""" Logistic Regression """ # Author: Gael Varoquaux # Fabian Pedregosa # Alexandre Gramfort # Manoj Kumar # Lars Buitinck # Simon Wu # Arthur Mensch n_features: grad[-1] = z0.sum() return out, grad def _logistic_loss(w, X, y, alpha, sample_weight=None): """Computes the logistic loss. Parameters ---------- w : ndarray of shape (n_features,) or (n_features + 1,) Coefficient vector. X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : ndarray of shape (n_samples,) Array of labels. alpha : float Regularization parameter. alpha is equal to 1 / C. sample_weight : array-like of shape (n_samples,) default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- out : float Logistic loss. """ w, c, yz = _intercept_dot(w, X, y) if sample_weight is None: sample_weight = np.ones(y.shape[0]) # Logistic loss is the negative of the log of the logistic function. out = -np.sum(sample_weight * log_logistic(yz)) + .5 * alpha * np.dot(w, w) return out def _logistic_grad_hess(w, X, y, alpha, sample_weight=None): """Computes the gradient and the Hessian, in the case of a logistic loss. Parameters ---------- w : ndarray of shape (n_features,) or (n_features + 1,) Coefficient vector. X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. y : ndarray of shape (n_samples,) Array of labels. alpha : float Regularization parameter. alpha is equal to 1 / C. sample_weight : array-like of shape (n_samples,) default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- grad : ndarray of shape (n_features,) or (n_features + 1,) Logistic gradient. Hs : callable Function that takes the gradient as a parameter and returns the matrix product of the Hessian and gradient. """ n_samples, n_features = X.shape grad = np.empty_like(w) fit_intercept = grad.shape[0] > n_features w, c, yz = _intercept_dot(w, X, y) if sample_weight is None: sample_weight = np.ones(y.shape[0]) z = expit(yz) z0 = sample_weight * (z - 1) * y grad[:n_features] = safe_sparse_dot(X.T, z0) + alpha * w # Case where we fit the intercept. if fit_intercept: grad[-1] = z0.sum() # The mat-vec product of the Hessian d = sample_weight * z * (1 - z) if sparse.issparse(X): dX = safe_sparse_dot(sparse.dia_matrix((d, 0), shape=(n_samples, n_samples)), X) else: # Precompute as much as possible dX = d[:, np.newaxis] * X if fit_intercept: # Calculate the double derivative with respect to intercept # In the case of sparse matrices this returns a matrix object. dd_intercept = np.squeeze(np.array(dX.sum(axis=0))) def Hs(s): ret = np.empty_like(s) ret[:n_features] = X.T.dot(dX.dot(s[:n_features])) ret[:n_features] += alpha * s[:n_features] # For the fit intercept case. if fit_intercept: ret[:n_features] += s[-1] * dd_intercept ret[-1] = dd_intercept.dot(s[:n_features]) ret[-1] += d.sum() * s[-1] return ret return grad, Hs def _multinomial_loss(w, X, Y, alpha, sample_weight): """Computes multinomial loss and class probabilities. Parameters ---------- w : ndarray of shape (n_classes * n_features,) or (n_classes * (n_features + 1),) Coefficient vector. X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. Y : ndarray of shape (n_samples, n_classes) Transformed labels according to the output of LabelBinarizer. alpha : float Regularization parameter. alpha is equal to 1 / C. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. Returns ------- loss : float Multinomial loss. p : ndarray of shape (n_samples, n_classes) Estimated class probabilities. w : ndarray of shape (n_classes, n_features) Reshaped param vector excluding intercept terms. Reference --------- Bishop, C. M. (2006). Pattern recognition and machine learning. Springer. (Chapter 4.3.4) """ n_classes = Y.shape[1] n_features = X.shape[1] fit_intercept = w.size == (n_classes * (n_features + 1)) w = w.reshape(n_classes, -1) sample_weight = sample_weight[:, np.newaxis] if fit_intercept: intercept = w[:, -1] w = w[:, :-1] else: intercept = 0 p = safe_sparse_dot(X, w.T) p += intercept p -= logsumexp(p, axis=1)[:, np.newaxis] loss = -(sample_weight * Y * p).sum() loss += 0.5 * alpha * squared_norm(w) p = np.exp(p, p) return loss, p, w def _multinomial_loss_grad(w, X, Y, alpha, sample_weight): """Computes the multinomial loss, gradient and class probabilities. Parameters ---------- w : ndarray of shape (n_classes * n_features,) or (n_classes * (n_features + 1),) Coefficient vector. X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. Y : ndarray of shape (n_samples, n_classes) Transformed labels according to the output of LabelBinarizer. alpha : float Regularization parameter. alpha is equal to 1 / C. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. Returns ------- loss : float Multinomial loss. grad : ndarray of shape (n_classes * n_features,) or \ (n_classes * (n_features + 1),) Ravelled gradient of the multinomial loss. p : ndarray of shape (n_samples, n_classes) Estimated class probabilities Reference --------- Bishop, C. M. (2006). Pattern recognition and machine learning. Springer. (Chapter 4.3.4) """ n_classes = Y.shape[1] n_features = X.shape[1] fit_intercept = (w.size == n_classes * (n_features + 1)) grad = np.zeros((n_classes, n_features + bool(fit_intercept)), dtype=X.dtype) loss, p, w = _multinomial_loss(w, X, Y, alpha, sample_weight) sample_weight = sample_weight[:, np.newaxis] diff = sample_weight * (p - Y) grad[:, :n_features] = safe_sparse_dot(diff.T, X) grad[:, :n_features] += alpha * w if fit_intercept: grad[:, -1] = diff.sum(axis=0) return loss, grad.ravel(), p def _multinomial_grad_hess(w, X, Y, alpha, sample_weight): """ Computes the gradient and the Hessian, in the case of a multinomial loss. Parameters ---------- w : ndarray of shape (n_classes * n_features,) or (n_classes * (n_features + 1),) Coefficient vector. X : {array-like, sparse matrix} of shape (n_samples, n_features) Training data. Y : ndarray of shape (n_samples, n_classes) Transformed labels according to the output of LabelBinarizer. alpha : float Regularization parameter. alpha is equal to 1 / C. sample_weight : array-like of shape (n_samples,) Array of weights that are assigned to individual samples. Returns ------- grad : ndarray of shape (n_classes * n_features,) or \ (n_classes * (n_features + 1),) Ravelled gradient of the multinomial loss. hessp : callable Function that takes in a vector input of shape (n_classes * n_features) or (n_classes * (n_features + 1)) and returns matrix-vector product with hessian. References ---------- Barak A. Pearlmutter (1993). Fast Exact Multiplication by the Hessian. http://www.bcl.hamilton.ie/~barak/papers/nc-hessian.pdf """ n_features = X.shape[1] n_classes = Y.shape[1] fit_intercept = w.size == (n_classes * (n_features + 1)) # `loss` is unused. Refactoring to avoid computing it does not # significantly speed up the computation and decreases readability loss, grad, p = _multinomial_loss_grad(w, X, Y, alpha, sample_weight) sample_weight = sample_weight[:, np.newaxis] # Hessian-vector product derived by applying the R-operator on the gradient # of the multinomial loss function. def hessp(v): v = v.reshape(n_classes, -1) if fit_intercept: inter_terms = v[:, -1] v = v[:, :-1] else: inter_terms = 0 # r_yhat holds the result of applying the R-operator on the multinomial # estimator. r_yhat = safe_sparse_dot(X, v.T) r_yhat += inter_terms r_yhat += (-p * r_yhat).sum(axis=1)[:, np.newaxis] r_yhat *= p r_yhat *= sample_weight hessProd = np.zeros((n_classes, n_features + bool(fit_intercept))) hessProd[:, :n_features] = safe_sparse_dot(r_yhat.T, X) hessProd[:, :n_features] += v * alpha if fit_intercept: hessProd[:, -1] = r_yhat.sum(axis=0) return hessProd.ravel() return grad, hessp def _check_solver(solver, penalty, dual): all_solvers = ['liblinear', 'newton-cg', 'lbfgs', 'sag', 'saga'] if solver not in all_solvers: raise ValueError("Logistic Regression supports only solvers in %s, got" " %s." % (all_solvers, solver)) all_penalties = ['l1', 'l2', 'elasticnet', 'none'] if penalty not in all_penalties: raise ValueError("Logistic Regression supports only penalties in %s," " got %s." % (all_penalties, penalty)) if solver not in ['liblinear', 'saga'] and penalty not in ('l2', 'none'): raise ValueError("Solver %s supports only 'l2' or 'none' penalties, " "got %s penalty." % (solver, penalty)) if solver != 'liblinear' and dual: raise ValueError("Solver %s supports only " "dual=False, got dual=%s" % (solver, dual)) if penalty == 'elasticnet' and solver != 'saga': raise ValueError("Only 'saga' solver supports elasticnet penalty," " got solver={}.".format(solver)) if solver == 'liblinear' and penalty == 'none': raise ValueError( "penalty='none' is not supported for the liblinear solver" ) return solver def _check_multi_class(multi_class, solver, n_classes): if multi_class == 'auto': if solver == 'liblinear': multi_class = 'ovr' elif n_classes > 2: multi_class = 'multinomial' else: multi_class = 'ovr' if multi_class not in ('multinomial', 'ovr'): raise ValueError("multi_class should be 'multinomial', 'ovr' or " "'auto'. Got %s." % multi_class) if multi_class == 'multinomial' and solver == 'liblinear': raise ValueError("Solver %s does not support " "a multinomial backend." % solver) return multi_class def _logistic_regression_path(X, y, pos_class=None, Cs=10, fit_intercept=True, max_iter=100, tol=1e-4, verbose=0, solver='lbfgs', coef=None, class_weight=None, dual=False, penalty='l2', intercept_scaling=1., multi_class='auto', random_state=None, check_input=True, max_squared_sum=None, sample_weight=None, l1_ratio=None): """Compute a Logistic Regression model for a list of regularization parameters. This is an implementation that uses the result of the previous model to speed up computations along the set of solutions, making it faster than sequentially calling LogisticRegression for the different parameters. Note that there will be no speedup with liblinear solver, since it does not handle warm-starting. Read more in the :ref:`User Guide `. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Input data. y : array-like of shape (n_samples,) or (n_samples, n_targets) Input data, target values. pos_class : int, default=None The class with respect to which we perform a one-vs-all fit. If None, then it is assumed that the given problem is binary. Cs : int or array-like of shape (n_cs,), default=10 List of values for the regularization parameter or integer specifying the number of regularization parameters that should be used. In this case, the parameters will be chosen in a logarithmic scale between 1e-4 and 1e4. fit_intercept : bool, default=True Whether to fit an intercept for the model. In this case the shape of the returned array is (n_cs, n_features + 1). max_iter : int, default=100 Maximum number of iterations for the solver. tol : float, default=1e-4 Stopping criterion. For the newton-cg and lbfgs solvers, the iteration will stop when ``max{|g_i | i = 1, ..., n} <= tol`` where ``g_i`` is the i-th component of the gradient. verbose : int, default=0 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}, \ default='lbfgs' Numerical solver to use. coef : array-like of shape (n_features,), default=None Initialization value for coefficients of logistic regression. Useless for liblinear solver. class_weight : dict or 'balanced', default=None Weights associated with classes in the form ``{class_label: weight}``. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified. dual : bool, default=False Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. penalty : {'l1', 'l2', 'elasticnet'}, default='l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is only supported by the 'saga' solver. intercept_scaling : float, default=1. Useful only when the solver 'liblinear' is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a "synthetic" feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes ``intercept_scaling * synthetic_feature_weight``. Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. multi_class : {'ovr', 'multinomial', 'auto'}, default='auto' If the option chosen is 'ovr', then a binary problem is fit for each label. For 'multinomial' the loss minimised is the multinomial loss fit across the entire probability distribution, *even when the data is binary*. 'multinomial' is unavailable when solver='liblinear'. 'auto' selects 'ovr' if the data is binary, or if solver='liblinear', and otherwise selects 'multinomial'. .. versionadded:: 0.18 Stochastic Average Gradient descent solver for 'multinomial' case. .. versionchanged:: 0.22 Default changed from 'ovr' to 'auto' in 0.22. random_state : int, RandomState instance, default=None Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the data. See :term:`Glossary ` for details. check_input : bool, default=True If False, the input arrays X and y will not be checked. max_squared_sum : float, default=None Maximum squared sum of X over samples. Used only in SAG solver. If None, it will be computed, going through all the samples. The value should be precomputed to speed up cross validation. sample_weight : array-like of shape(n_samples,), default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. l1_ratio : float, default=None The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2. Returns ------- coefs : ndarray of shape (n_cs, n_features) or (n_cs, n_features + 1) List of coefficients for the Logistic Regression model. If fit_intercept is set to True then the second dimension will be n_features + 1, where the last item represents the intercept. For ``multiclass='multinomial'``, the shape is (n_classes, n_cs, n_features) or (n_classes, n_cs, n_features + 1). Cs : ndarray Grid of Cs used for cross-validation. n_iter : array of shape (n_cs,) Actual number of iteration for each Cs. Notes ----- You might get slightly different results with the solver liblinear than with the others since this uses LIBLINEAR which penalizes the intercept. .. versionchanged:: 0.19 The "copy" parameter was removed. """ if isinstance(Cs, numbers.Integral): Cs = np.logspace(-4, 4, Cs) solver = _check_solver(solver, penalty, dual) # Preprocessing. if check_input: X = check_array(X, accept_sparse='csr', dtype=np.float64, accept_large_sparse=solver != 'liblinear') y = check_array(y, ensure_2d=False, dtype=None) check_consistent_length(X, y) _, n_features = X.shape classes = np.unique(y) random_state = check_random_state(random_state) multi_class = _check_multi_class(multi_class, solver, len(classes)) if pos_class is None and multi_class != 'multinomial': if (classes.size > 2): raise ValueError('To fit OvR, use the pos_class argument') # np.unique(y) gives labels in sorted order. pos_class = classes[1] # If sample weights exist, convert them to array (support for lists) # and check length # Otherwise set them to 1 for all examples sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype) # If class_weights is a dict (provided by the user), the weights # are assigned to the original labels. If it is "balanced", then # the class_weights are assigned after masking the labels with a OvR. le = LabelEncoder() if isinstance(class_weight, dict) or multi_class == 'multinomial': class_weight_ = compute_class_weight(class_weight, classes=classes, y=y) sample_weight *= class_weight_[le.fit_transform(y)] # For doing a ovr, we need to mask the labels first. for the # multinomial case this is not necessary. if multi_class == 'ovr': w0 = np.zeros(n_features + int(fit_intercept), dtype=X.dtype) mask_classes = np.array([-1, 1]) mask = (y == pos_class) y_bin = np.ones(y.shape, dtype=X.dtype) y_bin[~mask] = -1. # for compute_class_weight if class_weight == "balanced": class_weight_ = compute_class_weight(class_weight, classes=mask_classes, y=y_bin) sample_weight *= class_weight_[le.fit_transform(y_bin)] else: if solver not in ['sag', 'saga']: lbin = LabelBinarizer() Y_multi = lbin.fit_transform(y) if Y_multi.shape[1] == 1: Y_multi = np.hstack([1 - Y_multi, Y_multi]) else: # SAG multinomial solver needs LabelEncoder, not LabelBinarizer le = LabelEncoder() Y_multi = le.fit_transform(y).astype(X.dtype, copy=False) w0 = np.zeros((classes.size, n_features + int(fit_intercept)), order='F', dtype=X.dtype) if coef is not None: # it must work both giving the bias term and not if multi_class == 'ovr': if coef.size not in (n_features, w0.size): raise ValueError( 'Initialization coef is of shape %d, expected shape ' '%d or %d' % (coef.size, n_features, w0.size)) w0[:coef.size] = coef else: # For binary problems coef.shape[0] should be 1, otherwise it # should be classes.size. n_classes = classes.size if n_classes == 2: n_classes = 1 if (coef.shape[0] != n_classes or coef.shape[1] not in (n_features, n_features + 1)): raise ValueError( 'Initialization coef is of shape (%d, %d), expected ' 'shape (%d, %d) or (%d, %d)' % ( coef.shape[0], coef.shape[1], classes.size, n_features, classes.size, n_features + 1)) if n_classes == 1: w0[0, :coef.shape[1]] = -coef w0[1, :coef.shape[1]] = coef else: w0[:, :coef.shape[1]] = coef if multi_class == 'multinomial': # scipy.optimize.minimize and newton-cg accepts only # ravelled parameters. if solver in ['lbfgs', 'newton-cg']: w0 = w0.ravel() target = Y_multi if solver == 'lbfgs': def func(x, *args): return _multinomial_loss_grad(x, *args)[0:2] elif solver == 'newton-cg': def func(x, *args): return _multinomial_loss(x, *args)[0] def grad(x, *args): return _multinomial_loss_grad(x, *args)[1] hess = _multinomial_grad_hess warm_start_sag = {'coef': w0.T} else: target = y_bin if solver == 'lbfgs': func = _logistic_loss_and_grad elif solver == 'newton-cg': func = _logistic_loss def grad(x, *args): return _logistic_loss_and_grad(x, *args)[1] hess = _logistic_grad_hess warm_start_sag = {'coef': np.expand_dims(w0, axis=1)} coefs = list() n_iter = np.zeros(len(Cs), dtype=np.int32) for i, C in enumerate(Cs): if solver == 'lbfgs': iprint = [-1, 50, 1, 100, 101][ np.searchsorted(np.array([0, 1, 2, 3]), verbose)] opt_res = optimize.minimize( func, w0, method="L-BFGS-B", jac=True, args=(X, target, 1. / C, sample_weight), options={"iprint": iprint, "gtol": tol, "maxiter": max_iter} ) n_iter_i = _check_optimize_result( solver, opt_res, max_iter, extra_warning_msg=_LOGISTIC_SOLVER_CONVERGENCE_MSG) w0, loss = opt_res.x, opt_res.fun elif solver == 'newton-cg': args = (X, target, 1. / C, sample_weight) w0, n_iter_i = _newton_cg(hess, func, grad, w0, args=args, maxiter=max_iter, tol=tol) elif solver == 'liblinear': coef_, intercept_, n_iter_i, = _fit_liblinear( X, target, C, fit_intercept, intercept_scaling, None, penalty, dual, verbose, max_iter, tol, random_state, sample_weight=sample_weight) if fit_intercept: w0 = np.concatenate([coef_.ravel(), intercept_]) else: w0 = coef_.ravel() elif solver in ['sag', 'saga']: if multi_class == 'multinomial': target = target.astype(X.dtype, copy=False) loss = 'multinomial' else: loss = 'log' # alpha is for L2-norm, beta is for L1-norm if penalty == 'l1': alpha = 0. beta = 1. / C elif penalty == 'l2': alpha = 1. / C beta = 0. else: # Elastic-Net penalty alpha = (1. / C) * (1 - l1_ratio) beta = (1. / C) * l1_ratio w0, n_iter_i, warm_start_sag = sag_solver( X, target, sample_weight, loss, alpha, beta, max_iter, tol, verbose, random_state, False, max_squared_sum, warm_start_sag, is_saga=(solver == 'saga')) else: raise ValueError("solver must be one of {'liblinear', 'lbfgs', " "'newton-cg', 'sag'}, got '%s' instead" % solver) if multi_class == 'multinomial': n_classes = max(2, classes.size) multi_w0 = np.reshape(w0, (n_classes, -1)) if n_classes == 2: multi_w0 = multi_w0[1][np.newaxis, :] coefs.append(multi_w0.copy()) else: coefs.append(w0.copy()) n_iter[i] = n_iter_i return np.array(coefs), np.array(Cs), n_iter # helper function for LogisticCV def _log_reg_scoring_path(X, y, train, test, pos_class=None, Cs=10, scoring=None, fit_intercept=False, max_iter=100, tol=1e-4, class_weight=None, verbose=0, solver='lbfgs', penalty='l2', dual=False, intercept_scaling=1., multi_class='auto', random_state=None, max_squared_sum=None, sample_weight=None, l1_ratio=None): """Computes scores across logistic_regression_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 labels. train : list of indices The indices of the train set. test : list of indices The indices of the test set. pos_class : int, default=None The class with respect to which we perform a one-vs-all fit. If None, then it is assumed that the given problem is binary. Cs : int or list of floats, default=10 Each of the values in Cs describes the inverse of regularization strength. If Cs is as an int, then a grid of Cs values are chosen in a logarithmic scale between 1e-4 and 1e4. If not provided, then a fixed set of values for Cs are used. scoring : callable, default=None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. For a list of scoring functions that can be used, look at :mod:`sklearn.metrics`. The default scoring option used is accuracy_score. fit_intercept : bool, default=False If False, then the bias term is set to zero. Else the last term of each coef_ gives us the intercept. max_iter : int, default=100 Maximum number of iterations for the solver. tol : float, default=1e-4 Tolerance for stopping criteria. class_weight : dict or 'balanced', default=None Weights associated with classes in the form ``{class_label: weight}``. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))`` Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified. verbose : int, default=0 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}, \ default='lbfgs' Decides which solver to use. penalty : {'l1', 'l2', 'elasticnet'}, default='l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is only supported by the 'saga' solver. dual : bool, default=False Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. intercept_scaling : float, default=1. Useful only when the solver 'liblinear' is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a "synthetic" feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. multi_class : {'auto', 'ovr', 'multinomial'}, default='auto' If the option chosen is 'ovr', then a binary problem is fit for each label. For 'multinomial' the loss minimised is the multinomial loss fit across the entire probability distribution, *even when the data is binary*. 'multinomial' is unavailable when solver='liblinear'. random_state : int, RandomState instance, default=None Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the data. See :term:`Glossary ` for details. max_squared_sum : float, default=None Maximum squared sum of X over samples. Used only in SAG solver. If None, it will be computed, going through all the samples. The value should be precomputed to speed up cross validation. sample_weight : array-like of shape(n_samples,), default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. l1_ratio : float, default=None The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2. Returns ------- coefs : ndarray of shape (n_cs, n_features) or (n_cs, n_features + 1) List of coefficients for the Logistic Regression model. If fit_intercept is set to True then the second dimension will be n_features + 1, where the last item represents the intercept. Cs : ndarray Grid of Cs used for cross-validation. scores : ndarray of shape (n_cs,) Scores obtained for each Cs. n_iter : ndarray of shape(n_cs,) Actual number of iteration for each Cs. """ X_train = X[train] X_test = X[test] y_train = y[train] y_test = y[test] if sample_weight is not None: sample_weight = _check_sample_weight(sample_weight, X) sample_weight = sample_weight[train] coefs, Cs, n_iter = _logistic_regression_path( X_train, y_train, Cs=Cs, l1_ratio=l1_ratio, fit_intercept=fit_intercept, solver=solver, max_iter=max_iter, class_weight=class_weight, pos_class=pos_class, multi_class=multi_class, tol=tol, verbose=verbose, dual=dual, penalty=penalty, intercept_scaling=intercept_scaling, random_state=random_state, check_input=False, max_squared_sum=max_squared_sum, sample_weight=sample_weight) log_reg = LogisticRegression(solver=solver, multi_class=multi_class) # The score method of Logistic Regression has a classes_ attribute. if multi_class == 'ovr': log_reg.classes_ = np.array([-1, 1]) elif multi_class == 'multinomial': log_reg.classes_ = np.unique(y_train) else: raise ValueError("multi_class should be either multinomial or ovr, " "got %d" % multi_class) if pos_class is not None: mask = (y_test == pos_class) y_test = np.ones(y_test.shape, dtype=np.float64) y_test[~mask] = -1. scores = list() scoring = get_scorer(scoring) for w in coefs: if multi_class == 'ovr': w = w[np.newaxis, :] if fit_intercept: log_reg.coef_ = w[:, :-1] log_reg.intercept_ = w[:, -1] else: log_reg.coef_ = w log_reg.intercept_ = 0. if scoring is None: scores.append(log_reg.score(X_test, y_test)) else: scores.append(scoring(log_reg, X_test, y_test)) return coefs, Cs, np.array(scores), n_iter class LogisticRegression(BaseEstimator, LinearClassifierMixin, SparseCoefMixin): """ Logistic Regression (aka logit, MaxEnt) classifier. In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the 'multi_class' option is set to 'ovr', and uses the cross-entropy loss if the 'multi_class' option is set to 'multinomial'. (Currently the 'multinomial' option is supported only by the 'lbfgs', 'sag', 'saga' and 'newton-cg' solvers.) This class implements regularized logistic regression using the 'liblinear' library, 'newton-cg', 'sag', 'saga' and 'lbfgs' solvers. **Note that regularization is applied by default**. It can handle both dense and sparse input. Use C-ordered arrays or CSR matrices containing 64-bit floats for optimal performance; any other input format will be converted (and copied). The 'newton-cg', 'sag', and 'lbfgs' solvers support only L2 regularization with primal formulation, or no regularization. The 'liblinear' solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. The Elastic-Net regularization is only supported by the 'saga' solver. Read more in the :ref:`User Guide `. Parameters ---------- penalty : {'l1', 'l2', 'elasticnet', 'none'}, default='l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is only supported by the 'saga' solver. If 'none' (not supported by the liblinear solver), no regularization is applied. .. versionadded:: 0.19 l1 penalty with SAGA solver (allowing 'multinomial' + L1) dual : bool, default=False Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. tol : float, default=1e-4 Tolerance for stopping criteria. C : float, default=1.0 Inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization. fit_intercept : bool, default=True Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. intercept_scaling : float, default=1 Useful only when the solver 'liblinear' is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a "synthetic" feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes ``intercept_scaling * synthetic_feature_weight``. Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. class_weight : dict or 'balanced', default=None Weights associated with classes in the form ``{class_label: weight}``. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified. .. versionadded:: 0.17 *class_weight='balanced'* random_state : int, RandomState instance, default=None Used when ``solver`` == 'sag', 'saga' or 'liblinear' to shuffle the data. See :term:`Glossary ` for details. solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'}, \ default='lbfgs' Algorithm to use in the optimization problem. - For small datasets, 'liblinear' is a good choice, whereas 'sag' and 'saga' are faster for large ones. - For multiclass problems, only 'newton-cg', 'sag', 'saga' and 'lbfgs' handle multinomial loss; 'liblinear' is limited to one-versus-rest schemes. - 'newton-cg', 'lbfgs', 'sag' and 'saga' handle L2 or no penalty - 'liblinear' and 'saga' also handle L1 penalty - 'saga' also supports 'elasticnet' penalty - 'liblinear' does not support setting ``penalty='none'`` Note that 'sag' and 'saga' fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing. .. versionadded:: 0.17 Stochastic Average Gradient descent solver. .. versionadded:: 0.19 SAGA solver. .. versionchanged:: 0.22 The default solver changed from 'liblinear' to 'lbfgs' in 0.22. max_iter : int, default=100 Maximum number of iterations taken for the solvers to converge. multi_class : {'auto', 'ovr', 'multinomial'}, default='auto' If the option chosen is 'ovr', then a binary problem is fit for each label. For 'multinomial' the loss minimised is the multinomial loss fit across the entire probability distribution, *even when the data is binary*. 'multinomial' is unavailable when solver='liblinear'. 'auto' selects 'ovr' if the data is binary, or if solver='liblinear', and otherwise selects 'multinomial'. .. versionadded:: 0.18 Stochastic Average Gradient descent solver for 'multinomial' case. .. versionchanged:: 0.22 Default changed from 'ovr' to 'auto' in 0.22. verbose : int, default=0 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. 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. Useless for liblinear solver. See :term:`the Glossary `. .. versionadded:: 0.17 *warm_start* to support *lbfgs*, *newton-cg*, *sag*, *saga* solvers. n_jobs : int, default=None Number of CPU cores used when parallelizing over classes if multi_class='ovr'". This parameter is ignored when the ``solver`` is set to 'liblinear' regardless of whether 'multi_class' is specified or not. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. l1_ratio : float, default=None The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2. Attributes ---------- classes_ : ndarray of shape (n_classes, ) A list of class labels known to the classifier. coef_ : ndarray of shape (1, n_features) or (n_classes, n_features) Coefficient of the features in the decision function. `coef_` is of shape (1, n_features) when the given problem is binary. In particular, when `multi_class='multinomial'`, `coef_` corresponds to outcome 1 (True) and `-coef_` corresponds to outcome 0 (False). intercept_ : ndarray of shape (1,) or (n_classes,) Intercept (a.k.a. bias) added to the decision function. If `fit_intercept` is set to False, the intercept is set to zero. `intercept_` is of shape (1,) when the given problem is binary. In particular, when `multi_class='multinomial'`, `intercept_` corresponds to outcome 1 (True) and `-intercept_` corresponds to outcome 0 (False). n_iter_ : ndarray of shape (n_classes,) or (1, ) Actual number of iterations for all classes. If binary or multinomial, it returns only 1 element. For liblinear solver, only the maximum number of iteration across all classes is given. .. versionchanged:: 0.20 In SciPy <= 1.0.0 the number of lbfgs iterations may exceed ``max_iter``. ``n_iter_`` will now report at most ``max_iter``. See Also -------- SGDClassifier : Incrementally trained logistic regression (when given the parameter ``loss="log"``). LogisticRegressionCV : Logistic regression with built-in cross validation. Notes ----- The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon, to have slightly different results for the same input data. If that happens, try with a smaller tol parameter. Predict output may not match that of standalone liblinear in certain cases. See :ref:`differences from liblinear ` in the narrative documentation. References ---------- L-BFGS-B -- Software for Large-scale Bound-constrained Optimization Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales. http://users.iems.northwestern.edu/~nocedal/lbfgsb.html LIBLINEAR -- A Library for Large Linear Classification https://www.csie.ntu.edu.tw/~cjlin/liblinear/ SAG -- Mark Schmidt, Nicolas Le Roux, and Francis Bach Minimizing Finite Sums with the Stochastic Average Gradient https://hal.inria.fr/hal-00860051/document SAGA -- Defazio, A., Bach F. & Lacoste-Julien S. (2014). SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives https://arxiv.org/abs/1407.0202 Hsiang-Fu Yu, Fang-Lan Huang, Chih-Jen Lin (2011). Dual coordinate descent methods for logistic regression and maximum entropy models. Machine Learning 85(1-2):41-75. https://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf Examples -------- >>> from sklearn.datasets import load_iris >>> from sklearn.linear_model import LogisticRegression >>> X, y = load_iris(return_X_y=True) >>> clf = LogisticRegression(random_state=0).fit(X, y) >>> clf.predict(X[:2, :]) array([0, 0]) >>> clf.predict_proba(X[:2, :]) array([[9.8...e-01, 1.8...e-02, 1.4...e-08], [9.7...e-01, 2.8...e-02, ...e-08]]) >>> clf.score(X, y) 0.97... """ @_deprecate_positional_args def __init__(self, penalty='l2', *, dual=False, tol=1e-4, C=1.0, fit_intercept=True, intercept_scaling=1, class_weight=None, random_state=None, solver='lbfgs', max_iter=100, multi_class='auto', verbose=0, warm_start=False, n_jobs=None, l1_ratio=None): self.penalty = penalty self.dual = dual self.tol = tol self.C = C self.fit_intercept = fit_intercept self.intercept_scaling = intercept_scaling self.class_weight = class_weight self.random_state = random_state self.solver = solver self.max_iter = max_iter self.multi_class = multi_class self.verbose = verbose self.warm_start = warm_start self.n_jobs = n_jobs self.l1_ratio = l1_ratio def fit(self, X, y, sample_weight=None): """ Fit the model according to the given training data. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Training vector, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) Target vector relative to X. sample_weight : array-like of shape (n_samples,) default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. .. versionadded:: 0.17 *sample_weight* support to LogisticRegression. Returns ------- self Fitted estimator. Notes ----- The SAGA solver supports both float64 and float32 bit arrays. """ solver = _check_solver(self.solver, self.penalty, self.dual) if not isinstance(self.C, numbers.Number) or self.C < 0: raise ValueError("Penalty term must be positive; got (C=%r)" % self.C) if self.penalty == 'elasticnet': if (not isinstance(self.l1_ratio, numbers.Number) or self.l1_ratio < 0 or self.l1_ratio > 1): raise ValueError("l1_ratio must be between 0 and 1;" " got (l1_ratio=%r)" % self.l1_ratio) elif self.l1_ratio is not None: warnings.warn("l1_ratio parameter is only used when penalty is " "'elasticnet'. Got " "(penalty={})".format(self.penalty)) if self.penalty == 'none': if self.C != 1.0: # default values warnings.warn( "Setting penalty='none' will ignore the C and l1_ratio " "parameters" ) # Note that check for l1_ratio is done right above C_ = np.inf penalty = 'l2' else: C_ = self.C penalty = self.penalty if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0: raise ValueError("Maximum number of iteration must be positive;" " got (max_iter=%r)" % self.max_iter) if not isinstance(self.tol, numbers.Number) or self.tol < 0: raise ValueError("Tolerance for stopping criteria must be " "positive; got (tol=%r)" % self.tol) if solver == 'lbfgs': _dtype = np.float64 else: _dtype = [np.float64, np.float32] X, y = self._validate_data(X, y, accept_sparse='csr', dtype=_dtype, order="C", accept_large_sparse=solver != 'liblinear') check_classification_targets(y) self.classes_ = np.unique(y) multi_class = _check_multi_class(self.multi_class, solver, len(self.classes_)) if solver == 'liblinear': if effective_n_jobs(self.n_jobs) != 1: warnings.warn("'n_jobs' > 1 does not have any effect when" " 'solver' is set to 'liblinear'. Got 'n_jobs'" " = {}.".format(effective_n_jobs(self.n_jobs))) self.coef_, self.intercept_, n_iter_ = _fit_liblinear( X, y, self.C, self.fit_intercept, self.intercept_scaling, self.class_weight, self.penalty, self.dual, self.verbose, self.max_iter, self.tol, self.random_state, sample_weight=sample_weight) self.n_iter_ = np.array([n_iter_]) return self if solver in ['sag', 'saga']: max_squared_sum = row_norms(X, squared=True).max() else: max_squared_sum = None n_classes = len(self.classes_) classes_ = self.classes_ if n_classes < 2: raise ValueError("This solver needs samples of at least 2 classes" " in the data, but the data contains only one" " class: %r" % classes_[0]) if len(self.classes_) == 2: n_classes = 1 classes_ = classes_[1:] if self.warm_start: warm_start_coef = getattr(self, 'coef_', None) else: warm_start_coef = None if warm_start_coef is not None and self.fit_intercept: warm_start_coef = np.append(warm_start_coef, self.intercept_[:, np.newaxis], axis=1) self.coef_ = list() self.intercept_ = np.zeros(n_classes) # Hack so that we iterate only once for the multinomial case. if multi_class == 'multinomial': classes_ = [None] warm_start_coef = [warm_start_coef] if warm_start_coef is None: warm_start_coef = [None] * n_classes path_func = delayed(_logistic_regression_path) # The SAG solver releases the GIL so it's more efficient to use # threads for this solver. if solver in ['sag', 'saga']: prefer = 'threads' else: prefer = 'processes' fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose, **_joblib_parallel_args(prefer=prefer))( path_func(X, y, pos_class=class_, Cs=[C_], l1_ratio=self.l1_ratio, fit_intercept=self.fit_intercept, tol=self.tol, verbose=self.verbose, solver=solver, multi_class=multi_class, max_iter=self.max_iter, class_weight=self.class_weight, check_input=False, random_state=self.random_state, coef=warm_start_coef_, penalty=penalty, max_squared_sum=max_squared_sum, sample_weight=sample_weight) for class_, warm_start_coef_ in zip(classes_, warm_start_coef)) fold_coefs_, _, n_iter_ = zip(*fold_coefs_) self.n_iter_ = np.asarray(n_iter_, dtype=np.int32)[:, 0] n_features = X.shape[1] if multi_class == 'multinomial': self.coef_ = fold_coefs_[0][0] else: self.coef_ = np.asarray(fold_coefs_) self.coef_ = self.coef_.reshape(n_classes, n_features + int(self.fit_intercept)) if self.fit_intercept: self.intercept_ = self.coef_[:, -1] self.coef_ = self.coef_[:, :-1] return self def predict_proba(self, X): """ Probability estimates. The returned estimates for all classes are ordered by the label of classes. For a multi_class problem, if multi_class is set to be "multinomial" the softmax function is used to find the predicted probability of each class. Else use a one-vs-rest approach, i.e calculate the probability of each class assuming it to be positive using the logistic function. and normalize these values across all the classes. Parameters ---------- X : array-like of shape (n_samples, n_features) Vector to be scored, where `n_samples` is the number of samples and `n_features` is the number of features. Returns ------- T : array-like of shape (n_samples, n_classes) Returns the probability of the sample for each class in the model, where classes are ordered as they are in ``self.classes_``. """ check_is_fitted(self) ovr = (self.multi_class in ["ovr", "warn"] or (self.multi_class == 'auto' and (self.classes_.size <= 2 or self.solver == 'liblinear'))) if ovr: return super()._predict_proba_lr(X) else: decision = self.decision_function(X) if decision.ndim == 1: # Workaround for multi_class="multinomial" and binary outcomes # which requires softmax prediction with only a 1D decision. decision_2d = np.c_[-decision, decision] else: decision_2d = decision return softmax(decision_2d, copy=False) def predict_log_proba(self, X): """ Predict logarithm of probability estimates. The returned estimates for all classes are ordered by the label of classes. Parameters ---------- X : array-like of shape (n_samples, n_features) Vector to be scored, where `n_samples` is the number of samples and `n_features` is the number of features. Returns ------- T : array-like of shape (n_samples, n_classes) Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in ``self.classes_``. """ return np.log(self.predict_proba(X)) class LogisticRegressionCV(LogisticRegression, BaseEstimator, LinearClassifierMixin): """Logistic Regression CV (aka logit, MaxEnt) classifier. See glossary entry for :term:`cross-validation estimator`. This class implements logistic regression using liblinear, newton-cg, sag of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2 regularization with primal formulation. The liblinear solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty. Elastic-Net penalty is only supported by the saga solver. For the grid of `Cs` values and `l1_ratios` values, the best hyperparameter is selected by the cross-validator :class:`~sklearn.model_selection.StratifiedKFold`, but it can be changed using the :term:`cv` parameter. The 'newton-cg', 'sag', 'saga' and 'lbfgs' solvers can warm-start the coefficients (see :term:`Glossary`). Read more in the :ref:`User Guide `. Parameters ---------- Cs : int or list of floats, default=10 Each of the values in Cs describes the inverse of regularization strength. If Cs is as an int, then a grid of Cs values are chosen in a logarithmic scale between 1e-4 and 1e4. Like in support vector machines, smaller values specify stronger regularization. fit_intercept : bool, default=True Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. cv : int or cross-validation generator, default=None The default cross-validation generator used is Stratified K-Folds. If an integer is provided, then it is the number of folds used. See the module :mod:`sklearn.model_selection` module for the list of possible cross-validation objects. .. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold. dual : bool, default=False Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. penalty : {'l1', 'l2', 'elasticnet'}, default='l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is only supported by the 'saga' solver. scoring : str or callable, default=None A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. For a list of scoring functions that can be used, look at :mod:`sklearn.metrics`. The default scoring option used is 'accuracy'. solver : {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'}, \ default='lbfgs' Algorithm to use in the optimization problem. - For small datasets, 'liblinear' is a good choice, whereas 'sag' and 'saga' are faster for large ones. - For multiclass problems, only 'newton-cg', 'sag', 'saga' and 'lbfgs' handle multinomial loss; 'liblinear' is limited to one-versus-rest schemes. - 'newton-cg', 'lbfgs' and 'sag' only handle L2 penalty, whereas 'liblinear' and 'saga' handle L1 penalty. - 'liblinear' might be slower in LogisticRegressionCV because it does not handle warm-starting. Note that 'sag' and 'saga' fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing. .. versionadded:: 0.17 Stochastic Average Gradient descent solver. .. versionadded:: 0.19 SAGA solver. tol : float, default=1e-4 Tolerance for stopping criteria. max_iter : int, default=100 Maximum number of iterations of the optimization algorithm. class_weight : dict or 'balanced', default=None Weights associated with classes in the form ``{class_label: weight}``. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified. .. versionadded:: 0.17 class_weight == 'balanced' n_jobs : int, default=None Number of CPU cores used during the cross-validation loop. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. verbose : int, default=0 For the 'liblinear', 'sag' and 'lbfgs' solvers set verbose to any positive number for verbosity. refit : bool, default=True If set to True, the scores are averaged across all folds, and the coefs and the C that corresponds to the best score is taken, and a final refit is done using these parameters. Otherwise the coefs, intercepts and C that correspond to the best scores across folds are averaged. intercept_scaling : float, default=1 Useful only when the solver 'liblinear' is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a "synthetic" feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes ``intercept_scaling * synthetic_feature_weight``. Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. multi_class : {'auto, 'ovr', 'multinomial'}, default='auto' If the option chosen is 'ovr', then a binary problem is fit for each label. For 'multinomial' the loss minimised is the multinomial loss fit across the entire probability distribution, *even when the data is binary*. 'multinomial' is unavailable when solver='liblinear'. 'auto' selects 'ovr' if the data is binary, or if solver='liblinear', and otherwise selects 'multinomial'. .. versionadded:: 0.18 Stochastic Average Gradient descent solver for 'multinomial' case. .. versionchanged:: 0.22 Default changed from 'ovr' to 'auto' in 0.22. random_state : int, RandomState instance, default=None Used when `solver='sag'`, 'saga' or 'liblinear' to shuffle the data. Note that this only applies to the solver and not the cross-validation generator. See :term:`Glossary ` for details. l1_ratios : list of float, default=None The list of Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only used if ``penalty='elasticnet'``. A value of 0 is equivalent to using ``penalty='l2'``, while 1 is equivalent to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination of L1 and L2. Attributes ---------- classes_ : ndarray of shape (n_classes, ) A list of class labels known to the classifier. coef_ : ndarray of shape (1, n_features) or (n_classes, n_features) Coefficient of the features in the decision function. `coef_` is of shape (1, n_features) when the given problem is binary. intercept_ : ndarray of shape (1,) or (n_classes,) Intercept (a.k.a. bias) added to the decision function. If `fit_intercept` is set to False, the intercept is set to zero. `intercept_` is of shape(1,) when the problem is binary. Cs_ : ndarray of shape (n_cs) Array of C i.e. inverse of regularization parameter values used for cross-validation. l1_ratios_ : ndarray of shape (n_l1_ratios) Array of l1_ratios used for cross-validation. If no l1_ratio is used (i.e. penalty is not 'elasticnet'), this is set to ``[None]`` coefs_paths_ : ndarray of shape (n_folds, n_cs, n_features) or \ (n_folds, n_cs, n_features + 1) dict with classes as the keys, and the path of coefficients obtained during cross-validating across each fold and then across each Cs after doing an OvR for the corresponding class as values. If the 'multi_class' option is set to 'multinomial', then the coefs_paths are the coefficients corresponding to each class. Each dict value has shape ``(n_folds, n_cs, n_features)`` or ``(n_folds, n_cs, n_features + 1)`` depending on whether the intercept is fit or not. If ``penalty='elasticnet'``, the shape is ``(n_folds, n_cs, n_l1_ratios_, n_features)`` or ``(n_folds, n_cs, n_l1_ratios_, n_features + 1)``. scores_ : dict dict with classes as the keys, and the values as the grid of scores obtained during cross-validating each fold, after doing an OvR for the corresponding class. If the 'multi_class' option given is 'multinomial' then the same scores are repeated across all classes, since this is the multinomial class. Each dict value has shape ``(n_folds, n_cs`` or ``(n_folds, n_cs, n_l1_ratios)`` if ``penalty='elasticnet'``. C_ : ndarray of shape (n_classes,) or (n_classes - 1,) Array of C that maps to the best scores across every class. If refit is set to False, then for each class, the best C is the average of the C's that correspond to the best scores for each fold. `C_` is of shape(n_classes,) when the problem is binary. l1_ratio_ : ndarray of shape (n_classes,) or (n_classes - 1,) Array of l1_ratio that maps to the best scores across every class. If refit is set to False, then for each class, the best l1_ratio is the average of the l1_ratio's that correspond to the best scores for each fold. `l1_ratio_` is of shape(n_classes,) when the problem is binary. n_iter_ : ndarray of shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs) Actual number of iterations for all classes, folds and Cs. In the binary or multinomial cases, the first dimension is equal to 1. If ``penalty='elasticnet'``, the shape is ``(n_classes, n_folds, n_cs, n_l1_ratios)`` or ``(1, n_folds, n_cs, n_l1_ratios)``. Examples -------- >>> from sklearn.datasets import load_iris >>> from sklearn.linear_model import LogisticRegressionCV >>> X, y = load_iris(return_X_y=True) >>> clf = LogisticRegressionCV(cv=5, random_state=0).fit(X, y) >>> clf.predict(X[:2, :]) array([0, 0]) >>> clf.predict_proba(X[:2, :]).shape (2, 3) >>> clf.score(X, y) 0.98... See also -------- LogisticRegression """ @_deprecate_positional_args def __init__(self, *, Cs=10, fit_intercept=True, cv=None, dual=False, penalty='l2', scoring=None, solver='lbfgs', tol=1e-4, max_iter=100, class_weight=None, n_jobs=None, verbose=0, refit=True, intercept_scaling=1., multi_class='auto', random_state=None, l1_ratios=None): self.Cs = Cs self.fit_intercept = fit_intercept self.cv = cv self.dual = dual self.penalty = penalty self.scoring = scoring self.tol = tol self.max_iter = max_iter self.class_weight = class_weight self.n_jobs = n_jobs self.verbose = verbose self.solver = solver self.refit = refit self.intercept_scaling = intercept_scaling self.multi_class = multi_class self.random_state = random_state self.l1_ratios = l1_ratios def fit(self, X, y, sample_weight=None): """Fit the model according to the given training data. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Training vector, where n_samples is the number of samples and n_features is the number of features. y : array-like of shape (n_samples,) Target vector relative to X. sample_weight : array-like of shape (n_samples,) default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- self : object """ solver = _check_solver(self.solver, self.penalty, self.dual) if not isinstance(self.max_iter, numbers.Number) or self.max_iter < 0: raise ValueError("Maximum number of iteration must be positive;" " got (max_iter=%r)" % self.max_iter) if not isinstance(self.tol, numbers.Number) or self.tol < 0: raise ValueError("Tolerance for stopping criteria must be " "positive; got (tol=%r)" % self.tol) if self.penalty == 'elasticnet': if self.l1_ratios is None or len(self.l1_ratios) == 0 or any( (not isinstance(l1_ratio, numbers.Number) or l1_ratio < 0 or l1_ratio > 1) for l1_ratio in self.l1_ratios): raise ValueError("l1_ratios must be a list of numbers between " "0 and 1; got (l1_ratios=%r)" % self.l1_ratios) l1_ratios_ = self.l1_ratios else: if self.l1_ratios is not None: warnings.warn("l1_ratios parameter is only used when penalty " "is 'elasticnet'. Got (penalty={})".format( self.penalty)) l1_ratios_ = [None] if self.penalty == 'none': raise ValueError( "penalty='none' is not useful and not supported by " "LogisticRegressionCV." ) X, y = self._validate_data(X, y, accept_sparse='csr', dtype=np.float64, order="C", accept_large_sparse=solver != 'liblinear') check_classification_targets(y) class_weight = self.class_weight # Encode for string labels label_encoder = LabelEncoder().fit(y) y = label_encoder.transform(y) if isinstance(class_weight, dict): class_weight = {label_encoder.transform([cls])[0]: v for cls, v in class_weight.items()} # The original class labels classes = self.classes_ = label_encoder.classes_ encoded_labels = label_encoder.transform(label_encoder.classes_) multi_class = _check_multi_class(self.multi_class, solver, len(classes)) if solver in ['sag', 'saga']: max_squared_sum = row_norms(X, squared=True).max() else: max_squared_sum = None # init cross-validation generator cv = check_cv(self.cv, y, classifier=True) folds = list(cv.split(X, y)) # Use the label encoded classes n_classes = len(encoded_labels) if n_classes < 2: raise ValueError("This solver needs samples of at least 2 classes" " in the data, but the data contains only one" " class: %r" % classes[0]) if n_classes == 2: # OvR in case of binary problems is as good as fitting # the higher label n_classes = 1 encoded_labels = encoded_labels[1:] classes = classes[1:] # We need this hack to iterate only once over labels, in the case of # multi_class = multinomial, without changing the value of the labels. if multi_class == 'multinomial': iter_encoded_labels = iter_classes = [None] else: iter_encoded_labels = encoded_labels iter_classes = classes # compute the class weights for the entire dataset y if class_weight == "balanced": class_weight = compute_class_weight( class_weight, classes=np.arange(len(self.classes_)), y=y) class_weight = dict(enumerate(class_weight)) path_func = delayed(_log_reg_scoring_path) # The SAG solver releases the GIL so it's more efficient to use # threads for this solver. if self.solver in ['sag', 'saga']: prefer = 'threads' else: prefer = 'processes' fold_coefs_ = Parallel(n_jobs=self.n_jobs, verbose=self.verbose, **_joblib_parallel_args(prefer=prefer))( path_func(X, y, train, test, pos_class=label, Cs=self.Cs, fit_intercept=self.fit_intercept, penalty=self.penalty, dual=self.dual, solver=solver, tol=self.tol, max_iter=self.max_iter, verbose=self.verbose, class_weight=class_weight, scoring=self.scoring, multi_class=multi_class, intercept_scaling=self.intercept_scaling, random_state=self.random_state, max_squared_sum=max_squared_sum, sample_weight=sample_weight, l1_ratio=l1_ratio ) for label in iter_encoded_labels for train, test in folds for l1_ratio in l1_ratios_) # _log_reg_scoring_path will output different shapes depending on the # multi_class param, so we need to reshape the outputs accordingly. # Cs is of shape (n_classes . n_folds . n_l1_ratios, n_Cs) and all the # rows are equal, so we just take the first one. # After reshaping, # - scores is of shape (n_classes, n_folds, n_Cs . n_l1_ratios) # - coefs_paths is of shape # (n_classes, n_folds, n_Cs . n_l1_ratios, n_features) # - n_iter is of shape # (n_classes, n_folds, n_Cs . n_l1_ratios) or # (1, n_folds, n_Cs . n_l1_ratios) coefs_paths, Cs, scores, n_iter_ = zip(*fold_coefs_) self.Cs_ = Cs[0] if multi_class == 'multinomial': coefs_paths = np.reshape( coefs_paths, (len(folds), len(l1_ratios_) * len(self.Cs_), n_classes, -1) ) # equiv to coefs_paths = np.moveaxis(coefs_paths, (0, 1, 2, 3), # (1, 2, 0, 3)) coefs_paths = np.swapaxes(coefs_paths, 0, 1) coefs_paths = np.swapaxes(coefs_paths, 0, 2) self.n_iter_ = np.reshape( n_iter_, (1, len(folds), len(self.Cs_) * len(l1_ratios_)) ) # repeat same scores across all classes scores = np.tile(scores, (n_classes, 1, 1)) else: coefs_paths = np.reshape( coefs_paths, (n_classes, len(folds), len(self.Cs_) * len(l1_ratios_), -1) ) self.n_iter_ = np.reshape( n_iter_, (n_classes, len(folds), len(self.Cs_) * len(l1_ratios_)) ) scores = np.reshape(scores, (n_classes, len(folds), -1)) self.scores_ = dict(zip(classes, scores)) self.coefs_paths_ = dict(zip(classes, coefs_paths)) self.C_ = list() self.l1_ratio_ = list() self.coef_ = np.empty((n_classes, X.shape[1])) self.intercept_ = np.zeros(n_classes) for index, (cls, encoded_label) in enumerate( zip(iter_classes, iter_encoded_labels)): if multi_class == 'ovr': scores = self.scores_[cls] coefs_paths = self.coefs_paths_[cls] else: # For multinomial, all scores are the same across classes scores = scores[0] # coefs_paths will keep its original shape because # logistic_regression_path expects it this way if self.refit: # best_index is between 0 and (n_Cs . n_l1_ratios - 1) # for example, with n_cs=2 and n_l1_ratios=3 # the layout of scores is # [c1, c2, c1, c2, c1, c2] # l1_1 , l1_2 , l1_3 best_index = scores.sum(axis=0).argmax() best_index_C = best_index % len(self.Cs_) C_ = self.Cs_[best_index_C] self.C_.append(C_) best_index_l1 = best_index // len(self.Cs_) l1_ratio_ = l1_ratios_[best_index_l1] self.l1_ratio_.append(l1_ratio_) if multi_class == 'multinomial': coef_init = np.mean(coefs_paths[:, :, best_index, :], axis=1) else: coef_init = np.mean(coefs_paths[:, best_index, :], axis=0) # Note that y is label encoded and hence pos_class must be # the encoded label / None (for 'multinomial') w, _, _ = _logistic_regression_path( X, y, pos_class=encoded_label, Cs=[C_], solver=solver, fit_intercept=self.fit_intercept, coef=coef_init, max_iter=self.max_iter, tol=self.tol, penalty=self.penalty, class_weight=class_weight, multi_class=multi_class, verbose=max(0, self.verbose - 1), random_state=self.random_state, check_input=False, max_squared_sum=max_squared_sum, sample_weight=sample_weight, l1_ratio=l1_ratio_) w = w[0] else: # Take the best scores across every fold and the average of # all coefficients corresponding to the best scores. best_indices = np.argmax(scores, axis=1) if multi_class == 'ovr': w = np.mean([coefs_paths[i, best_indices[i], :] for i in range(len(folds))], axis=0) else: w = np.mean([coefs_paths[:, i, best_indices[i], :] for i in range(len(folds))], axis=0) best_indices_C = best_indices % len(self.Cs_) self.C_.append(np.mean(self.Cs_[best_indices_C])) if self.penalty == 'elasticnet': best_indices_l1 = best_indices // len(self.Cs_) self.l1_ratio_.append(np.mean(l1_ratios_[best_indices_l1])) else: self.l1_ratio_.append(None) if multi_class == 'multinomial': self.C_ = np.tile(self.C_, n_classes) self.l1_ratio_ = np.tile(self.l1_ratio_, n_classes) self.coef_ = w[:, :X.shape[1]] if self.fit_intercept: self.intercept_ = w[:, -1] else: self.coef_[index] = w[: X.shape[1]] if self.fit_intercept: self.intercept_[index] = w[-1] self.C_ = np.asarray(self.C_) self.l1_ratio_ = np.asarray(self.l1_ratio_) self.l1_ratios_ = np.asarray(l1_ratios_) # if elasticnet was used, add the l1_ratios dimension to some # attributes if self.l1_ratios is not None: # with n_cs=2 and n_l1_ratios=3 # the layout of scores is # [c1, c2, c1, c2, c1, c2] # l1_1 , l1_2 , l1_3 # To get a 2d array with the following layout # l1_1, l1_2, l1_3 # c1 [[ . , . , . ], # c2 [ . , . , . ]] # We need to first reshape and then transpose. # The same goes for the other arrays for cls, coefs_path in self.coefs_paths_.items(): self.coefs_paths_[cls] = coefs_path.reshape( (len(folds), self.l1_ratios_.size, self.Cs_.size, -1)) self.coefs_paths_[cls] = np.transpose(self.coefs_paths_[cls], (0, 2, 1, 3)) for cls, score in self.scores_.items(): self.scores_[cls] = score.reshape( (len(folds), self.l1_ratios_.size, self.Cs_.size)) self.scores_[cls] = np.transpose(self.scores_[cls], (0, 2, 1)) self.n_iter_ = self.n_iter_.reshape( (-1, len(folds), self.l1_ratios_.size, self.Cs_.size)) self.n_iter_ = np.transpose(self.n_iter_, (0, 1, 3, 2)) return self def score(self, X, y, sample_weight=None): """Returns the score using the `scoring` option on the given test data and labels. Parameters ---------- X : array-like of shape (n_samples, n_features) Test samples. y : array-like of shape (n_samples,) True labels for X. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- score : float Score of self.predict(X) wrt. y. """ scoring = self.scoring or 'accuracy' scoring = get_scorer(scoring) return scoring(self, X, y, sample_weight=sample_weight)