diff --git "a/llmeval-env/lib/python3.10/site-packages/sklearn/linear_model/_coordinate_descent.py" "b/llmeval-env/lib/python3.10/site-packages/sklearn/linear_model/_coordinate_descent.py" new file mode 100644--- /dev/null +++ "b/llmeval-env/lib/python3.10/site-packages/sklearn/linear_model/_coordinate_descent.py" @@ -0,0 +1,3182 @@ +# Author: Alexandre Gramfort +# Fabian Pedregosa +# Olivier Grisel +# Gael Varoquaux +# +# License: BSD 3 clause + +import numbers +import sys +import warnings +from abc import ABC, abstractmethod +from functools import partial +from numbers import Integral, Real + +import numpy as np +from joblib import effective_n_jobs +from scipy import sparse + +from ..base import MultiOutputMixin, RegressorMixin, _fit_context +from ..model_selection import check_cv +from ..utils import Bunch, check_array, check_scalar +from ..utils._metadata_requests import ( + MetadataRouter, + MethodMapping, + _raise_for_params, + get_routing_for_object, +) +from ..utils._param_validation import Interval, StrOptions, validate_params +from ..utils.extmath import safe_sparse_dot +from ..utils.metadata_routing import ( + _routing_enabled, + process_routing, +) +from ..utils.parallel import Parallel, delayed +from ..utils.validation import ( + _check_sample_weight, + check_consistent_length, + check_is_fitted, + check_random_state, + column_or_1d, + has_fit_parameter, +) + +# mypy error: Module 'sklearn.linear_model' has no attribute '_cd_fast' +from . import _cd_fast as cd_fast # type: ignore +from ._base import LinearModel, _pre_fit, _preprocess_data + + +def _set_order(X, y, order="C"): + """Change the order of X and y if necessary. + + Parameters + ---------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data. + + y : ndarray of shape (n_samples,) + Target values. + + order : {None, 'C', 'F'} + If 'C', dense arrays are returned as C-ordered, sparse matrices in csr + format. If 'F', dense arrays are return as F-ordered, sparse matrices + in csc format. + + Returns + ------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data with guaranteed order. + + y : ndarray of shape (n_samples,) + Target values with guaranteed order. + """ + if order not in [None, "C", "F"]: + raise ValueError( + "Unknown value for order. Got {} instead of None, 'C' or 'F'.".format(order) + ) + sparse_X = sparse.issparse(X) + sparse_y = sparse.issparse(y) + if order is not None: + sparse_format = "csc" if order == "F" else "csr" + if sparse_X: + X = X.asformat(sparse_format, copy=False) + else: + X = np.asarray(X, order=order) + if sparse_y: + y = y.asformat(sparse_format) + else: + y = np.asarray(y, order=order) + return X, y + + +############################################################################### +# Paths functions + + +def _alpha_grid( + X, + y, + Xy=None, + l1_ratio=1.0, + fit_intercept=True, + eps=1e-3, + n_alphas=100, + copy_X=True, +): + """Compute the grid of alpha values for elastic net parameter search + + Parameters + ---------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data. Pass directly as Fortran-contiguous data to avoid + unnecessary memory duplication + + y : ndarray of shape (n_samples,) or (n_samples, n_outputs) + Target values + + Xy : array-like of shape (n_features,) or (n_features, n_outputs),\ + default=None + Xy = np.dot(X.T, y) that can be precomputed. + + l1_ratio : float, default=1.0 + The elastic net mixing parameter, with ``0 < l1_ratio <= 1``. + For ``l1_ratio = 0`` the penalty is an L2 penalty. (currently not + supported) ``For l1_ratio = 1`` it is an L1 penalty. For + ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2. + + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3`` + + n_alphas : int, default=100 + Number of alphas along the regularization path + + fit_intercept : bool, default=True + Whether to fit an intercept or not + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + """ + if l1_ratio == 0: + raise ValueError( + "Automatic alpha grid generation is not supported for" + " l1_ratio=0. Please supply a grid by providing " + "your estimator with the appropriate `alphas=` " + "argument." + ) + n_samples = len(y) + + sparse_center = False + if Xy is None: + X_sparse = sparse.issparse(X) + sparse_center = X_sparse and fit_intercept + X = check_array( + X, accept_sparse="csc", copy=(copy_X and fit_intercept and not X_sparse) + ) + if not X_sparse: + # X can be touched inplace thanks to the above line + X, y, _, _, _ = _preprocess_data( + X, y, fit_intercept=fit_intercept, copy=False + ) + Xy = safe_sparse_dot(X.T, y, dense_output=True) + + if sparse_center: + # Workaround to find alpha_max for sparse matrices. + # since we should not destroy the sparsity of such matrices. + _, _, X_offset, _, X_scale = _preprocess_data( + X, y, fit_intercept=fit_intercept + ) + mean_dot = X_offset * np.sum(y) + + if Xy.ndim == 1: + Xy = Xy[:, np.newaxis] + + if sparse_center: + if fit_intercept: + Xy -= mean_dot[:, np.newaxis] + + alpha_max = np.sqrt(np.sum(Xy**2, axis=1)).max() / (n_samples * l1_ratio) + + if alpha_max <= np.finfo(float).resolution: + alphas = np.empty(n_alphas) + alphas.fill(np.finfo(float).resolution) + return alphas + + return np.geomspace(alpha_max, alpha_max * eps, num=n_alphas) + + +@validate_params( + { + "X": ["array-like", "sparse matrix"], + "y": ["array-like", "sparse matrix"], + "eps": [Interval(Real, 0, None, closed="neither")], + "n_alphas": [Interval(Integral, 1, None, closed="left")], + "alphas": ["array-like", None], + "precompute": [StrOptions({"auto"}), "boolean", "array-like"], + "Xy": ["array-like", None], + "copy_X": ["boolean"], + "coef_init": ["array-like", None], + "verbose": ["verbose"], + "return_n_iter": ["boolean"], + "positive": ["boolean"], + }, + prefer_skip_nested_validation=True, +) +def lasso_path( + X, + y, + *, + eps=1e-3, + n_alphas=100, + alphas=None, + precompute="auto", + Xy=None, + copy_X=True, + coef_init=None, + verbose=False, + return_n_iter=False, + positive=False, + **params, +): + """Compute Lasso path with coordinate descent. + + The Lasso optimization function varies for mono and multi-outputs. + + For mono-output tasks it is:: + + (1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1 + + For multi-output tasks it is:: + + (1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21 + + Where:: + + ||W||_21 = \\sum_i \\sqrt{\\sum_j w_{ij}^2} + + i.e. the sum of norm of each row. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data. Pass directly as Fortran-contiguous data to avoid + unnecessary memory duplication. If ``y`` is mono-output then ``X`` + can be sparse. + + y : {array-like, sparse matrix} of shape (n_samples,) or \ + (n_samples, n_targets) + Target values. + + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path. + + alphas : array-like, default=None + List of alphas where to compute the models. + If ``None`` alphas are set automatically. + + precompute : 'auto', bool or array-like of shape \ + (n_features, n_features), default='auto' + Whether to use a precomputed Gram matrix to speed up + calculations. If set to ``'auto'`` let us decide. The Gram + matrix can also be passed as argument. + + Xy : array-like of shape (n_features,) or (n_features, n_targets),\ + default=None + Xy = np.dot(X.T, y) that can be precomputed. It is useful + only when the Gram matrix is precomputed. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + coef_init : array-like of shape (n_features, ), default=None + The initial values of the coefficients. + + verbose : bool or int, default=False + Amount of verbosity. + + return_n_iter : bool, default=False + Whether to return the number of iterations or not. + + positive : bool, default=False + If set to True, forces coefficients to be positive. + (Only allowed when ``y.ndim == 1``). + + **params : kwargs + Keyword arguments passed to the coordinate descent solver. + + Returns + ------- + alphas : ndarray of shape (n_alphas,) + The alphas along the path where models are computed. + + coefs : ndarray of shape (n_features, n_alphas) or \ + (n_targets, n_features, n_alphas) + Coefficients along the path. + + dual_gaps : ndarray of shape (n_alphas,) + The dual gaps at the end of the optimization for each alpha. + + n_iters : list of int + The number of iterations taken by the coordinate descent optimizer to + reach the specified tolerance for each alpha. + + See Also + -------- + lars_path : Compute Least Angle Regression or Lasso path using LARS + algorithm. + Lasso : The Lasso is a linear model that estimates sparse coefficients. + LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars. + LassoCV : Lasso linear model with iterative fitting along a regularization + path. + LassoLarsCV : Cross-validated Lasso using the LARS algorithm. + sklearn.decomposition.sparse_encode : Estimator that can be used to + transform signals into sparse linear combination of atoms from a fixed. + + Notes + ----- + For an example, see + :ref:`examples/linear_model/plot_lasso_coordinate_descent_path.py + `. + + To avoid unnecessary memory duplication the X argument of the fit method + should be directly passed as a Fortran-contiguous numpy array. + + Note that in certain cases, the Lars solver may be significantly + faster to implement this functionality. In particular, linear + interpolation can be used to retrieve model coefficients between the + values output by lars_path + + Examples + -------- + + Comparing lasso_path and lars_path with interpolation: + + >>> import numpy as np + >>> from sklearn.linear_model import lasso_path + >>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T + >>> y = np.array([1, 2, 3.1]) + >>> # Use lasso_path to compute a coefficient path + >>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5]) + >>> print(coef_path) + [[0. 0. 0.46874778] + [0.2159048 0.4425765 0.23689075]] + + >>> # Now use lars_path and 1D linear interpolation to compute the + >>> # same path + >>> from sklearn.linear_model import lars_path + >>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso') + >>> from scipy import interpolate + >>> coef_path_continuous = interpolate.interp1d(alphas[::-1], + ... coef_path_lars[:, ::-1]) + >>> print(coef_path_continuous([5., 1., .5])) + [[0. 0. 0.46915237] + [0.2159048 0.4425765 0.23668876]] + """ + return enet_path( + X, + y, + l1_ratio=1.0, + eps=eps, + n_alphas=n_alphas, + alphas=alphas, + precompute=precompute, + Xy=Xy, + copy_X=copy_X, + coef_init=coef_init, + verbose=verbose, + positive=positive, + return_n_iter=return_n_iter, + **params, + ) + + +@validate_params( + { + "X": ["array-like", "sparse matrix"], + "y": ["array-like", "sparse matrix"], + "l1_ratio": [Interval(Real, 0.0, 1.0, closed="both")], + "eps": [Interval(Real, 0.0, None, closed="neither")], + "n_alphas": [Interval(Integral, 1, None, closed="left")], + "alphas": ["array-like", None], + "precompute": [StrOptions({"auto"}), "boolean", "array-like"], + "Xy": ["array-like", None], + "copy_X": ["boolean"], + "coef_init": ["array-like", None], + "verbose": ["verbose"], + "return_n_iter": ["boolean"], + "positive": ["boolean"], + "check_input": ["boolean"], + }, + prefer_skip_nested_validation=True, +) +def enet_path( + X, + y, + *, + l1_ratio=0.5, + eps=1e-3, + n_alphas=100, + alphas=None, + precompute="auto", + Xy=None, + copy_X=True, + coef_init=None, + verbose=False, + return_n_iter=False, + positive=False, + check_input=True, + **params, +): + """Compute elastic net path with coordinate descent. + + The elastic net optimization function varies for mono and multi-outputs. + + For mono-output tasks it is:: + + 1 / (2 * n_samples) * ||y - Xw||^2_2 + + alpha * l1_ratio * ||w||_1 + + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2 + + For multi-output tasks it is:: + + (1 / (2 * n_samples)) * ||Y - XW||_Fro^2 + + alpha * l1_ratio * ||W||_21 + + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2 + + Where:: + + ||W||_21 = \\sum_i \\sqrt{\\sum_j w_{ij}^2} + + i.e. the sum of norm of each row. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data. Pass directly as Fortran-contiguous data to avoid + unnecessary memory duplication. If ``y`` is mono-output then ``X`` + can be sparse. + + y : {array-like, sparse matrix} of shape (n_samples,) or \ + (n_samples, n_targets) + Target values. + + l1_ratio : float, default=0.5 + Number between 0 and 1 passed to elastic net (scaling between + l1 and l2 penalties). ``l1_ratio=1`` corresponds to the Lasso. + + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path. + + alphas : array-like, default=None + List of alphas where to compute the models. + If None alphas are set automatically. + + precompute : 'auto', bool or array-like of shape \ + (n_features, n_features), default='auto' + Whether to use a precomputed Gram matrix to speed up + calculations. If set to ``'auto'`` let us decide. The Gram + matrix can also be passed as argument. + + Xy : array-like of shape (n_features,) or (n_features, n_targets),\ + default=None + Xy = np.dot(X.T, y) that can be precomputed. It is useful + only when the Gram matrix is precomputed. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + coef_init : array-like of shape (n_features, ), default=None + The initial values of the coefficients. + + verbose : bool or int, default=False + Amount of verbosity. + + return_n_iter : bool, default=False + Whether to return the number of iterations or not. + + positive : bool, default=False + If set to True, forces coefficients to be positive. + (Only allowed when ``y.ndim == 1``). + + check_input : bool, default=True + If set to False, the input validation checks are skipped (including the + Gram matrix when provided). It is assumed that they are handled + by the caller. + + **params : kwargs + Keyword arguments passed to the coordinate descent solver. + + Returns + ------- + alphas : ndarray of shape (n_alphas,) + The alphas along the path where models are computed. + + coefs : ndarray of shape (n_features, n_alphas) or \ + (n_targets, n_features, n_alphas) + Coefficients along the path. + + dual_gaps : ndarray of shape (n_alphas,) + The dual gaps at the end of the optimization for each alpha. + + n_iters : list of int + The number of iterations taken by the coordinate descent optimizer to + reach the specified tolerance for each alpha. + (Is returned when ``return_n_iter`` is set to True). + + See Also + -------- + MultiTaskElasticNet : Multi-task ElasticNet model trained with L1/L2 mixed-norm \ + as regularizer. + MultiTaskElasticNetCV : Multi-task L1/L2 ElasticNet with built-in cross-validation. + ElasticNet : Linear regression with combined L1 and L2 priors as regularizer. + ElasticNetCV : Elastic Net model with iterative fitting along a regularization path. + + Notes + ----- + For an example, see + :ref:`examples/linear_model/plot_lasso_coordinate_descent_path.py + `. + """ + X_offset_param = params.pop("X_offset", None) + X_scale_param = params.pop("X_scale", None) + sample_weight = params.pop("sample_weight", None) + tol = params.pop("tol", 1e-4) + max_iter = params.pop("max_iter", 1000) + random_state = params.pop("random_state", None) + selection = params.pop("selection", "cyclic") + + if len(params) > 0: + raise ValueError("Unexpected parameters in params", params.keys()) + + # We expect X and y to be already Fortran ordered when bypassing + # checks + if check_input: + X = check_array( + X, + accept_sparse="csc", + dtype=[np.float64, np.float32], + order="F", + copy=copy_X, + ) + y = check_array( + y, + accept_sparse="csc", + dtype=X.dtype.type, + order="F", + copy=False, + ensure_2d=False, + ) + if Xy is not None: + # Xy should be a 1d contiguous array or a 2D C ordered array + Xy = check_array( + Xy, dtype=X.dtype.type, order="C", copy=False, ensure_2d=False + ) + + n_samples, n_features = X.shape + + multi_output = False + if y.ndim != 1: + multi_output = True + n_targets = y.shape[1] + + if multi_output and positive: + raise ValueError("positive=True is not allowed for multi-output (y.ndim != 1)") + + # MultiTaskElasticNet does not support sparse matrices + if not multi_output and sparse.issparse(X): + if X_offset_param is not None: + # As sparse matrices are not actually centered we need this to be passed to + # the CD solver. + X_sparse_scaling = X_offset_param / X_scale_param + X_sparse_scaling = np.asarray(X_sparse_scaling, dtype=X.dtype) + else: + X_sparse_scaling = np.zeros(n_features, dtype=X.dtype) + + # X should have been passed through _pre_fit already if function is called + # from ElasticNet.fit + if check_input: + X, y, _, _, _, precompute, Xy = _pre_fit( + X, + y, + Xy, + precompute, + fit_intercept=False, + copy=False, + check_input=check_input, + ) + if alphas is None: + # No need to normalize of fit_intercept: it has been done + # above + alphas = _alpha_grid( + X, + y, + Xy=Xy, + l1_ratio=l1_ratio, + fit_intercept=False, + eps=eps, + n_alphas=n_alphas, + copy_X=False, + ) + elif len(alphas) > 1: + alphas = np.sort(alphas)[::-1] # make sure alphas are properly ordered + + n_alphas = len(alphas) + dual_gaps = np.empty(n_alphas) + n_iters = [] + + rng = check_random_state(random_state) + if selection not in ["random", "cyclic"]: + raise ValueError("selection should be either random or cyclic.") + random = selection == "random" + + if not multi_output: + coefs = np.empty((n_features, n_alphas), dtype=X.dtype) + else: + coefs = np.empty((n_targets, n_features, n_alphas), dtype=X.dtype) + + if coef_init is None: + coef_ = np.zeros(coefs.shape[:-1], dtype=X.dtype, order="F") + else: + coef_ = np.asfortranarray(coef_init, dtype=X.dtype) + + for i, alpha in enumerate(alphas): + # account for n_samples scaling in objectives between here and cd_fast + l1_reg = alpha * l1_ratio * n_samples + l2_reg = alpha * (1.0 - l1_ratio) * n_samples + if not multi_output and sparse.issparse(X): + model = cd_fast.sparse_enet_coordinate_descent( + w=coef_, + alpha=l1_reg, + beta=l2_reg, + X_data=X.data, + X_indices=X.indices, + X_indptr=X.indptr, + y=y, + sample_weight=sample_weight, + X_mean=X_sparse_scaling, + max_iter=max_iter, + tol=tol, + rng=rng, + random=random, + positive=positive, + ) + elif multi_output: + model = cd_fast.enet_coordinate_descent_multi_task( + coef_, l1_reg, l2_reg, X, y, max_iter, tol, rng, random + ) + elif isinstance(precompute, np.ndarray): + # We expect precompute to be already Fortran ordered when bypassing + # checks + if check_input: + precompute = check_array(precompute, dtype=X.dtype.type, order="C") + model = cd_fast.enet_coordinate_descent_gram( + coef_, + l1_reg, + l2_reg, + precompute, + Xy, + y, + max_iter, + tol, + rng, + random, + positive, + ) + elif precompute is False: + model = cd_fast.enet_coordinate_descent( + coef_, l1_reg, l2_reg, X, y, max_iter, tol, rng, random, positive + ) + else: + raise ValueError( + "Precompute should be one of True, False, 'auto' or array-like. Got %r" + % precompute + ) + coef_, dual_gap_, eps_, n_iter_ = model + coefs[..., i] = coef_ + # we correct the scale of the returned dual gap, as the objective + # in cd_fast is n_samples * the objective in this docstring. + dual_gaps[i] = dual_gap_ / n_samples + n_iters.append(n_iter_) + + if verbose: + if verbose > 2: + print(model) + elif verbose > 1: + print("Path: %03i out of %03i" % (i, n_alphas)) + else: + sys.stderr.write(".") + + if return_n_iter: + return alphas, coefs, dual_gaps, n_iters + return alphas, coefs, dual_gaps + + +############################################################################### +# ElasticNet model + + +class ElasticNet(MultiOutputMixin, RegressorMixin, LinearModel): + """Linear regression with combined L1 and L2 priors as regularizer. + + Minimizes the objective function:: + + 1 / (2 * n_samples) * ||y - Xw||^2_2 + + alpha * l1_ratio * ||w||_1 + + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2 + + If you are interested in controlling the L1 and L2 penalty + separately, keep in mind that this is equivalent to:: + + a * ||w||_1 + 0.5 * b * ||w||_2^2 + + where:: + + alpha = a + b and l1_ratio = a / (a + b) + + The parameter l1_ratio corresponds to alpha in the glmnet R package while + alpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio + = 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable, + unless you supply your own sequence of alpha. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + alpha : float, default=1.0 + Constant that multiplies the penalty terms. Defaults to 1.0. + See the notes for the exact mathematical meaning of this + parameter. ``alpha = 0`` is equivalent to an ordinary least square, + solved by the :class:`LinearRegression` object. For numerical + reasons, using ``alpha = 0`` with the ``Lasso`` object is not advised. + Given this, you should use the :class:`LinearRegression` object. + + l1_ratio : float, default=0.5 + The ElasticNet mixing parameter, with ``0 <= l1_ratio <= 1``. For + ``l1_ratio = 0`` the penalty is an L2 penalty. ``For l1_ratio = 1`` it + is an L1 penalty. For ``0 < l1_ratio < 1``, the penalty is a + combination of L1 and L2. + + fit_intercept : bool, default=True + Whether the intercept should be estimated or not. If ``False``, the + data is assumed to be already centered. + + precompute : bool or array-like of shape (n_features, n_features),\ + default=False + Whether to use a precomputed Gram matrix to speed up + calculations. The Gram matrix can also be passed as argument. + For sparse input this option is always ``False`` to preserve sparsity. + + max_iter : int, default=1000 + The maximum number of iterations. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``, see Notes below. + + warm_start : bool, default=False + When set to ``True``, reuse the solution of the previous call to fit as + initialization, otherwise, just erase the previous solution. + See :term:`the Glossary `. + + positive : bool, default=False + When set to ``True``, forces the coefficients to be positive. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + coef_ : ndarray of shape (n_features,) or (n_targets, n_features) + Parameter vector (w in the cost function formula). + + sparse_coef_ : sparse matrix of shape (n_features,) or \ + (n_targets, n_features) + Sparse representation of the `coef_`. + + intercept_ : float or ndarray of shape (n_targets,) + Independent term in decision function. + + n_iter_ : list of int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance. + + dual_gap_ : float or ndarray of shape (n_targets,) + Given param alpha, the dual gaps at the end of the optimization, + same shape as each observation of y. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + ElasticNetCV : Elastic net model with best model selection by + cross-validation. + SGDRegressor : Implements elastic net regression with incremental training. + SGDClassifier : Implements logistic regression with elastic net penalty + (``SGDClassifier(loss="log_loss", penalty="elasticnet")``). + + Notes + ----- + To avoid unnecessary memory duplication the X argument of the fit method + should be directly passed as a Fortran-contiguous numpy array. + + The precise stopping criteria based on `tol` are the following: First, check that + that maximum coordinate update, i.e. :math:`\\max_j |w_j^{new} - w_j^{old}|` + is smaller than `tol` times the maximum absolute coefficient, :math:`\\max_j |w_j|`. + If so, then additionally check whether the dual gap is smaller than `tol` times + :math:`||y||_2^2 / n_{\text{samples}}`. + + Examples + -------- + >>> from sklearn.linear_model import ElasticNet + >>> from sklearn.datasets import make_regression + + >>> X, y = make_regression(n_features=2, random_state=0) + >>> regr = ElasticNet(random_state=0) + >>> regr.fit(X, y) + ElasticNet(random_state=0) + >>> print(regr.coef_) + [18.83816048 64.55968825] + >>> print(regr.intercept_) + 1.451... + >>> print(regr.predict([[0, 0]])) + [1.451...] + """ + + _parameter_constraints: dict = { + "alpha": [Interval(Real, 0, None, closed="left")], + "l1_ratio": [Interval(Real, 0, 1, closed="both")], + "fit_intercept": ["boolean"], + "precompute": ["boolean", "array-like"], + "max_iter": [Interval(Integral, 1, None, closed="left"), None], + "copy_X": ["boolean"], + "tol": [Interval(Real, 0, None, closed="left")], + "warm_start": ["boolean"], + "positive": ["boolean"], + "random_state": ["random_state"], + "selection": [StrOptions({"cyclic", "random"})], + } + + path = staticmethod(enet_path) + + def __init__( + self, + alpha=1.0, + *, + l1_ratio=0.5, + fit_intercept=True, + precompute=False, + max_iter=1000, + copy_X=True, + tol=1e-4, + warm_start=False, + positive=False, + random_state=None, + selection="cyclic", + ): + self.alpha = alpha + self.l1_ratio = l1_ratio + self.fit_intercept = fit_intercept + self.precompute = precompute + self.max_iter = max_iter + self.copy_X = copy_X + self.tol = tol + self.warm_start = warm_start + self.positive = positive + self.random_state = random_state + self.selection = selection + + @_fit_context(prefer_skip_nested_validation=True) + def fit(self, X, y, sample_weight=None, check_input=True): + """Fit model with coordinate descent. + + Parameters + ---------- + X : {ndarray, sparse matrix} of (n_samples, n_features) + Data. + + y : ndarray of shape (n_samples,) or (n_samples, n_targets) + Target. Will be cast to X's dtype if necessary. + + sample_weight : float or array-like of shape (n_samples,), default=None + Sample weights. Internally, the `sample_weight` vector will be + rescaled to sum to `n_samples`. + + .. versionadded:: 0.23 + + check_input : bool, default=True + Allow to bypass several input checking. + Don't use this parameter unless you know what you do. + + Returns + ------- + self : object + Fitted estimator. + + Notes + ----- + Coordinate descent is an algorithm that considers each column of + data at a time hence it will automatically convert the X input + as a Fortran-contiguous numpy array if necessary. + + To avoid memory re-allocation it is advised to allocate the + initial data in memory directly using that format. + """ + if self.alpha == 0: + warnings.warn( + ( + "With alpha=0, this algorithm does not converge " + "well. You are advised to use the LinearRegression " + "estimator" + ), + stacklevel=2, + ) + + # Remember if X is copied + X_copied = False + # We expect X and y to be float64 or float32 Fortran ordered arrays + # when bypassing checks + if check_input: + X_copied = self.copy_X and self.fit_intercept + X, y = self._validate_data( + X, + y, + accept_sparse="csc", + order="F", + dtype=[np.float64, np.float32], + copy=X_copied, + multi_output=True, + y_numeric=True, + ) + y = check_array( + y, order="F", copy=False, dtype=X.dtype.type, ensure_2d=False + ) + + n_samples, n_features = X.shape + alpha = self.alpha + + if isinstance(sample_weight, numbers.Number): + sample_weight = None + if sample_weight is not None: + if check_input: + sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype) + # TLDR: Rescale sw to sum up to n_samples. + # Long: The objective function of Enet + # + # 1/2 * np.average(squared error, weights=sw) + # + alpha * penalty (1) + # + # is invariant under rescaling of sw. + # But enet_path coordinate descent minimizes + # + # 1/2 * sum(squared error) + alpha' * penalty (2) + # + # and therefore sets + # + # alpha' = n_samples * alpha (3) + # + # inside its function body, which results in objective (2) being + # equivalent to (1) in case of no sw. + # With sw, however, enet_path should set + # + # alpha' = sum(sw) * alpha (4) + # + # Therefore, we use the freedom of Eq. (1) to rescale sw before + # calling enet_path, i.e. + # + # sw *= n_samples / sum(sw) + # + # such that sum(sw) = n_samples. This way, (3) and (4) are the same. + sample_weight = sample_weight * (n_samples / np.sum(sample_weight)) + # Note: Alternatively, we could also have rescaled alpha instead + # of sample_weight: + # + # alpha *= np.sum(sample_weight) / n_samples + + # Ensure copying happens only once, don't do it again if done above. + # X and y will be rescaled if sample_weight is not None, order='F' + # ensures that the returned X and y are still F-contiguous. + should_copy = self.copy_X and not X_copied + X, y, X_offset, y_offset, X_scale, precompute, Xy = _pre_fit( + X, + y, + None, + self.precompute, + fit_intercept=self.fit_intercept, + copy=should_copy, + check_input=check_input, + sample_weight=sample_weight, + ) + # coordinate descent needs F-ordered arrays and _pre_fit might have + # called _rescale_data + if check_input or sample_weight is not None: + X, y = _set_order(X, y, order="F") + if y.ndim == 1: + y = y[:, np.newaxis] + if Xy is not None and Xy.ndim == 1: + Xy = Xy[:, np.newaxis] + + n_targets = y.shape[1] + + if not self.warm_start or not hasattr(self, "coef_"): + coef_ = np.zeros((n_targets, n_features), dtype=X.dtype, order="F") + else: + coef_ = self.coef_ + if coef_.ndim == 1: + coef_ = coef_[np.newaxis, :] + + dual_gaps_ = np.zeros(n_targets, dtype=X.dtype) + self.n_iter_ = [] + + for k in range(n_targets): + if Xy is not None: + this_Xy = Xy[:, k] + else: + this_Xy = None + _, this_coef, this_dual_gap, this_iter = self.path( + X, + y[:, k], + l1_ratio=self.l1_ratio, + eps=None, + n_alphas=None, + alphas=[alpha], + precompute=precompute, + Xy=this_Xy, + copy_X=True, + coef_init=coef_[k], + verbose=False, + return_n_iter=True, + positive=self.positive, + check_input=False, + # from here on **params + tol=self.tol, + X_offset=X_offset, + X_scale=X_scale, + max_iter=self.max_iter, + random_state=self.random_state, + selection=self.selection, + sample_weight=sample_weight, + ) + coef_[k] = this_coef[:, 0] + dual_gaps_[k] = this_dual_gap[0] + self.n_iter_.append(this_iter[0]) + + if n_targets == 1: + self.n_iter_ = self.n_iter_[0] + self.coef_ = coef_[0] + self.dual_gap_ = dual_gaps_[0] + else: + self.coef_ = coef_ + self.dual_gap_ = dual_gaps_ + + self._set_intercept(X_offset, y_offset, X_scale) + + # check for finiteness of coefficients + if not all(np.isfinite(w).all() for w in [self.coef_, self.intercept_]): + raise ValueError( + "Coordinate descent iterations resulted in non-finite parameter" + " values. The input data may contain large values and need to" + " be preprocessed." + ) + + # return self for chaining fit and predict calls + return self + + @property + def sparse_coef_(self): + """Sparse representation of the fitted `coef_`.""" + return sparse.csr_matrix(self.coef_) + + def _decision_function(self, X): + """Decision function of the linear model. + + Parameters + ---------- + X : numpy array or scipy.sparse matrix of shape (n_samples, n_features) + + Returns + ------- + T : ndarray of shape (n_samples,) + The predicted decision function. + """ + check_is_fitted(self) + if sparse.issparse(X): + return safe_sparse_dot(X, self.coef_.T, dense_output=True) + self.intercept_ + else: + return super()._decision_function(X) + + +############################################################################### +# Lasso model + + +class Lasso(ElasticNet): + """Linear Model trained with L1 prior as regularizer (aka the Lasso). + + The optimization objective for Lasso is:: + + (1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1 + + Technically the Lasso model is optimizing the same objective function as + the Elastic Net with ``l1_ratio=1.0`` (no L2 penalty). + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + alpha : float, default=1.0 + Constant that multiplies the L1 term, controlling regularization + strength. `alpha` must be a non-negative float i.e. in `[0, inf)`. + + When `alpha = 0`, the objective is equivalent to ordinary least + squares, solved by the :class:`LinearRegression` object. For numerical + reasons, using `alpha = 0` with the `Lasso` object is not advised. + Instead, you should use the :class:`LinearRegression` object. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to False, no intercept will be used in calculations + (i.e. data is expected to be centered). + + precompute : bool or array-like of shape (n_features, n_features),\ + default=False + Whether to use a precomputed Gram matrix to speed up + calculations. The Gram matrix can also be passed as argument. + For sparse input this option is always ``False`` to preserve sparsity. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``, see Notes below. + + warm_start : bool, default=False + When set to True, reuse the solution of the previous call to fit as + initialization, otherwise, just erase the previous solution. + See :term:`the Glossary `. + + positive : bool, default=False + When set to ``True``, forces the coefficients to be positive. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + coef_ : ndarray of shape (n_features,) or (n_targets, n_features) + Parameter vector (w in the cost function formula). + + dual_gap_ : float or ndarray of shape (n_targets,) + Given param alpha, the dual gaps at the end of the optimization, + same shape as each observation of y. + + sparse_coef_ : sparse matrix of shape (n_features, 1) or \ + (n_targets, n_features) + Readonly property derived from ``coef_``. + + intercept_ : float or ndarray of shape (n_targets,) + Independent term in decision function. + + n_iter_ : int or list of int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + lars_path : Regularization path using LARS. + lasso_path : Regularization path using Lasso. + LassoLars : Lasso Path along the regularization parameter using LARS algorithm. + LassoCV : Lasso alpha parameter by cross-validation. + LassoLarsCV : Lasso least angle parameter algorithm by cross-validation. + sklearn.decomposition.sparse_encode : Sparse coding array estimator. + + Notes + ----- + The algorithm used to fit the model is coordinate descent. + + To avoid unnecessary memory duplication the X argument of the fit method + should be directly passed as a Fortran-contiguous numpy array. + + Regularization improves the conditioning of the problem and + reduces the variance of the estimates. Larger values specify stronger + regularization. Alpha corresponds to `1 / (2C)` in other linear + models such as :class:`~sklearn.linear_model.LogisticRegression` or + :class:`~sklearn.svm.LinearSVC`. If an array is passed, penalties are + assumed to be specific to the targets. Hence they must correspond in + number. + + The precise stopping criteria based on `tol` are the following: First, check that + that maximum coordinate update, i.e. :math:`\\max_j |w_j^{new} - w_j^{old}|` + is smaller than `tol` times the maximum absolute coefficient, :math:`\\max_j |w_j|`. + If so, then additionally check whether the dual gap is smaller than `tol` times + :math:`||y||_2^2 / n_{\\text{samples}}`. + + The target can be a 2-dimensional array, resulting in the optimization of the + following objective:: + + (1 / (2 * n_samples)) * ||Y - XW||^2_F + alpha * ||W||_11 + + where :math:`||W||_{1,1}` is the sum of the magnitude of the matrix coefficients. + It should not be confused with :class:`~sklearn.linear_model.MultiTaskLasso` which + instead penalizes the :math:`L_{2,1}` norm of the coefficients, yielding row-wise + sparsity in the coefficients. + + Examples + -------- + >>> from sklearn import linear_model + >>> clf = linear_model.Lasso(alpha=0.1) + >>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2]) + Lasso(alpha=0.1) + >>> print(clf.coef_) + [0.85 0. ] + >>> print(clf.intercept_) + 0.15... + """ + + _parameter_constraints: dict = { + **ElasticNet._parameter_constraints, + } + _parameter_constraints.pop("l1_ratio") + + path = staticmethod(enet_path) + + def __init__( + self, + alpha=1.0, + *, + fit_intercept=True, + precompute=False, + copy_X=True, + max_iter=1000, + tol=1e-4, + warm_start=False, + positive=False, + random_state=None, + selection="cyclic", + ): + super().__init__( + alpha=alpha, + l1_ratio=1.0, + fit_intercept=fit_intercept, + precompute=precompute, + copy_X=copy_X, + max_iter=max_iter, + tol=tol, + warm_start=warm_start, + positive=positive, + random_state=random_state, + selection=selection, + ) + + +############################################################################### +# Functions for CV with paths functions + + +def _path_residuals( + X, + y, + sample_weight, + train, + test, + fit_intercept, + path, + path_params, + alphas=None, + l1_ratio=1, + X_order=None, + dtype=None, +): + """Returns the MSE for the models computed by 'path'. + + 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. + + sample_weight : None or array-like of shape (n_samples,) + Sample weights. + + train : list of indices + The indices of the train set. + + test : list of indices + The indices of the test set. + + path : callable + Function returning a list of models on the path. See + enet_path for an example of signature. + + path_params : dictionary + Parameters passed to the path function. + + alphas : array-like, default=None + Array of float that is used for cross-validation. If not + provided, computed using 'path'. + + l1_ratio : float, default=1 + float between 0 and 1 passed to ElasticNet (scaling between + l1 and l2 penalties). For ``l1_ratio = 0`` the penalty is an + L2 penalty. For ``l1_ratio = 1`` it is an L1 penalty. For ``0 + < l1_ratio < 1``, the penalty is a combination of L1 and L2. + + X_order : {'F', 'C'}, default=None + The order of the arrays expected by the path function to + avoid memory copies. + + dtype : a numpy dtype, default=None + The dtype of the arrays expected by the path function to + avoid memory copies. + """ + X_train = X[train] + y_train = y[train] + X_test = X[test] + y_test = y[test] + if sample_weight is None: + sw_train, sw_test = None, None + else: + sw_train = sample_weight[train] + sw_test = sample_weight[test] + n_samples = X_train.shape[0] + # TLDR: Rescale sw_train to sum up to n_samples on the training set. + # See TLDR and long comment inside ElasticNet.fit. + sw_train *= n_samples / np.sum(sw_train) + # Note: Alternatively, we could also have rescaled alpha instead + # of sample_weight: + # + # alpha *= np.sum(sample_weight) / n_samples + + if not sparse.issparse(X): + for array, array_input in ( + (X_train, X), + (y_train, y), + (X_test, X), + (y_test, y), + ): + if array.base is not array_input and not array.flags["WRITEABLE"]: + # fancy indexing should create a writable copy but it doesn't + # for read-only memmaps (cf. numpy#14132). + array.setflags(write=True) + + if y.ndim == 1: + precompute = path_params["precompute"] + else: + # No Gram variant of multi-task exists right now. + # Fall back to default enet_multitask + precompute = False + + X_train, y_train, X_offset, y_offset, X_scale, precompute, Xy = _pre_fit( + X_train, + y_train, + None, + precompute, + fit_intercept=fit_intercept, + copy=False, + sample_weight=sw_train, + ) + + path_params = path_params.copy() + path_params["Xy"] = Xy + path_params["X_offset"] = X_offset + path_params["X_scale"] = X_scale + path_params["precompute"] = precompute + path_params["copy_X"] = False + path_params["alphas"] = alphas + # needed for sparse cd solver + path_params["sample_weight"] = sw_train + + if "l1_ratio" in path_params: + path_params["l1_ratio"] = l1_ratio + + # Do the ordering and type casting here, as if it is done in the path, + # X is copied and a reference is kept here + X_train = check_array(X_train, accept_sparse="csc", dtype=dtype, order=X_order) + alphas, coefs, _ = path(X_train, y_train, **path_params) + del X_train, y_train + + if y.ndim == 1: + # Doing this so that it becomes coherent with multioutput. + coefs = coefs[np.newaxis, :, :] + y_offset = np.atleast_1d(y_offset) + y_test = y_test[:, np.newaxis] + + intercepts = y_offset[:, np.newaxis] - np.dot(X_offset, coefs) + X_test_coefs = safe_sparse_dot(X_test, coefs) + residues = X_test_coefs - y_test[:, :, np.newaxis] + residues += intercepts + if sample_weight is None: + this_mse = (residues**2).mean(axis=0) + else: + this_mse = np.average(residues**2, weights=sw_test, axis=0) + + return this_mse.mean(axis=0) + + +class LinearModelCV(MultiOutputMixin, LinearModel, ABC): + """Base class for iterative model fitting along a regularization path.""" + + _parameter_constraints: dict = { + "eps": [Interval(Real, 0, None, closed="neither")], + "n_alphas": [Interval(Integral, 1, None, closed="left")], + "alphas": ["array-like", None], + "fit_intercept": ["boolean"], + "precompute": [StrOptions({"auto"}), "array-like", "boolean"], + "max_iter": [Interval(Integral, 1, None, closed="left")], + "tol": [Interval(Real, 0, None, closed="left")], + "copy_X": ["boolean"], + "cv": ["cv_object"], + "verbose": ["verbose"], + "n_jobs": [Integral, None], + "positive": ["boolean"], + "random_state": ["random_state"], + "selection": [StrOptions({"cyclic", "random"})], + } + + @abstractmethod + def __init__( + self, + eps=1e-3, + n_alphas=100, + alphas=None, + fit_intercept=True, + precompute="auto", + max_iter=1000, + tol=1e-4, + copy_X=True, + cv=None, + verbose=False, + n_jobs=None, + positive=False, + random_state=None, + selection="cyclic", + ): + self.eps = eps + self.n_alphas = n_alphas + self.alphas = alphas + self.fit_intercept = fit_intercept + self.precompute = precompute + self.max_iter = max_iter + self.tol = tol + self.copy_X = copy_X + self.cv = cv + self.verbose = verbose + self.n_jobs = n_jobs + self.positive = positive + self.random_state = random_state + self.selection = selection + + @abstractmethod + def _get_estimator(self): + """Model to be fitted after the best alpha has been determined.""" + + @abstractmethod + def _is_multitask(self): + """Bool indicating if class is meant for multidimensional target.""" + + @staticmethod + @abstractmethod + def path(X, y, **kwargs): + """Compute path with coordinate descent.""" + + @_fit_context(prefer_skip_nested_validation=True) + def fit(self, X, y, sample_weight=None, **params): + """Fit linear model with coordinate descent. + + Fit is on grid of alphas and best alpha estimated by cross-validation. + + Parameters + ---------- + X : {array-like, sparse matrix} of shape (n_samples, n_features) + Training data. Pass directly as Fortran-contiguous data + to avoid unnecessary memory duplication. If y is mono-output, + X can be sparse. + + y : array-like of shape (n_samples,) or (n_samples, n_targets) + Target values. + + sample_weight : float or array-like of shape (n_samples,), \ + default=None + Sample weights used for fitting and evaluation of the weighted + mean squared error of each cv-fold. Note that the cross validated + MSE that is finally used to find the best model is the unweighted + mean over the (weighted) MSEs of each test fold. + + **params : dict, default=None + Parameters to be passed to the CV splitter. + + .. versionadded:: 1.4 + Only available if `enable_metadata_routing=True`, + which can be set by using + ``sklearn.set_config(enable_metadata_routing=True)``. + See :ref:`Metadata Routing User Guide ` for + more details. + + Returns + ------- + self : object + Returns an instance of fitted model. + """ + _raise_for_params(params, self, "fit") + + # This makes sure that there is no duplication in memory. + # Dealing right with copy_X is important in the following: + # Multiple functions touch X and subsamples of X and can induce a + # lot of duplication of memory + copy_X = self.copy_X and self.fit_intercept + + check_y_params = dict( + copy=False, dtype=[np.float64, np.float32], ensure_2d=False + ) + if isinstance(X, np.ndarray) or sparse.issparse(X): + # Keep a reference to X + reference_to_old_X = X + # Let us not impose fortran ordering so far: it is + # not useful for the cross-validation loop and will be done + # by the model fitting itself + + # Need to validate separately here. + # We can't pass multi_output=True because that would allow y to be + # csr. We also want to allow y to be 64 or 32 but check_X_y only + # allows to convert for 64. + check_X_params = dict( + accept_sparse="csc", dtype=[np.float64, np.float32], copy=False + ) + X, y = self._validate_data( + X, y, validate_separately=(check_X_params, check_y_params) + ) + if sparse.issparse(X): + if hasattr(reference_to_old_X, "data") and not np.may_share_memory( + reference_to_old_X.data, X.data + ): + # X is a sparse matrix and has been copied + copy_X = False + elif not np.may_share_memory(reference_to_old_X, X): + # X has been copied + copy_X = False + del reference_to_old_X + else: + # Need to validate separately here. + # We can't pass multi_output=True because that would allow y to be + # csr. We also want to allow y to be 64 or 32 but check_X_y only + # allows to convert for 64. + check_X_params = dict( + accept_sparse="csc", + dtype=[np.float64, np.float32], + order="F", + copy=copy_X, + ) + X, y = self._validate_data( + X, y, validate_separately=(check_X_params, check_y_params) + ) + copy_X = False + + check_consistent_length(X, y) + + if not self._is_multitask(): + if y.ndim > 1 and y.shape[1] > 1: + raise ValueError( + "For multi-task outputs, use MultiTask%s" % self.__class__.__name__ + ) + y = column_or_1d(y, warn=True) + else: + if sparse.issparse(X): + raise TypeError("X should be dense but a sparse matrix waspassed") + elif y.ndim == 1: + raise ValueError( + "For mono-task outputs, use %sCV" % self.__class__.__name__[9:] + ) + + if isinstance(sample_weight, numbers.Number): + sample_weight = None + if sample_weight is not None: + sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype) + + model = self._get_estimator() + + # All LinearModelCV parameters except 'cv' are acceptable + path_params = self.get_params() + + # Pop `intercept` that is not parameter of the path function + path_params.pop("fit_intercept", None) + + if "l1_ratio" in path_params: + l1_ratios = np.atleast_1d(path_params["l1_ratio"]) + # For the first path, we need to set l1_ratio + path_params["l1_ratio"] = l1_ratios[0] + else: + l1_ratios = [ + 1, + ] + path_params.pop("cv", None) + path_params.pop("n_jobs", None) + + alphas = self.alphas + n_l1_ratio = len(l1_ratios) + + check_scalar_alpha = partial( + check_scalar, + target_type=Real, + min_val=0.0, + include_boundaries="left", + ) + + if alphas is None: + alphas = [ + _alpha_grid( + X, + y, + l1_ratio=l1_ratio, + fit_intercept=self.fit_intercept, + eps=self.eps, + n_alphas=self.n_alphas, + copy_X=self.copy_X, + ) + for l1_ratio in l1_ratios + ] + else: + # Making sure alphas entries are scalars. + for index, alpha in enumerate(alphas): + check_scalar_alpha(alpha, f"alphas[{index}]") + # Making sure alphas is properly ordered. + alphas = np.tile(np.sort(alphas)[::-1], (n_l1_ratio, 1)) + + # We want n_alphas to be the number of alphas used for each l1_ratio. + n_alphas = len(alphas[0]) + path_params.update({"n_alphas": n_alphas}) + + path_params["copy_X"] = copy_X + # We are not computing in parallel, we can modify X + # inplace in the folds + if effective_n_jobs(self.n_jobs) > 1: + path_params["copy_X"] = False + + # init cross-validation generator + cv = check_cv(self.cv) + + if _routing_enabled(): + splitter_supports_sample_weight = get_routing_for_object(cv).consumes( + method="split", params=["sample_weight"] + ) + if ( + sample_weight is not None + and not splitter_supports_sample_weight + and not has_fit_parameter(self, "sample_weight") + ): + raise ValueError( + "The CV splitter and underlying estimator do not support" + " sample weights." + ) + + if splitter_supports_sample_weight: + params["sample_weight"] = sample_weight + + routed_params = process_routing(self, "fit", **params) + + if sample_weight is not None and not has_fit_parameter( + self, "sample_weight" + ): + # MultiTaskElasticNetCV does not (yet) support sample_weight + sample_weight = None + else: + routed_params = Bunch() + routed_params.splitter = Bunch(split=Bunch()) + + # Compute path for all folds and compute MSE to get the best alpha + folds = list(cv.split(X, y, **routed_params.splitter.split)) + best_mse = np.inf + + # We do a double for loop folded in one, in order to be able to + # iterate in parallel on l1_ratio and folds + jobs = ( + delayed(_path_residuals)( + X, + y, + sample_weight, + train, + test, + self.fit_intercept, + self.path, + path_params, + alphas=this_alphas, + l1_ratio=this_l1_ratio, + X_order="F", + dtype=X.dtype.type, + ) + for this_l1_ratio, this_alphas in zip(l1_ratios, alphas) + for train, test in folds + ) + mse_paths = Parallel( + n_jobs=self.n_jobs, + verbose=self.verbose, + prefer="threads", + )(jobs) + mse_paths = np.reshape(mse_paths, (n_l1_ratio, len(folds), -1)) + # The mean is computed over folds. + mean_mse = np.mean(mse_paths, axis=1) + self.mse_path_ = np.squeeze(np.moveaxis(mse_paths, 2, 1)) + for l1_ratio, l1_alphas, mse_alphas in zip(l1_ratios, alphas, mean_mse): + i_best_alpha = np.argmin(mse_alphas) + this_best_mse = mse_alphas[i_best_alpha] + if this_best_mse < best_mse: + best_alpha = l1_alphas[i_best_alpha] + best_l1_ratio = l1_ratio + best_mse = this_best_mse + + self.l1_ratio_ = best_l1_ratio + self.alpha_ = best_alpha + if self.alphas is None: + self.alphas_ = np.asarray(alphas) + if n_l1_ratio == 1: + self.alphas_ = self.alphas_[0] + # Remove duplicate alphas in case alphas is provided. + else: + self.alphas_ = np.asarray(alphas[0]) + + # Refit the model with the parameters selected + common_params = { + name: value + for name, value in self.get_params().items() + if name in model.get_params() + } + model.set_params(**common_params) + model.alpha = best_alpha + model.l1_ratio = best_l1_ratio + model.copy_X = copy_X + precompute = getattr(self, "precompute", None) + if isinstance(precompute, str) and precompute == "auto": + model.precompute = False + + if sample_weight is None: + # MultiTaskElasticNetCV does not (yet) support sample_weight, even + # not sample_weight=None. + model.fit(X, y) + else: + model.fit(X, y, sample_weight=sample_weight) + if not hasattr(self, "l1_ratio"): + del self.l1_ratio_ + self.coef_ = model.coef_ + self.intercept_ = model.intercept_ + self.dual_gap_ = model.dual_gap_ + self.n_iter_ = model.n_iter_ + return self + + def _more_tags(self): + # Note: check_sample_weights_invariance(kind='ones') should work, but + # currently we can only mark a whole test as xfail. + return { + "_xfail_checks": { + "check_sample_weights_invariance": ( + "zero sample_weight is not equivalent to removing samples" + ), + } + } + + def get_metadata_routing(self): + """Get metadata routing of this object. + + Please check :ref:`User Guide ` on how the routing + mechanism works. + + .. versionadded:: 1.4 + + Returns + ------- + routing : MetadataRouter + A :class:`~sklearn.utils.metadata_routing.MetadataRouter` encapsulating + routing information. + """ + router = ( + MetadataRouter(owner=self.__class__.__name__) + .add_self_request(self) + .add( + splitter=check_cv(self.cv), + method_mapping=MethodMapping().add(callee="split", caller="fit"), + ) + ) + return router + + +class LassoCV(RegressorMixin, LinearModelCV): + """Lasso linear model with iterative fitting along a regularization path. + + See glossary entry for :term:`cross-validation estimator`. + + The best model is selected by cross-validation. + + The optimization objective for Lasso is:: + + (1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1 + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path. + + alphas : array-like, default=None + List of alphas where to compute the models. + If ``None`` alphas are set automatically. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + precompute : 'auto', bool or array-like of shape \ + (n_features, n_features), default='auto' + Whether to use a precomputed Gram matrix to speed up + calculations. If set to ``'auto'`` let us decide. The Gram + matrix can also be passed as argument. + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + cv : int, cross-validation generator or iterable, default=None + Determines the cross-validation splitting strategy. + Possible inputs for cv are: + + - None, to use the default 5-fold cross-validation, + - int, to specify the number of folds. + - :term:`CV splitter`, + - An iterable yielding (train, test) splits as arrays of indices. + + For int/None inputs, :class:`~sklearn.model_selection.KFold` is used. + + Refer :ref:`User Guide ` for the various + cross-validation strategies that can be used here. + + .. versionchanged:: 0.22 + ``cv`` default value if None changed from 3-fold to 5-fold. + + verbose : bool or int, default=False + Amount of verbosity. + + n_jobs : int, default=None + Number of CPUs to use during the cross validation. + ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. + ``-1`` means using all processors. See :term:`Glossary ` + for more details. + + positive : bool, default=False + If positive, restrict regression coefficients to be positive. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + alpha_ : float + The amount of penalization chosen by cross validation. + + coef_ : ndarray of shape (n_features,) or (n_targets, n_features) + Parameter vector (w in the cost function formula). + + intercept_ : float or ndarray of shape (n_targets,) + Independent term in decision function. + + mse_path_ : ndarray of shape (n_alphas, n_folds) + Mean square error for the test set on each fold, varying alpha. + + alphas_ : ndarray of shape (n_alphas,) + The grid of alphas used for fitting. + + dual_gap_ : float or ndarray of shape (n_targets,) + The dual gap at the end of the optimization for the optimal alpha + (``alpha_``). + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance for the optimal alpha. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + lars_path : Compute Least Angle Regression or Lasso path using LARS + algorithm. + lasso_path : Compute Lasso path with coordinate descent. + Lasso : The Lasso is a linear model that estimates sparse coefficients. + LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars. + LassoCV : Lasso linear model with iterative fitting along a regularization + path. + LassoLarsCV : Cross-validated Lasso using the LARS algorithm. + + Notes + ----- + In `fit`, once the best parameter `alpha` is found through + cross-validation, the model is fit again using the entire training set. + + To avoid unnecessary memory duplication the `X` argument of the `fit` + method should be directly passed as a Fortran-contiguous numpy array. + + For an example, see + :ref:`examples/linear_model/plot_lasso_model_selection.py + `. + + :class:`LassoCV` leads to different results than a hyperparameter + search using :class:`~sklearn.model_selection.GridSearchCV` with a + :class:`Lasso` model. In :class:`LassoCV`, a model for a given + penalty `alpha` is warm started using the coefficients of the + closest model (trained at the previous iteration) on the + regularization path. It tends to speed up the hyperparameter + search. + + Examples + -------- + >>> from sklearn.linear_model import LassoCV + >>> from sklearn.datasets import make_regression + >>> X, y = make_regression(noise=4, random_state=0) + >>> reg = LassoCV(cv=5, random_state=0).fit(X, y) + >>> reg.score(X, y) + 0.9993... + >>> reg.predict(X[:1,]) + array([-78.4951...]) + """ + + path = staticmethod(lasso_path) + + def __init__( + self, + *, + eps=1e-3, + n_alphas=100, + alphas=None, + fit_intercept=True, + precompute="auto", + max_iter=1000, + tol=1e-4, + copy_X=True, + cv=None, + verbose=False, + n_jobs=None, + positive=False, + random_state=None, + selection="cyclic", + ): + super().__init__( + eps=eps, + n_alphas=n_alphas, + alphas=alphas, + fit_intercept=fit_intercept, + precompute=precompute, + max_iter=max_iter, + tol=tol, + copy_X=copy_X, + cv=cv, + verbose=verbose, + n_jobs=n_jobs, + positive=positive, + random_state=random_state, + selection=selection, + ) + + def _get_estimator(self): + return Lasso() + + def _is_multitask(self): + return False + + def _more_tags(self): + return {"multioutput": False} + + +class ElasticNetCV(RegressorMixin, LinearModelCV): + """Elastic Net model with iterative fitting along a regularization path. + + See glossary entry for :term:`cross-validation estimator`. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + l1_ratio : float or list of float, default=0.5 + Float between 0 and 1 passed to ElasticNet (scaling between + l1 and l2 penalties). For ``l1_ratio = 0`` + the penalty is an L2 penalty. For ``l1_ratio = 1`` it is an L1 penalty. + For ``0 < l1_ratio < 1``, the penalty is a combination of L1 and L2 + This parameter can be a list, in which case the different + values are tested by cross-validation and the one giving the best + prediction score is used. Note that a good choice of list of + values for l1_ratio is often to put more values close to 1 + (i.e. Lasso) and less close to 0 (i.e. Ridge), as in ``[.1, .5, .7, + .9, .95, .99, 1]``. + + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path, used for each l1_ratio. + + alphas : array-like, default=None + List of alphas where to compute the models. + If None alphas are set automatically. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + precompute : 'auto', bool or array-like of shape \ + (n_features, n_features), default='auto' + Whether to use a precomputed Gram matrix to speed up + calculations. If set to ``'auto'`` let us decide. The Gram + matrix can also be passed as argument. + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + cv : int, cross-validation generator or iterable, default=None + Determines the cross-validation splitting strategy. + Possible inputs for cv are: + + - None, to use the default 5-fold cross-validation, + - int, to specify the number of folds. + - :term:`CV splitter`, + - An iterable yielding (train, test) splits as arrays of indices. + + For int/None inputs, :class:`~sklearn.model_selection.KFold` is used. + + Refer :ref:`User Guide ` for the various + cross-validation strategies that can be used here. + + .. versionchanged:: 0.22 + ``cv`` default value if None changed from 3-fold to 5-fold. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + verbose : bool or int, default=0 + Amount of verbosity. + + n_jobs : int, default=None + Number of CPUs to use during the cross validation. + ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. + ``-1`` means using all processors. See :term:`Glossary ` + for more details. + + positive : bool, default=False + When set to ``True``, forces the coefficients to be positive. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + alpha_ : float + The amount of penalization chosen by cross validation. + + l1_ratio_ : float + The compromise between l1 and l2 penalization chosen by + cross validation. + + coef_ : ndarray of shape (n_features,) or (n_targets, n_features) + Parameter vector (w in the cost function formula). + + intercept_ : float or ndarray of shape (n_targets, n_features) + Independent term in the decision function. + + mse_path_ : ndarray of shape (n_l1_ratio, n_alpha, n_folds) + Mean square error for the test set on each fold, varying l1_ratio and + alpha. + + alphas_ : ndarray of shape (n_alphas,) or (n_l1_ratio, n_alphas) + The grid of alphas used for fitting, for each l1_ratio. + + dual_gap_ : float + The dual gaps at the end of the optimization for the optimal alpha. + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance for the optimal alpha. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + enet_path : Compute elastic net path with coordinate descent. + ElasticNet : Linear regression with combined L1 and L2 priors as regularizer. + + Notes + ----- + In `fit`, once the best parameters `l1_ratio` and `alpha` are found through + cross-validation, the model is fit again using the entire training set. + + To avoid unnecessary memory duplication the `X` argument of the `fit` + method should be directly passed as a Fortran-contiguous numpy array. + + The parameter `l1_ratio` corresponds to alpha in the glmnet R package + while alpha corresponds to the lambda parameter in glmnet. + More specifically, the optimization objective is:: + + 1 / (2 * n_samples) * ||y - Xw||^2_2 + + alpha * l1_ratio * ||w||_1 + + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2 + + If you are interested in controlling the L1 and L2 penalty + separately, keep in mind that this is equivalent to:: + + a * L1 + b * L2 + + for:: + + alpha = a + b and l1_ratio = a / (a + b). + + For an example, see + :ref:`examples/linear_model/plot_lasso_model_selection.py + `. + + Examples + -------- + >>> from sklearn.linear_model import ElasticNetCV + >>> from sklearn.datasets import make_regression + + >>> X, y = make_regression(n_features=2, random_state=0) + >>> regr = ElasticNetCV(cv=5, random_state=0) + >>> regr.fit(X, y) + ElasticNetCV(cv=5, random_state=0) + >>> print(regr.alpha_) + 0.199... + >>> print(regr.intercept_) + 0.398... + >>> print(regr.predict([[0, 0]])) + [0.398...] + """ + + _parameter_constraints: dict = { + **LinearModelCV._parameter_constraints, + "l1_ratio": [Interval(Real, 0, 1, closed="both"), "array-like"], + } + + path = staticmethod(enet_path) + + def __init__( + self, + *, + l1_ratio=0.5, + eps=1e-3, + n_alphas=100, + alphas=None, + fit_intercept=True, + precompute="auto", + max_iter=1000, + tol=1e-4, + cv=None, + copy_X=True, + verbose=0, + n_jobs=None, + positive=False, + random_state=None, + selection="cyclic", + ): + self.l1_ratio = l1_ratio + self.eps = eps + self.n_alphas = n_alphas + self.alphas = alphas + self.fit_intercept = fit_intercept + self.precompute = precompute + self.max_iter = max_iter + self.tol = tol + self.cv = cv + self.copy_X = copy_X + self.verbose = verbose + self.n_jobs = n_jobs + self.positive = positive + self.random_state = random_state + self.selection = selection + + def _get_estimator(self): + return ElasticNet() + + def _is_multitask(self): + return False + + def _more_tags(self): + return {"multioutput": False} + + +############################################################################### +# Multi Task ElasticNet and Lasso models (with joint feature selection) + + +class MultiTaskElasticNet(Lasso): + """Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer. + + The optimization objective for MultiTaskElasticNet is:: + + (1 / (2 * n_samples)) * ||Y - XW||_Fro^2 + + alpha * l1_ratio * ||W||_21 + + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2 + + Where:: + + ||W||_21 = sum_i sqrt(sum_j W_ij ^ 2) + + i.e. the sum of norms of each row. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + alpha : float, default=1.0 + Constant that multiplies the L1/L2 term. Defaults to 1.0. + + l1_ratio : float, default=0.5 + The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. + For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it + is an L2 penalty. + For ``0 < l1_ratio < 1``, the penalty is a combination of L1/L2 and L2. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + warm_start : bool, default=False + When set to ``True``, reuse the solution of the previous call to fit as + initialization, otherwise, just erase the previous solution. + See :term:`the Glossary `. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + intercept_ : ndarray of shape (n_targets,) + Independent term in decision function. + + coef_ : ndarray of shape (n_targets, n_features) + Parameter vector (W in the cost function formula). If a 1D y is + passed in at fit (non multi-task usage), ``coef_`` is then a 1D array. + Note that ``coef_`` stores the transpose of ``W``, ``W.T``. + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance. + + dual_gap_ : float + The dual gaps at the end of the optimization. + + eps_ : float + The tolerance scaled scaled by the variance of the target `y`. + + sparse_coef_ : sparse matrix of shape (n_features,) or \ + (n_targets, n_features) + Sparse representation of the `coef_`. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + MultiTaskElasticNetCV : Multi-task L1/L2 ElasticNet with built-in + cross-validation. + ElasticNet : Linear regression with combined L1 and L2 priors as regularizer. + MultiTaskLasso : Multi-task Lasso model trained with L1/L2 + mixed-norm as regularizer. + + Notes + ----- + The algorithm used to fit the model is coordinate descent. + + To avoid unnecessary memory duplication the X and y arguments of the fit + method should be directly passed as Fortran-contiguous numpy arrays. + + Examples + -------- + >>> from sklearn import linear_model + >>> clf = linear_model.MultiTaskElasticNet(alpha=0.1) + >>> clf.fit([[0,0], [1, 1], [2, 2]], [[0, 0], [1, 1], [2, 2]]) + MultiTaskElasticNet(alpha=0.1) + >>> print(clf.coef_) + [[0.45663524 0.45612256] + [0.45663524 0.45612256]] + >>> print(clf.intercept_) + [0.0872422 0.0872422] + """ + + _parameter_constraints: dict = { + **ElasticNet._parameter_constraints, + } + for param in ("precompute", "positive"): + _parameter_constraints.pop(param) + + def __init__( + self, + alpha=1.0, + *, + l1_ratio=0.5, + fit_intercept=True, + copy_X=True, + max_iter=1000, + tol=1e-4, + warm_start=False, + random_state=None, + selection="cyclic", + ): + self.l1_ratio = l1_ratio + self.alpha = alpha + self.fit_intercept = fit_intercept + self.max_iter = max_iter + self.copy_X = copy_X + self.tol = tol + self.warm_start = warm_start + self.random_state = random_state + self.selection = selection + + @_fit_context(prefer_skip_nested_validation=True) + def fit(self, X, y): + """Fit MultiTaskElasticNet model with coordinate descent. + + Parameters + ---------- + X : ndarray of shape (n_samples, n_features) + Data. + y : ndarray of shape (n_samples, n_targets) + Target. Will be cast to X's dtype if necessary. + + Returns + ------- + self : object + Fitted estimator. + + Notes + ----- + Coordinate descent is an algorithm that considers each column of + data at a time hence it will automatically convert the X input + as a Fortran-contiguous numpy array if necessary. + + To avoid memory re-allocation it is advised to allocate the + initial data in memory directly using that format. + """ + # Need to validate separately here. + # We can't pass multi_output=True because that would allow y to be csr. + check_X_params = dict( + dtype=[np.float64, np.float32], + order="F", + copy=self.copy_X and self.fit_intercept, + ) + check_y_params = dict(ensure_2d=False, order="F") + X, y = self._validate_data( + X, y, validate_separately=(check_X_params, check_y_params) + ) + check_consistent_length(X, y) + y = y.astype(X.dtype) + + if hasattr(self, "l1_ratio"): + model_str = "ElasticNet" + else: + model_str = "Lasso" + if y.ndim == 1: + raise ValueError("For mono-task outputs, use %s" % model_str) + + n_samples, n_features = X.shape + n_targets = y.shape[1] + + X, y, X_offset, y_offset, X_scale = _preprocess_data( + X, y, fit_intercept=self.fit_intercept, copy=False + ) + + if not self.warm_start or not hasattr(self, "coef_"): + self.coef_ = np.zeros( + (n_targets, n_features), dtype=X.dtype.type, order="F" + ) + + l1_reg = self.alpha * self.l1_ratio * n_samples + l2_reg = self.alpha * (1.0 - self.l1_ratio) * n_samples + + self.coef_ = np.asfortranarray(self.coef_) # coef contiguous in memory + + random = self.selection == "random" + + ( + self.coef_, + self.dual_gap_, + self.eps_, + self.n_iter_, + ) = cd_fast.enet_coordinate_descent_multi_task( + self.coef_, + l1_reg, + l2_reg, + X, + y, + self.max_iter, + self.tol, + check_random_state(self.random_state), + random, + ) + + # account for different objective scaling here and in cd_fast + self.dual_gap_ /= n_samples + + self._set_intercept(X_offset, y_offset, X_scale) + + # return self for chaining fit and predict calls + return self + + def _more_tags(self): + return {"multioutput_only": True} + + +class MultiTaskLasso(MultiTaskElasticNet): + """Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer. + + The optimization objective for Lasso is:: + + (1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21 + + Where:: + + ||W||_21 = \\sum_i \\sqrt{\\sum_j w_{ij}^2} + + i.e. the sum of norm of each row. + + Read more in the :ref:`User Guide `. + + Parameters + ---------- + alpha : float, default=1.0 + Constant that multiplies the L1/L2 term. Defaults to 1.0. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + warm_start : bool, default=False + When set to ``True``, reuse the solution of the previous call to fit as + initialization, otherwise, just erase the previous solution. + See :term:`the Glossary `. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + coef_ : ndarray of shape (n_targets, n_features) + Parameter vector (W in the cost function formula). + Note that ``coef_`` stores the transpose of ``W``, ``W.T``. + + intercept_ : ndarray of shape (n_targets,) + Independent term in decision function. + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance. + + dual_gap_ : ndarray of shape (n_alphas,) + The dual gaps at the end of the optimization for each alpha. + + eps_ : float + The tolerance scaled scaled by the variance of the target `y`. + + sparse_coef_ : sparse matrix of shape (n_features,) or \ + (n_targets, n_features) + Sparse representation of the `coef_`. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + Lasso: Linear Model trained with L1 prior as regularizer (aka the Lasso). + MultiTaskLassoCV: Multi-task L1 regularized linear model with built-in + cross-validation. + MultiTaskElasticNetCV: Multi-task L1/L2 ElasticNet with built-in cross-validation. + + Notes + ----- + The algorithm used to fit the model is coordinate descent. + + To avoid unnecessary memory duplication the X and y arguments of the fit + method should be directly passed as Fortran-contiguous numpy arrays. + + Examples + -------- + >>> from sklearn import linear_model + >>> clf = linear_model.MultiTaskLasso(alpha=0.1) + >>> clf.fit([[0, 1], [1, 2], [2, 4]], [[0, 0], [1, 1], [2, 3]]) + MultiTaskLasso(alpha=0.1) + >>> print(clf.coef_) + [[0. 0.60809415] + [0. 0.94592424]] + >>> print(clf.intercept_) + [-0.41888636 -0.87382323] + """ + + _parameter_constraints: dict = { + **MultiTaskElasticNet._parameter_constraints, + } + _parameter_constraints.pop("l1_ratio") + + def __init__( + self, + alpha=1.0, + *, + fit_intercept=True, + copy_X=True, + max_iter=1000, + tol=1e-4, + warm_start=False, + random_state=None, + selection="cyclic", + ): + self.alpha = alpha + self.fit_intercept = fit_intercept + self.max_iter = max_iter + self.copy_X = copy_X + self.tol = tol + self.warm_start = warm_start + self.l1_ratio = 1.0 + self.random_state = random_state + self.selection = selection + + +class MultiTaskElasticNetCV(RegressorMixin, LinearModelCV): + """Multi-task L1/L2 ElasticNet with built-in cross-validation. + + See glossary entry for :term:`cross-validation estimator`. + + The optimization objective for MultiTaskElasticNet is:: + + (1 / (2 * n_samples)) * ||Y - XW||^Fro_2 + + alpha * l1_ratio * ||W||_21 + + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2 + + Where:: + + ||W||_21 = \\sum_i \\sqrt{\\sum_j w_{ij}^2} + + i.e. the sum of norm of each row. + + Read more in the :ref:`User Guide `. + + .. versionadded:: 0.15 + + Parameters + ---------- + l1_ratio : float or list of float, default=0.5 + The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. + For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it + is an L2 penalty. + For ``0 < l1_ratio < 1``, the penalty is a combination of L1/L2 and L2. + This parameter can be a list, in which case the different + values are tested by cross-validation and the one giving the best + prediction score is used. Note that a good choice of list of + values for l1_ratio is often to put more values close to 1 + (i.e. Lasso) and less close to 0 (i.e. Ridge), as in ``[.1, .5, .7, + .9, .95, .99, 1]``. + + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path. + + alphas : array-like, default=None + List of alphas where to compute the models. + If not provided, set automatically. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + cv : int, cross-validation generator or iterable, default=None + Determines the cross-validation splitting strategy. + Possible inputs for cv are: + + - None, to use the default 5-fold cross-validation, + - int, to specify the number of folds. + - :term:`CV splitter`, + - An iterable yielding (train, test) splits as arrays of indices. + + For int/None inputs, :class:`~sklearn.model_selection.KFold` is used. + + Refer :ref:`User Guide ` for the various + cross-validation strategies that can be used here. + + .. versionchanged:: 0.22 + ``cv`` default value if None changed from 3-fold to 5-fold. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + verbose : bool or int, default=0 + Amount of verbosity. + + n_jobs : int, default=None + Number of CPUs to use during the cross validation. Note that this is + used only if multiple values for l1_ratio are given. + ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. + ``-1`` means using all processors. See :term:`Glossary ` + for more details. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + intercept_ : ndarray of shape (n_targets,) + Independent term in decision function. + + coef_ : ndarray of shape (n_targets, n_features) + Parameter vector (W in the cost function formula). + Note that ``coef_`` stores the transpose of ``W``, ``W.T``. + + alpha_ : float + The amount of penalization chosen by cross validation. + + mse_path_ : ndarray of shape (n_alphas, n_folds) or \ + (n_l1_ratio, n_alphas, n_folds) + Mean square error for the test set on each fold, varying alpha. + + alphas_ : ndarray of shape (n_alphas,) or (n_l1_ratio, n_alphas) + The grid of alphas used for fitting, for each l1_ratio. + + l1_ratio_ : float + Best l1_ratio obtained by cross-validation. + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance for the optimal alpha. + + dual_gap_ : float + The dual gap at the end of the optimization for the optimal alpha. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + MultiTaskElasticNet : Multi-task L1/L2 ElasticNet with built-in cross-validation. + ElasticNetCV : Elastic net model with best model selection by + cross-validation. + MultiTaskLassoCV : Multi-task Lasso model trained with L1 norm + as regularizer and built-in cross-validation. + + Notes + ----- + The algorithm used to fit the model is coordinate descent. + + In `fit`, once the best parameters `l1_ratio` and `alpha` are found through + cross-validation, the model is fit again using the entire training set. + + To avoid unnecessary memory duplication the `X` and `y` arguments of the + `fit` method should be directly passed as Fortran-contiguous numpy arrays. + + Examples + -------- + >>> from sklearn import linear_model + >>> clf = linear_model.MultiTaskElasticNetCV(cv=3) + >>> clf.fit([[0,0], [1, 1], [2, 2]], + ... [[0, 0], [1, 1], [2, 2]]) + MultiTaskElasticNetCV(cv=3) + >>> print(clf.coef_) + [[0.52875032 0.46958558] + [0.52875032 0.46958558]] + >>> print(clf.intercept_) + [0.00166409 0.00166409] + """ + + _parameter_constraints: dict = { + **LinearModelCV._parameter_constraints, + "l1_ratio": [Interval(Real, 0, 1, closed="both"), "array-like"], + } + _parameter_constraints.pop("precompute") + _parameter_constraints.pop("positive") + + path = staticmethod(enet_path) + + def __init__( + self, + *, + l1_ratio=0.5, + eps=1e-3, + n_alphas=100, + alphas=None, + fit_intercept=True, + max_iter=1000, + tol=1e-4, + cv=None, + copy_X=True, + verbose=0, + n_jobs=None, + random_state=None, + selection="cyclic", + ): + self.l1_ratio = l1_ratio + self.eps = eps + self.n_alphas = n_alphas + self.alphas = alphas + self.fit_intercept = fit_intercept + self.max_iter = max_iter + self.tol = tol + self.cv = cv + self.copy_X = copy_X + self.verbose = verbose + self.n_jobs = n_jobs + self.random_state = random_state + self.selection = selection + + def _get_estimator(self): + return MultiTaskElasticNet() + + def _is_multitask(self): + return True + + def _more_tags(self): + return {"multioutput_only": True} + + # This is necessary as LinearModelCV now supports sample_weight while + # MultiTaskElasticNet does not (yet). + def fit(self, X, y, **params): + """Fit MultiTaskElasticNet model with coordinate descent. + + Fit is on grid of alphas and best alpha estimated by cross-validation. + + Parameters + ---------- + X : ndarray of shape (n_samples, n_features) + Training data. + y : ndarray of shape (n_samples, n_targets) + Training target variable. Will be cast to X's dtype if necessary. + + **params : dict, default=None + Parameters to be passed to the CV splitter. + + .. versionadded:: 1.4 + Only available if `enable_metadata_routing=True`, + which can be set by using + ``sklearn.set_config(enable_metadata_routing=True)``. + See :ref:`Metadata Routing User Guide ` for + more details. + + Returns + ------- + self : object + Returns MultiTaskElasticNet instance. + """ + return super().fit(X, y, **params) + + +class MultiTaskLassoCV(RegressorMixin, LinearModelCV): + """Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer. + + See glossary entry for :term:`cross-validation estimator`. + + The optimization objective for MultiTaskLasso is:: + + (1 / (2 * n_samples)) * ||Y - XW||^Fro_2 + alpha * ||W||_21 + + Where:: + + ||W||_21 = \\sum_i \\sqrt{\\sum_j w_{ij}^2} + + i.e. the sum of norm of each row. + + Read more in the :ref:`User Guide `. + + .. versionadded:: 0.15 + + Parameters + ---------- + eps : float, default=1e-3 + Length of the path. ``eps=1e-3`` means that + ``alpha_min / alpha_max = 1e-3``. + + n_alphas : int, default=100 + Number of alphas along the regularization path. + + alphas : array-like, default=None + List of alphas where to compute the models. + If not provided, set automatically. + + fit_intercept : bool, default=True + Whether to calculate the intercept for this model. If set + to false, no intercept will be used in calculations + (i.e. data is expected to be centered). + + max_iter : int, default=1000 + The maximum number of iterations. + + tol : float, default=1e-4 + The tolerance for the optimization: if the updates are + smaller than ``tol``, the optimization code checks the + dual gap for optimality and continues until it is smaller + than ``tol``. + + copy_X : bool, default=True + If ``True``, X will be copied; else, it may be overwritten. + + cv : int, cross-validation generator or iterable, default=None + Determines the cross-validation splitting strategy. + Possible inputs for cv are: + + - None, to use the default 5-fold cross-validation, + - int, to specify the number of folds. + - :term:`CV splitter`, + - An iterable yielding (train, test) splits as arrays of indices. + + For int/None inputs, :class:`~sklearn.model_selection.KFold` is used. + + Refer :ref:`User Guide ` for the various + cross-validation strategies that can be used here. + + .. versionchanged:: 0.22 + ``cv`` default value if None changed from 3-fold to 5-fold. + + verbose : bool or int, default=False + Amount of verbosity. + + n_jobs : int, default=None + Number of CPUs to use during the cross validation. Note that this is + used only if multiple values for l1_ratio are given. + ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. + ``-1`` means using all processors. See :term:`Glossary ` + for more details. + + random_state : int, RandomState instance, default=None + The seed of the pseudo random number generator that selects a random + feature to update. Used when ``selection`` == 'random'. + Pass an int for reproducible output across multiple function calls. + See :term:`Glossary `. + + selection : {'cyclic', 'random'}, default='cyclic' + If set to 'random', a random coefficient is updated every iteration + rather than looping over features sequentially by default. This + (setting to 'random') often leads to significantly faster convergence + especially when tol is higher than 1e-4. + + Attributes + ---------- + intercept_ : ndarray of shape (n_targets,) + Independent term in decision function. + + coef_ : ndarray of shape (n_targets, n_features) + Parameter vector (W in the cost function formula). + Note that ``coef_`` stores the transpose of ``W``, ``W.T``. + + alpha_ : float + The amount of penalization chosen by cross validation. + + mse_path_ : ndarray of shape (n_alphas, n_folds) + Mean square error for the test set on each fold, varying alpha. + + alphas_ : ndarray of shape (n_alphas,) + The grid of alphas used for fitting. + + n_iter_ : int + Number of iterations run by the coordinate descent solver to reach + the specified tolerance for the optimal alpha. + + dual_gap_ : float + The dual gap at the end of the optimization for the optimal alpha. + + n_features_in_ : int + Number of features seen during :term:`fit`. + + .. versionadded:: 0.24 + + 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 + -------- + MultiTaskElasticNet : Multi-task ElasticNet model trained with L1/L2 + mixed-norm as regularizer. + ElasticNetCV : Elastic net model with best model selection by + cross-validation. + MultiTaskElasticNetCV : Multi-task L1/L2 ElasticNet with built-in + cross-validation. + + Notes + ----- + The algorithm used to fit the model is coordinate descent. + + In `fit`, once the best parameter `alpha` is found through + cross-validation, the model is fit again using the entire training set. + + To avoid unnecessary memory duplication the `X` and `y` arguments of the + `fit` method should be directly passed as Fortran-contiguous numpy arrays. + + Examples + -------- + >>> from sklearn.linear_model import MultiTaskLassoCV + >>> from sklearn.datasets import make_regression + >>> from sklearn.metrics import r2_score + >>> X, y = make_regression(n_targets=2, noise=4, random_state=0) + >>> reg = MultiTaskLassoCV(cv=5, random_state=0).fit(X, y) + >>> r2_score(y, reg.predict(X)) + 0.9994... + >>> reg.alpha_ + 0.5713... + >>> reg.predict(X[:1,]) + array([[153.7971..., 94.9015...]]) + """ + + _parameter_constraints: dict = { + **LinearModelCV._parameter_constraints, + } + _parameter_constraints.pop("precompute") + _parameter_constraints.pop("positive") + + path = staticmethod(lasso_path) + + def __init__( + self, + *, + eps=1e-3, + n_alphas=100, + alphas=None, + fit_intercept=True, + max_iter=1000, + tol=1e-4, + copy_X=True, + cv=None, + verbose=False, + n_jobs=None, + random_state=None, + selection="cyclic", + ): + super().__init__( + eps=eps, + n_alphas=n_alphas, + alphas=alphas, + fit_intercept=fit_intercept, + max_iter=max_iter, + tol=tol, + copy_X=copy_X, + cv=cv, + verbose=verbose, + n_jobs=n_jobs, + random_state=random_state, + selection=selection, + ) + + def _get_estimator(self): + return MultiTaskLasso() + + def _is_multitask(self): + return True + + def _more_tags(self): + return {"multioutput_only": True} + + # This is necessary as LinearModelCV now supports sample_weight while + # MultiTaskElasticNet does not (yet). + def fit(self, X, y, **params): + """Fit MultiTaskLasso model with coordinate descent. + + Fit is on grid of alphas and best alpha estimated by cross-validation. + + Parameters + ---------- + X : ndarray of shape (n_samples, n_features) + Data. + y : ndarray of shape (n_samples, n_targets) + Target. Will be cast to X's dtype if necessary. + + **params : dict, default=None + Parameters to be passed to the CV splitter. + + .. versionadded:: 1.4 + Only available if `enable_metadata_routing=True`, + which can be set by using + ``sklearn.set_config(enable_metadata_routing=True)``. + See :ref:`Metadata Routing User Guide ` for + more details. + + Returns + ------- + self : object + Returns an instance of fitted model. + """ + return super().fit(X, y, **params)