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='warn', 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 <logistic_regression>`. Parameters ---------- X : array-like or sparse matrix, shape (n_samples, n_features) Input data. y : array-like, shape (n_samples,) or (n_samples, n_targets) Input data, target values. pos_class : int, 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 | array-like, shape (n_cs,) 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 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 Maximum number of iterations for the solver. tol : float 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 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'} Numerical solver to use. coef : array-like, shape (n_features,), default None Initialization value for coefficients of logistic regression. Useless for liblinear solver. class_weight : dict or 'balanced', optional 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 Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. penalty : str, 'l1', 'l2', or 'elasticnet' 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 : str, {'ovr', 'multinomial', 'auto'}, default: 'ovr' 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:: 0.20 Default will change from 'ovr' to 'auto' in 0.22. random_state : int, RandomState instance or None, optional, default None The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Used when ``solver`` == 'sag' or 'liblinear'. 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, shape(n_samples,) optional Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. l1_ratio : float or None, optional (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, 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, 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 if sample_weight is not None: sample_weight = np.array(sample_weight, dtype=X.dtype, order='C') check_consistent_length(y, sample_weight) default_weights = False else: sample_weight = np.ones(X.shape[0], dtype=X.dtype) default_weights = (class_weight is None) daal_ready = use_daal and solver in ['lbfgs', 'newton-cg' ] and not sparse.issparse(X) # 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, 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, mask_classes, y_bin) sample_weight *= class_weight_[le.fit_transform(y_bin)] daal_ready = daal_ready and (default_weights or np.allclose( sample_weight, np.ones_like(sample_weight))) if daal_ready: w0 = np.zeros(n_features + 1, dtype=X.dtype) y_bin[~mask] = 0. else: w0 = np.zeros(n_features + int(fit_intercept), dtype=X.dtype) else: daal_ready = daal_ready and (default_weights or np.allclose( sample_weight, np.ones_like(sample_weight))) if solver not in ['sag', 'saga']: if daal_ready: Y_multi = le.fit_transform(y).astype(X.dtype, copy=False) else: 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) if daal_ready: w0 = np.zeros((classes.size, n_features + 1), order='C', dtype=X.dtype) else: 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)) if daal_ready: w0[-coef.size:] = np.roll( coef, 1, -1) if coef.size != n_features else coef else: 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 daal_ready: w0[:, -coef.shape[1]:] = np.roll( coef, 1, -1) if coef.shape[1] != n_features else coef else: if n_classes == 1: w0[0, :coef.shape[1]] = -coef w0[1, :coef.shape[1]] = coef else: w0[:, :coef.shape[1]] = coef C_daal_multiplier = 1 # commented out because this is Py3 feature #def _map_to_binary_logistic_regression(): # nonlocal C_daal_multiplier # nonlocal w0 # C_daal_multiplier = 2 # w0 *= 2 if multi_class == 'multinomial': # fmin_l_bfgs_b and newton-cg accepts only ravelled parameters. if solver in ['lbfgs', 'newton-cg']: if daal_ready and classes.size == 2: w0_saved = w0 w0 = w0[-1:, :] w0 = w0.ravel() target = Y_multi if solver == 'lbfgs': if daal_ready: if classes.size == 2: # _map_to_binary_logistic_regression() C_daal_multiplier = 2 w0 *= 2 daal_extra_args_func = _daal4py_logistic_loss_extra_args else: daal_extra_args_func = _daal4py_cross_entropy_loss_extra_args func = _daal4py_loss_and_grad else: func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2] elif solver == 'newton-cg': if daal_ready: if classes.size == 2: # _map_to_binary_logistic_regression() C_daal_multiplier = 2 w0 *= 2 daal_extra_args_func = _daal4py_logistic_loss_extra_args else: daal_extra_args_func = _daal4py_cross_entropy_loss_extra_args func = _daal4py_loss_ grad = _daal4py_grad_ hess = _daal4py_grad_hess_ else: func = lambda x, *args: _multinomial_loss(x, *args)[0] grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1] hess = _multinomial_grad_hess warm_start_sag = {'coef': w0.T} else: target = y_bin if solver == 'lbfgs': if daal_ready: func = _daal4py_loss_and_grad daal_extra_args_func = _daal4py_logistic_loss_extra_args else: func = _logistic_loss_and_grad elif solver == 'newton-cg': if daal_ready: daal_extra_args_func = _daal4py_logistic_loss_extra_args func = _daal4py_loss_ grad = _daal4py_grad_ hess = _daal4py_grad_hess_ else: func = _logistic_loss grad = lambda x, *args: _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': if daal_ready: extra_args = daal_extra_args_func(classes.size, w0, X, target, 0., 0.5 / C / C_daal_multiplier, fit_intercept, value=True, gradient=True, hessian=False) else: extra_args = (X, target, 1. / C, sample_weight) iprint = [-1, 50, 1, 100, 101][np.searchsorted(np.array([0, 1, 2, 3]), verbose)] w0, loss, info = optimize.fmin_l_bfgs_b(func, w0, fprime=None, args=extra_args, iprint=iprint, pgtol=tol, maxiter=max_iter) if daal_ready and C_daal_multiplier == 2: w0 *= 0.5 if info["warnflag"] == 1: warnings.warn( "lbfgs failed to converge. Increase the number " "of iterations.", ConvergenceWarning) # In scipy <= 1.0.0, nit may exceed maxiter. # See https://github.com/scipy/scipy/issues/7854. n_iter_i = min(info['nit'], max_iter) elif solver == 'newton-cg': if daal_ready: def make_ncg_funcs(f, value=False, gradient=False, hessian=False): daal_penaltyL2 = 0.5 / C / C_daal_multiplier _obj_, X_, y_, n_samples = daal_extra_args_func( classes.size, w0, X, target, 0., daal_penaltyL2, fit_intercept, value=value, gradient=gradient, hessian=hessian) _func_ = lambda x, *args: f(x, _obj_, *args) return _func_, (X_, y_, n_samples, daal_penaltyL2) loss_func, extra_args = make_ncg_funcs(func, value=True) grad_func, _ = make_ncg_funcs(grad, gradient=True) grad_hess_func, _ = make_ncg_funcs(hess, gradient=True) w0, n_iter_i = newton_cg(grad_hess_func, loss_func, grad_func, w0, args=extra_args, maxiter=max_iter, tol=tol) else: 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': if daal_ready: if classes.size == 2: multi_w0 = w0[np.newaxis, :] else: multi_w0 = np.reshape(w0, (classes.size, -1)) else: 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(np.require(multi_w0, requirements='O')) else: coefs.append(np.require(w0, requirements='O')) n_iter[i] = n_iter_i if daal_ready: if fit_intercept: for i, ci in enumerate(coefs): coefs[i] = np.roll(ci, -1, -1) else: for i, ci in enumerate(coefs): coefs[i] = np.delete(ci, 0, axis=-1) return np.array(coefs), np.array(Cs), n_iter
def logistic_regression(X, y, fit_intercept=True, C=1e4, max_iter=100, tol=1e-4, verbose=0, solver='lbfgs', coef=None, class_weight=None, dual=False, penalty='l2', intercept_scaling=1., random_state=None, check_input=True, max_squared_sum=None, sample_weight=None): """Compute a Logistic Regression for possibly soft class labels y Based on logistic_regression_path, but assumes multinomial and removes multiple Cs logic Parameters ---------- X : array-like or sparse matrix, shape (n_samples, n_features) Input data. y : array-like, shape (n_samples,) or (n_samples, n_targets) Input data, target values. C : float regularization parameter that should be used. Default is 1e4. fit_intercept : bool 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 Maximum number of iterations for the solver. tol : float 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 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'} Numerical solver to use. coef : array-like, shape (n_features,), default None Initialization value for coefficients of logistic regression. Useless for liblinear solver. class_weight : dict or 'balanced', optional 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 Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. penalty : str, 'l1' or 'l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. 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. random_state : int, RandomState instance or None, optional, default None The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Used when ``solver`` == 'sag' or 'liblinear'. 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, shape(n_samples,) optional Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- coef : ndarray, shape (n_classes, n_features) or (n_classes, 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. Notes ----- You might get slightly different results with the solver liblinear than with the others since this uses LIBLINEAR which penalizes the intercept. """ 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 random_state = check_random_state(random_state) if len(y.shape) == 1: le = LabelBinarizer() y = le.fit_transform(y).astype(X.dtype, copy=False) # If sample weights exist, convert them to array (support for lists) # and check length # Otherwise set them to 1 for all examples if sample_weight is not None: sample_weight = np.array(sample_weight, dtype=X.dtype, order='C') check_consistent_length(y, sample_weight) else: sample_weight = np.ones(X.shape[0], 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. class_weight_ = compute_class_weight(class_weight, y) sample_weight *= class_weight_ Y_multi = y nclasses = Y_multi.shape[1] w0 = np.zeros((nclasses, 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 # For binary problems coef.shape[0] should be 1, otherwise it # should be nclasses. if nclasses == 2: nclasses = 1 if (coef.shape[0] != nclasses 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], nclasses, n_features, nclasses, n_features + 1)) if nclasses == 1: w0[0, :coef.shape[1]] = -coef w0[1, :coef.shape[1]] = coef else: w0[:, :coef.shape[1]] = coef # fmin_l_bfgs_b and newton-cg accepts only ravelled parameters. if solver in ['lbfgs', 'newton-cg']: w0 = w0.ravel() target = Y_multi warm_start_sag = {'coef': w0.T} if solver == 'lbfgs': func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2] iprint = [-1, 50, 1, 100, 101][np.searchsorted(np.array([0, 1, 2, 3]), verbose)] w0, loss, info = optimize.fmin_l_bfgs_b(func, w0, fprime=None, args=(X, target, 1. / C, sample_weight), iprint=iprint, pgtol=tol, maxiter=max_iter) if info["warnflag"] == 1: warnings.warn( "lbfgs failed to converge. Increase the number " "of iterations.", ConvergenceWarning) elif solver == 'newton-cg': func = lambda x, *args: _multinomial_loss(x, *args)[0] grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1] hess = _multinomial_grad_hess 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']: target = target.astype(np.float64) loss = 'multinomial' if penalty == 'l1': alpha = 0. beta = 1. / C else: alpha = 1. / C beta = 0. 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) nclasses = max(2, nclasses) multi_w0 = np.reshape(w0, (nclasses, -1)) if nclasses == 2: multi_w0 = multi_w0[1][np.newaxis, :] coef = multi_w0.copy() return coef
A, b = loader() else: raise NotImplementedError n_samples, n_features = A.shape if not os.path.exists('data'): os.mkdir('data') alpha = 1.0 / n_samples x0 = np.zeros(n_features) for it in range(3): print('Iteration %s' % it) _, _, _, trace_saga_x, trace_saga_time = sag_solver( A, b, sample_weight=None, loss='log', alpha=1., beta=0., max_iter=50, is_saga=True) trace_saga_func = [_logistic_loss(xi, A, b, 1.) for xi in trace_saga_x] np.save('data/saga_trace_time_%s_%s.npy' % (dataset, it), trace_saga_time - trace_saga_time[0]) np.save('data/saga_trace_func_%s_%s.npy' % (dataset, it), trace_saga_func) x, trace_sps_x, trace_sps_time = SPSAGA(A, b, np.zeros(n_features), alpha, 0, max_iter=40, line_search=False) trace_sps_func = [_logistic_loss(xi, A, b, 1.) for xi in trace_sps_x] np.save('data/sps_trace_time_%s_%s.npy' % (dataset, it), trace_sps_time) np.save('data/sps_trace_func_%s_%s.npy' % (dataset, it), trace_sps_func) x, trace_sps_x, trace_sps_time = SPSAGA(A, b, np.zeros(n_features), alpha, 0, max_iter=40, line_search=True) trace_sps_func = [_logistic_loss(xi, A, b, 1.) for xi in trace_sps_x] np.save('data/spsls_trace_time_%s_%s.npy' % (dataset, it), trace_sps_time) np.save('data/spsls_trace_func_%s_%s.npy' % (dataset, it), trace_sps_func)
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, copy=False, class_weight=None, dual=False, penalty='l2', intercept_scaling=1., multi_class='ovr', random_state=None, check_input=True, max_squared_sum=None, sample_weight=None, rho=None, q=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. Read more in the :ref:`User Guide <logistic_regression>`. Parameters ---------- X : array-like or sparse matrix, shape (n_samples, n_features) Input data. y : array-like, shape (n_samples,) Input data, target values. Cs : int | array-like, shape (n_cs,) 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. pos_class : int, 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. fit_intercept : bool 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 Maximum number of iterations for the solver. tol : float 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 For the liblinear and lbfgs solvers set verbose to any positive number for verbosity. solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag'} Numerical solver to use. coef : array-like, shape (n_features,), default None Initialization value for coefficients of logistic regression. Useless for liblinear solver. copy : bool, default False Whether or not to produce a copy of the data. A copy is not required anymore. This parameter is deprecated and will be removed in 0.19. class_weight : dict or 'balanced', optional 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 Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features. penalty : str, 'l1' or 'l2' Used to specify the norm used in the penalization. The 'newton-cg', 'sag' and 'lbfgs' solvers support only l2 penalties. intercept_scaling : float, default 1. This parameter is 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 : str, {'ovr', 'multinomial'} Multiclass option can be either 'ovr' or 'multinomial'. If the option chosen is 'ovr', then a binary problem is fit for each label. Else the loss minimised is the multinomial loss fit across the entire probability distribution. Works only for the 'lbfgs' and 'newton-cg' solvers. random_state : int seed, RandomState instance, or None (default) The seed of the pseudo random number generator to use when shuffling the data. 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, shape(n_samples,) optional Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. Returns ------- coefs : ndarray, 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. n_iter : array, shape (n_cs,) Actual number of iteration for each Cs. Notes ----- You might get slighly different results with the solver liblinear than with the others since this uses LIBLINEAR which penalizes the intercept. """ if copy: warnings.warn("A copy is not required anymore. The 'copy' parameter " "is deprecated and will be removed in 0.19.", DeprecationWarning) if isinstance(Cs, numbers.Integral): Cs = np.logspace(-4, 4, Cs) _check_solver_option(solver, multi_class, penalty, dual) # Preprocessing. if check_input or copy: X = check_array(X, accept_sparse='csr', dtype=np.float64) y = check_array(y, ensure_2d=False, copy=copy, dtype=None) check_consistent_length(X, y) _, n_features = X.shape classes = np.unique(y) random_state = check_random_state(random_state) 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 if sample_weight is not None: sample_weight = np.array(sample_weight, dtype=np.float64, order='C') check_consistent_length(y, sample_weight) else: sample_weight = np.ones(X.shape[0]) # 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': if solver == "liblinear": if classes.size == 2: # Reconstruct the weights with keys 1 and -1 temp = {1: class_weight[pos_class], -1: class_weight[classes[0]]} class_weight = temp.copy() else: raise ValueError("In LogisticRegressionCV the liblinear " "solver cannot handle multiclass with " "class_weight of type dict. Use the lbfgs, " "newton-cg or sag solvers or set " "class_weight='balanced'") else: class_weight_ = compute_class_weight(class_weight, classes, 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)) mask_classes = np.array([-1, 1]) mask = (y == pos_class) y_bin = np.ones(y.shape, dtype=np.float64) y_bin[~mask] = -1. # for compute_class_weight # 'auto' is deprecated and will be removed in 0.19 if class_weight in ("auto", "balanced"): class_weight_ = compute_class_weight(class_weight, mask_classes, y_bin) sample_weight *= class_weight_[le.fit_transform(y_bin)] else: lbin = LabelBinarizer() Y_binarized = lbin.fit_transform(y) if Y_binarized.shape[1] == 1: Y_binarized = np.hstack([1 - Y_binarized, Y_binarized]) w0 = np.zeros((Y_binarized.shape[1], n_features + int(fit_intercept)), order='F') 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_vectors = classes.size if n_vectors == 2: n_vectors = 1 if (coef.shape[0] != n_vectors 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)) w0[:, :coef.shape[1]] = coef if multi_class == 'multinomial': # fmin_l_bfgs_b and newton-cg accepts only ravelled parameters. w0 = w0.ravel() target = Y_binarized if solver == 'lbfgs': func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2] elif solver == 'newton-cg': func = lambda x, *args: _multinomial_loss(x, *args)[0] grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1] hess = _multinomial_grad_hess else: target = y_bin if solver == 'lbfgs': func = lambda *args: _logistic_loss_and_grad(rho=rho, q=q, *args) elif solver == 'newton-cg': func = _logistic_loss grad = lambda x, *args: _logistic_loss_and_grad(x, *args)[1] hess = _logistic_grad_hess coefs = list() warm_start_sag = {'coef': w0} n_iter = np.zeros(len(Cs), dtype=np.int32) for i, C in enumerate(Cs): if solver == 'lbfgs': try: w0, loss, info = optimize.fmin_l_bfgs_b( func, w0, fprime=None, args=(X, target, 1. / C, sample_weight), iprint=(verbose > 0) - 1, pgtol=tol, maxiter=max_iter) except TypeError: # old scipy doesn't have maxiter w0, loss, info = optimize.fmin_l_bfgs_b( func, w0, fprime=None, args=(X, target, 1. / C, sample_weight), iprint=(verbose > 0) - 1, pgtol=tol) if info["warnflag"] == 1 and verbose > 0: warnings.warn("lbfgs failed to converge. Increase the number " "of iterations.") try: n_iter_i = info['nit'] - 1 except: n_iter_i = info['funcalls'] - 1 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, class_weight, penalty, dual, verbose, max_iter, tol, random_state) if fit_intercept: w0 = np.concatenate([coef_.ravel(), intercept_]) else: w0 = coef_.ravel() elif solver == 'sag': w0, n_iter_i, warm_start_sag = sag_solver( X, target, sample_weight, 'log', 1. / C, max_iter, tol, verbose, random_state, False, max_squared_sum, warm_start_sag) else: raise ValueError("solver must be one of {'liblinear', 'lbfgs', " "'newton-cg', 'sag'}, got '%s' instead" % solver) if multi_class == 'multinomial': multi_w0 = np.reshape(w0, (classes.size, -1)) if classes.size == 2: multi_w0 = multi_w0[1][np.newaxis, :] coefs.append(multi_w0) else: coefs.append(w0.copy()) n_iter[i] = n_iter_i return coefs, np.array(Cs), n_iter