_intercept": ["boolean"],
|
|
"copy_X": ["boolean"],
|
|
"n_jobs": [None, Integral],
|
|
"positive": ["boolean"],
|
|
}
|
|
|
|
def __init__(
|
|
self,
|
|
*,
|
|
fit_intercept=True,
|
|
copy_X=True,
|
|
n_jobs=None,
|
|
positive=False,
|
|
):
|
|
self.fit_intercept = fit_intercept
|
|
self.copy_X = copy_X
|
|
self.n_jobs = n_jobs
|
|
self.positive = positive
|
|
|
|
@_fit_context(prefer_skip_nested_validation=True)
|
|
def fit(self, X, y, sample_weight=None):
|
|
"""
|
|
Fit linear model.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix} of shape (n_samples, n_features)
|
|
Training data.
|
|
|
|
y : array-like of shape (n_samples,) or (n_samples, n_targets)
|
|
Target values. Will be cast to X's dtype if necessary.
|
|
|
|
sample_weight : array-like of shape (n_samples,), default=None
|
|
Individual weights for each sample.
|
|
|
|
.. versionadded:: 0.17
|
|
parameter *sample_weight* support to LinearRegression.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Fitted Estimator.
|
|
"""
|
|
n_jobs_ = self.n_jobs
|
|
|
|
accept_sparse = False if self.positive else ["csr", "csc", "coo"]
|
|
|
|
X, y = self._validate_data(
|
|
X, y, accept_sparse=accept_sparse, y_numeric=True, multi_output=True
|
|
)
|
|
|
|
has_sw = sample_weight is not None
|
|
if has_sw:
|
|
sample_weight = _check_sample_weight(
|
|
sample_weight, X, dtype=X.dtype, only_non_negative=True
|
|
)
|
|
|
|
# Note that neither _rescale_data nor the rest of the fit method of
|
|
# LinearRegression can benefit from in-place operations when X is a
|
|
# sparse matrix. Therefore, let's not copy X when it is sparse.
|
|
copy_X_in_preprocess_data = self.copy_X and not sp.issparse(X)
|
|
|
|
X, y, X_offset, y_offset, X_scale = _preprocess_data(
|
|
X,
|
|
y,
|
|
fit_intercept=self.fit_intercept,
|
|
copy=copy_X_in_preprocess_data,
|
|
sample_weight=sample_weight,
|
|
)
|
|
|
|
if has_sw:
|
|
# Sample weight can be implemented via a simple rescaling. Note
|
|
# that we safely do inplace rescaling when _preprocess_data has
|
|
# already made a copy if requested.
|
|
X, y, sample_weight_sqrt = _rescale_data(
|
|
X, y, sample_weight, inplace=copy_X_in_preprocess_data
|
|
)
|
|
|
|
if self.positive:
|
|
if y.ndim < 2:
|
|
self.coef_ = optimize.nnls(X, y)[0]
|
|
else:
|
|
# scipy.optimize.nnls cannot handle y with shape (M, K)
|
|
outs = Parallel(n_jobs=n_jobs_)(
|
|
delayed(optimize.nnls)(X, y[:, j]) for j in range(y.shape[1])
|
|
)
|
|
self.coef_ = np.vstack([out[0] for out in outs])
|
|
elif sp.issparse(X):
|
|
X_offset_scale = X_offset / X_scale
|
|
|
|
if has_sw:
|
|
|
|
def matvec(b):
|
|
return X.dot(b) - sample_weight_sqrt * b.dot(X_offset_scale)
|
|
|
|
def rmatvec(b):
|
|
return X.T.dot(b) - X_offset_scale * b.dot(sample_weight_sqrt)
|
|
|
|
else:
|
|
|
|
def matvec(b):
|
|
return X.dot(b) - b.dot(X_offset_scale)
|
|
|
|
def rmatvec(b):
|
|
return X.T.dot(b) - X_offset_scale * b.sum()
|
|
|
|
X_centered = sparse.linalg.LinearOperator(
|
|
shape=X.shape, matvec=matvec, rmatvec=rmatvec
|
|
)
|
|
|
|
if y.ndim < 2:
|
|
self.coef_ = lsqr(X_centered, y)[0]
|
|
else:
|
|
# sparse_lstsq cannot handle y with shape (M, K)
|
|
outs = Parallel(n_jobs=n_jobs_)(
|
|
delayed(lsqr)(X_centered, y[:, j].ravel())
|
|
for j in range(y.shape[1])
|
|
)
|
|
self.coef_ = np.vstack([out[0] for out in outs])
|
|
else:
|
|
self.coef_, _, 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 _check_precomputed_gram_matrix(
|
|
X, precompute, X_offset, X_scale, rtol=None, atol=1e-5
|
|
):
|
|
"""Computes a single element of the gram matrix and compares it to
|
|
the corresponding element of the user supplied gram matrix.
|
|
|
|
If the values do not match a ValueError will be thrown.
|
|
|
|
Parameters
|
|
----------
|
|
X : ndarray of shape (n_samples, n_features)
|
|
Data array.
|
|
|
|
precompute : array-like of shape (n_features, n_features)
|
|
User-supplied gram matrix.
|
|
|
|
X_offset : ndarray of shape (n_features,)
|
|
Array of feature means used to center design matrix.
|
|
|
|
X_scale : ndarray of shape (n_features,)
|
|
Array of feature scale factors used to normalize design matrix.
|
|
|
|
rtol : float, default=None
|
|
Relative tolerance; see numpy.allclose
|
|
If None, it is set to 1e-4 for arrays of dtype numpy.float32 and 1e-7
|
|
otherwise.
|
|
|
|
atol : float, default=1e-5
|
|
absolute tolerance; see :func`numpy.allclose`. Note that the default
|
|
here is more tolerant than the default for
|
|
:func:`numpy.testing.assert_allclose`, where `atol=0`.
|
|
|
|
Raises
|
|
------
|
|
ValueError
|
|
Raised when the provided Gram matrix is not consistent.
|
|
"""
|
|
|
|
n_features = X.shape[1]
|
|
f1 = n_features // 2
|
|
f2 = min(f1 + 1, n_features - 1)
|
|
|
|
v1 = (X[:, f1] - X_offset[f1]) * X_scale[f1]
|
|
v2 = (X[:, f2] - X_offset[f2]) * X_scale[f2]
|
|
|
|
expected = np.dot(v1, v2)
|
|
actual = precompute[f1, f2]
|
|
|
|
dtypes = [precompute.dtype, expected.dtype]
|
|
if rtol is None:
|
|
rtols = [1e-4 if dtype == np.float32 else 1e-7 for dtype in dtypes]
|
|
rtol = max(rtols)
|
|
|
|
if not np.isclose(expected, actual, rtol=rtol, atol=atol):
|
|
raise ValueError(
|
|
"Gram matrix passed in via 'precompute' parameter "
|
|
"did not pass validation when a single element was "
|
|
"checked - please check that it was computed "
|
|
f"properly. For element ({f1},{f2}) we computed "
|
|
f"{expected} but the user-supplied value was "
|
|
f"{actual}."
|
|
)
|
|
|
|
|
|
def _pre_fit(
|
|
X,
|
|
y,
|
|
Xy,
|
|
precompute,
|
|
fit_intercept,
|
|
copy,
|
|
check_input=True,
|
|
sample_weight=None,
|
|
):
|
|
"""Function used at beginning of fit in linear models with L1 or L0 penalty.
|
|
|
|
This function applies _preprocess_data and additionally computes the gram matrix
|
|
`precompute` as needed as well as `Xy`.
|
|
"""
|
|
n_samples, n_features = X.shape
|
|
|
|
if sparse.issparse(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,
|
|
copy=False,
|
|
check_input=check_input,
|
|
sample_weight=sample_weight,
|
|
)
|
|
else:
|
|
# copy was done in fit if necessary
|
|
X, y, X_offset, y_offset, X_scale = _preprocess_data(
|
|
X,
|
|
y,
|
|
fit_intercept=fit_intercept,
|
|
copy=copy,
|
|
check_input=check_input,
|
|
sample_weight=sample_weight,
|
|
)
|
|
# Rescale only in dense case. Sparse cd solver directly deals with
|
|
# sample_weight.
|
|
if sample_weight is not None:
|
|
# This triggers copies anyway.
|
|
X, y, _ = _rescale_data(X, y, sample_weight=sample_weight)
|
|
|
|
if hasattr(precompute, "__array__"):
|
|
if fit_intercept and not np.allclose(X_offset, np.zeros(n_features)):
|
|
warnings.warn(
|
|
(
|
|
"Gram matrix was provided but X was centered to fit "
|
|
"intercept: recomputing Gram matrix."
|
|
),
|
|
UserWarning,
|
|
)
|
|
# TODO: instead of warning and recomputing, we could just center
|
|
# the user provided Gram matrix a-posteriori (after making a copy
|
|
# when `copy=True`).
|
|
# recompute Gram
|
|
precompute = "auto"
|
|
Xy = None
|
|
elif check_input:
|
|
# If we're going to use the user's precomputed gram matrix, we
|
|
# do a quick check to make sure its not totally bogus.
|
|
_check_precomputed_gram_matrix(X, precompute, X_offset, X_scale)
|
|
|
|
# precompute if n_samples > n_features
|
|
if isinstance(precompute, str) 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.result_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
|