o \i @sdZddlZddlmZddlZddlmZddlm Z m Z m Z m Z m Z ddlmZddlmZmZmZdd lmZdd lmZmZmZmZmZgd Z dQd dZ dRddZedgdgddgeddhdgddddddddZedgdgddgeeddddgeddhdgdddddddd d!Z edgdgddgeddhdgddddddd"d#Z!edgdgddgeddhdgddddddd$d%Z"edgdgddgeddhdgddddddd&d'Z#edgdgddgeddhdgddddddd(d)Z$edgdgddgeddhdgddddddd*d+Z%edgdgeddhdgddgd,ddddd-d.d/Z&d0d1Z'edgdgddgehd2dgd3gd4dddddd5d6d7Z(edgdgddgehd2ddgd3gd4dddddd5d8d9Z)edgdgd:ddd;d<Z*d=d>Z+edgdgddgeeddd?deeddd@dgdAdddddBdCdDZ,edgdgddgdEddddFdGdHZ-edgdgddgdEddddFdIdJZ.edgdgddgeeddd?deeddd@dgdAdddddBdKdLZ/edgdgddgeeddddgeddhdgddddddddMdNZ0edgdgddgeddhdgdddddddOdPZ1dS)SzMetrics to assess performance on regression task. Functions named as ``*_score`` return a scalar value to maximize: the higher the better. Function named as ``*_error`` or ``*_loss`` return a scalar value to minimize: the lower the better. N)Real)UndefinedMetricWarning)_average_find_matching_floating_dtype get_namespaceget_namespace_and_devicesize)_xlogy)Interval StrOptionsvalidate_params)_weighted_percentile)_check_sample_weight _num_samples check_arraycheck_consistent_length column_or_1d) max_errormean_absolute_errormean_squared_errormean_squared_log_errormedian_absolute_errormean_absolute_percentage_errormean_pinball_lossr2_scoreroot_mean_squared_log_errorroot_mean_squared_errorexplained_variance_scoremean_tweedie_deviancemean_poisson_deviancemean_gamma_devianced2_tweedie_scored2_pinball_scored2_absolute_error_scorenumericc CsLt||||d\}}t|||t|d|d}t|d|d}|dur)t|||d}|jdkr4||d}|jdkr?||d}|jd|jdkrWtd|jd|jd|jd}d }t |t rp||vrotd ||n'|durt|dd }|dkrtd ||jd krtd|jd d|d|dkrdnd} | ||||fS)aCheck that y_true, y_pred and sample_weight belong to the same regression task. To reduce redundancy when calling `_find_matching_floating_dtype`, please use `_check_reg_targets_with_floating_dtype` instead. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,) or None Sample weights. multioutput : array-like or string in ['raw_values', uniform_average', 'variance_weighted'] or None None is accepted due to backward compatibility of r2_score(). dtype : str or list, default="numeric" the dtype argument passed to check_array. xp : module, default=None Precomputed array namespace module. When passed, typically from a caller that has already performed inspection of its own inputs, skips array namespace inspection. Returns ------- type_true : one of {'continuous', continuous-multioutput'} The type of the true target data, as output by 'utils.multiclass.type_of_target'. y_true : array-like of shape (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,) or None Sample weights. multioutput : array-like of shape (n_outputs) or string in ['raw_values', uniform_average', 'variance_weighted'] or None Custom output weights if ``multioutput`` is array-like or just the corresponding argument if ``multioutput`` is a correct keyword. xpF) ensure_2ddtypeN)r))r*z`. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or array of floats If multioutput is 'raw_values', then mean absolute error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. MAE output is non-negative floating point. The best value is 0.0. Examples -------- >>> from sklearn.metrics import mean_absolute_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> mean_absolute_error(y_true, y_pred) 0.5 >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> mean_absolute_error(y_true, y_pred) 0.75 >>> mean_absolute_error(y_true, y_pred, multioutput='raw_values') array([0.5, 1. ]) >>> mean_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.85... r&r)weightsaxisr'r,r-NrH)rrDrabsr6r7float)r8r9r:r;r'r< output_errorsrr@r@rArsA    rr*both)closed)r8r9r:alphar;?r:rPr;c Cst||||\}}t|||||d\}}}}}||}||dk|j}|||d|d||} t| |dd} t|trF|dkrF| St|trQ|dkrQd}tt| |dS) aPinball loss for quantile regression. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. alpha : float, slope of the pinball loss, default=0.5, This loss is equivalent to :ref:`mean_absolute_error` when `alpha=0.5`, `alpha=0.95` is minimized by estimators of the 95th percentile. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats If multioutput is 'raw_values', then mean absolute error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. The pinball loss output is a non-negative floating point. The best value is 0.0. Examples -------- >>> from sklearn.metrics import mean_pinball_loss >>> y_true = [1, 2, 3] >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.1) 0.03... >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.1) 0.3... >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.9) 0.3... >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.9) 0.03... >>> mean_pinball_loss(y_true, y_true, alpha=0.1) 0.0 >>> mean_pinball_loss(y_true, y_true, alpha=0.9) 0.0 r&rr*rHrIr,r-NrJ)rrDastyper)rr6r7rL) r8r9r:rPr;r'r<diffsignlossrMr@r@rAr5sG   rc Cst||||\}}}t|||||d\}}}}}|j||jj|j|d}||}||||||} t | |dd} t |t rP|dkrJ| S|dkrPd}t | |d} t | S) a Mean absolute percentage error (MAPE) regression loss. Note that we are not using the common "percentage" definition: the percentage in the range [0, 100] is converted to a relative value in the range [0, 1] by dividing by 100. Thus, an error of 200% corresponds to a relative error of 2. Read more in the :ref:`User Guide `. .. versionadded:: 0.24 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like Defines aggregating of multiple output values. Array-like value defines weights used to average errors. If input is list then the shape must be (n_outputs,). 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats If multioutput is 'raw_values', then mean absolute percentage error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. MAPE output is non-negative floating point. The best value is 0.0. But note that bad predictions can lead to arbitrarily large MAPE values, especially if some `y_true` values are very close to zero. Note that we return a large value instead of `inf` when `y_true` is zero. Examples -------- >>> from sklearn.metrics import mean_absolute_percentage_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> mean_absolute_percentage_error(y_true, y_pred) 0.3273... >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> mean_absolute_percentage_error(y_true, y_pred) 0.5515... >>> mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.6198... >>> # the value when some element of the y_true is zero is arbitrarily high because >>> # of the division by epsilon >>> y_true = [1., 0., 2.4, 7.] >>> y_pred = [1.2, 0.1, 2.4, 8.] >>> mean_absolute_percentage_error(y_true, y_pred) 112589990684262.48 r&)r)devicerrSr,r-NrJ) rrDasarrayfinfofloat64epsr)rKmaximumrr6r7rL) r8r9r:r;r'r<device_epsilon y_true_absmaperMrr@r@rArs$M      rcCszt||||\}}t|||||d\}}}}}t||dd|d}t|tr3|dkr-|S|dkr3d}t||d}t|S) aZMean squared error regression loss. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or array of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import mean_squared_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> mean_squared_error(y_true, y_pred) 0.375 >>> y_true = [[0.5, 1],[-1, 1],[7, -6]] >>> y_pred = [[0, 2],[-1, 2],[8, -5]] >>> mean_squared_error(y_true, y_pred) 0.708... >>> mean_squared_error(y_true, y_pred, multioutput='raw_values') array([0.41666667, 1. ]) >>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.825... r&rr)rIrHr,r-NrJ)rrDrr6r7rL)r8r9r:r;r'r<rMrr@r@rArs@    rcCs^t||||\}}|t|||dd}t|tr%|dkr|S|dkr%d}t||d}t|S)aRoot mean squared error regression loss. Read more in the :ref:`User Guide `. .. versionadded:: 1.4 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import root_mean_squared_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> root_mean_squared_error(y_true, y_pred) 0.612... >>> y_true = [[0.5, 1],[-1, 1],[7, -6]] >>> y_pred = [[0, 2],[-1, 2],[8, -5]] >>> root_mean_squared_error(y_true, y_pred) 0.822... r,rGr-NrJ)rsqrtrr6r7rrL)r8r9r:r;r'r<rMrr@r@rAr[s;  rcCjt||\}}t|||||d\}}}}}||dks#||dkr'tdt||||||dS)aMean squared logarithmic error regression loss. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors when the input is of multioutput format. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import mean_squared_log_error >>> y_true = [3, 5, 2.5, 7] >>> y_pred = [2.5, 5, 4, 8] >>> mean_squared_log_error(y_true, y_pred) 0.039... >>> y_true = [[0.5, 1], [1, 2], [7, 6]] >>> y_pred = [[0.5, 2], [1, 2.5], [8, 8]] >>> mean_squared_log_error(y_true, y_pred) 0.044... >>> mean_squared_log_error(y_true, y_pred, multioutput='raw_values') array([0.00462428, 0.08377444]) >>> mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.060... r&r+zcMean Squared Logarithmic Error cannot be used when targets contain values less than or equal to -1.rG)rrDanyr4rlog1pr8r9r:r;r'r<r@r@rArsB  rcCrc)aoRoot mean squared logarithmic error regression loss. Read more in the :ref:`User Guide `. .. versionadded:: 1.4 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors when the input is of multioutput format. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import root_mean_squared_log_error >>> y_true = [3, 5, 2.5, 7] >>> y_pred = [2.5, 5, 4, 8] >>> root_mean_squared_log_error(y_true, y_pred) 0.199... r&r+zhRoot Mean Squared Logarithmic Error cannot be used when targets contain values less than or equal to -1.rG)rrDrdr4rrerfr@r@rArs8  r)r8r9r;r:)r;r:cCst||||\}}}}}|durtjt||dd}n tt|||d}t|tr9|dkr3|S|dkr9d}ttj||dS)a=Median absolute error regression loss. Median absolute error output is non-negative floating point. The best value is 0.0. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. sample_weight : array-like of shape (n_samples,), default=None Sample weights. .. versionadded:: 0.24 Returns ------- loss : float or ndarray of floats If multioutput is 'raw_values', then mean absolute error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. Examples -------- >>> from sklearn.metrics import median_absolute_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> median_absolute_error(y_true, y_pred) 0.5 >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> median_absolute_error(y_true, y_pred) 0.75 >>> median_absolute_error(y_true, y_pred, multioutput='raw_values') array([0.5, 1. ]) >>> median_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.85 NrrIr:r,r-rJ) rBnpmedianrKrr6r7rLaverage)r8r9r;r:r<rMr@r@rArUsA rcCs|j}|dk}|sd||} n$|dk} |j|g||d} || @} d|| || | | <d| | |@<t|trT|dkr?| S|dkrFd} n|dkrS|} ||sSd} n|} t| | d } t| dkrft| S| S) zCCommon part used by explained variance score and :math:`R^2` score.rr*)rXr)r,r-Nr.rJ)r)onesr6r7rdrr rL) numerator denominatorr=r; force_finiter'rXr)nonzero_denominator output_scoresnonzero_numerator valid_score avg_weightsresultr@r@rA_assemble_r2_explained_variances4    rw>r,r-r.boolean)r8r9r:r;rp)r:r;rpc Cst||||\}}}t|||||d\}}}}}t|||dd}t|||d|dd} t||dd} t|| d|dd} t| | |jd||||dS)a Explained variance regression score function. Best possible score is 1.0, lower values are worse. In the particular case when ``y_true`` is constant, the explained variance score is not finite: it is either ``NaN`` (perfect predictions) or ``-Inf`` (imperfect predictions). To prevent such non-finite numbers to pollute higher-level experiments such as a grid search cross-validation, by default these cases are replaced with 1.0 (perfect predictions) or 0.0 (imperfect predictions) respectively. If ``force_finite`` is set to ``False``, this score falls back on the original :math:`R^2` definition. .. note:: The Explained Variance score is similar to the :func:`R^2 score `, with the notable difference that it does not account for systematic offsets in the prediction. Most often the :func:`R^2 score ` should be preferred. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average', 'variance_weighted'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output scores. Array-like value defines weights used to average scores. 'raw_values' : Returns a full set of scores in case of multioutput input. 'uniform_average' : Scores of all outputs are averaged with uniform weight. 'variance_weighted' : Scores of all outputs are averaged, weighted by the variances of each individual output. force_finite : bool, default=True Flag indicating if ``NaN`` and ``-Inf`` scores resulting from constant data should be replaced with real numbers (``1.0`` if prediction is perfect, ``0.0`` otherwise). Default is ``True``, a convenient setting for hyperparameters' search procedures (e.g. grid search cross-validation). .. versionadded:: 1.1 Returns ------- score : float or ndarray of floats The explained variance or ndarray if 'multioutput' is 'raw_values'. See Also -------- r2_score : Similar metric, but accounting for systematic offsets in prediction. Notes ----- This is not a symmetric function. Examples -------- >>> from sklearn.metrics import explained_variance_score >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> explained_variance_score(y_true, y_pred) 0.957... >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> explained_variance_score(y_true, y_pred, multioutput='uniform_average') 0.983... >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2] >>> explained_variance_score(y_true, y_pred) 1.0 >>> explained_variance_score(y_true, y_pred, force_finite=False) nan >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2 + 1e-8] >>> explained_variance_score(y_true, y_pred) 0.0 >>> explained_variance_score(y_true, y_pred, force_finite=False) -inf r&rrSrr*rnror=r;rpr'rX)rrDrrwr3) r8r9r:r;rpr'r<rX y_diff_avgrn y_true_avgror@r@rArs(t  rc Cst||||\}}}t|||||d\}}}}}t|dkr*d}t|ttdS|dur;t|}|dddf} nd} |j| ||ddd} |j| |t |d||d ddd} t | | |j d ||||d S) aX:math:`R^2` (coefficient of determination) regression score function. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). In the general case when the true y is non-constant, a constant model that always predicts the average y disregarding the input features would get a :math:`R^2` score of 0.0. In the particular case when ``y_true`` is constant, the :math:`R^2` score is not finite: it is either ``NaN`` (perfect predictions) or ``-Inf`` (imperfect predictions). To prevent such non-finite numbers to pollute higher-level experiments such as a grid search cross-validation, by default these cases are replaced with 1.0 (perfect predictions) or 0.0 (imperfect predictions) respectively. You can set ``force_finite`` to ``False`` to prevent this fix from happening. Note: when the prediction residuals have zero mean, the :math:`R^2` score is identical to the :func:`Explained Variance score `. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average', 'variance_weighted'}, array-like of shape (n_outputs,) or None, default='uniform_average' Defines aggregating of multiple output scores. Array-like value defines weights used to average scores. Default is "uniform_average". 'raw_values' : Returns a full set of scores in case of multioutput input. 'uniform_average' : Scores of all outputs are averaged with uniform weight. 'variance_weighted' : Scores of all outputs are averaged, weighted by the variances of each individual output. .. versionchanged:: 0.19 Default value of multioutput is 'uniform_average'. force_finite : bool, default=True Flag indicating if ``NaN`` and ``-Inf`` scores resulting from constant data should be replaced with real numbers (``1.0`` if prediction is perfect, ``0.0`` otherwise). Default is ``True``, a convenient setting for hyperparameters' search procedures (e.g. grid search cross-validation). .. versionadded:: 1.1 Returns ------- z : float or ndarray of floats The :math:`R^2` score or ndarray of scores if 'multioutput' is 'raw_values'. Notes ----- This is not a symmetric function. Unlike most other scores, :math:`R^2` score may be negative (it need not actually be the square of a quantity R). This metric is not well-defined for single samples and will return a NaN value if n_samples is less than two. References ---------- .. [1] `Wikipedia entry on the Coefficient of determination `_ Examples -------- >>> from sklearn.metrics import r2_score >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> r2_score(y_true, y_pred) 0.948... >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> r2_score(y_true, y_pred, ... multioutput='variance_weighted') 0.938... >>> y_true = [1, 2, 3] >>> y_pred = [1, 2, 3] >>> r2_score(y_true, y_pred) 1.0 >>> y_true = [1, 2, 3] >>> y_pred = [2, 2, 2] >>> r2_score(y_true, y_pred) 0.0 >>> y_true = [1, 2, 3] >>> y_pred = [3, 2, 1] >>> r2_score(y_true, y_pred) -3.0 >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2] >>> r2_score(y_true, y_pred) 1.0 >>> r2_score(y_true, y_pred, force_finite=False) nan >>> y_true = [-2, -2, -2] >>> y_pred = [-2, -2, -2 + 1e-8] >>> r2_score(y_true, y_pred) 0.0 >>> r2_score(y_true, y_pred, force_finite=False) -inf r&rz9R^2 score is not well-defined with less than two samples.nanNg?rrg)rIrHr'r*ry) rrDrwarningswarnrrLrsumrrwr3) r8r9r:r;rpr'r<r^msgweightrnror@r@rArjs<    r)r8r9cCsRt||\}}t||dd|d\}}}}}|dkrtdt||||S)ad The max_error metric calculates the maximum residual error. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) Estimated target values. Returns ------- max_error : float A positive floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import max_error >>> y_true = [3, 2, 7, 1] >>> y_pred = [4, 2, 7, 1] >>> max_error(y_true, y_pred) 1.0 N)r:r;r'r0z&Multioutput not supported in max_error)rrBr4rLmaxrK)r8r9r'r<r?r@r@rArs" rc CsNt||\}}}|}|dkrBd|||dk|dd|d|d||||d|d|||d|d|}n]|dkrM||d}nR|dkr_dt|||||}n@|dkrsd|||||d}n,d||d|d|d||||d|d|||d|d|}tt||dS)z&Mean Tweedie deviance regression loss.rrrlr*rJ)rpowwherexlogylogrLr) r8r9r:powerr'r<r^pdevr@r@rA_mean_tweedie_devianceHs:  rrightleft)r8r9r:rr:rcCst||\}}t|||d|d\}}}}}|dkrtd|dur.t|}|ddtjf}d|d}|dkrF||dkrEt|dnA|dkrKn`. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. power : float, default=0 Tweedie power parameter. Either power <= 0 or power >= 1. The higher `p` the less weight is given to extreme deviations between true and predicted targets. - power < 0: Extreme stable distribution. Requires: y_pred > 0. - power = 0 : Normal distribution, output corresponds to mean_squared_error. y_true and y_pred can be any real numbers. - power = 1 : Poisson distribution. Requires: y_true >= 0 and y_pred > 0. - 1 < p < 2 : Compound Poisson distribution. Requires: y_true >= 0 and y_pred > 0. - power = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0. - power = 3 : Inverse Gaussian distribution. Requires: y_true > 0 and y_pred > 0. - otherwise : Positive stable distribution. Requires: y_true > 0 and y_pred > 0. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_tweedie_deviance >>> y_true = [2, 0, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_tweedie_deviance(y_true, y_pred, power=1) 1.4260... Nr;r'r0z2Multioutput not supported in mean_tweedie_deviancez'Mean Tweedie deviance error with power=z can only be used on rzstrictly positive y_pred.r*rz,non-negative y and strictly positive y_pred.zstrictly positive y and y_pred.r)rrDr4rrinewaxisrdr)r8r9r:rr'r<r?messager@r@rAris8<     rr8r9r:rhcCt|||ddS)adMean Poisson deviance regression loss. Poisson deviance is equivalent to the Tweedie deviance with the power parameter `power=1`. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. Requires y_true >= 0. y_pred : array-like of shape (n_samples,) Estimated target values. Requires y_pred > 0. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_poisson_deviance >>> y_true = [2, 0, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_poisson_deviance(y_true, y_pred) 1.4260... r*rrrr@r@rAr s(r cCr)aMean Gamma deviance regression loss. Gamma deviance is equivalent to the Tweedie deviance with the power parameter `power=2`. It is invariant to scaling of the target variable, and measures relative errors. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. Requires y_true > 0. y_pred : array-like of shape (n_samples,) Estimated target values. Requires y_pred > 0. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_gamma_deviance >>> y_true = [2, 0.5, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_gamma_deviance(y_true, y_pred) 1.0568... rrrrr@r@rAr!s)r!c Cst||\}}t|||d|d\}}}}}|dkrtdt|dkr/d}t|ttdS|j|dd |j|dd }}t ||||d }t |||d } t || ||d } d|| S) a :math:`D^2` regression score function, fraction of Tweedie deviance explained. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A model that always uses the empirical mean of `y_true` as constant prediction, disregarding the input features, gets a D^2 score of 0.0. Read more in the :ref:`User Guide `. .. versionadded:: 1.0 Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. power : float, default=0 Tweedie power parameter. Either power <= 0 or power >= 1. The higher `p` the less weight is given to extreme deviations between true and predicted targets. - power < 0: Extreme stable distribution. Requires: y_pred > 0. - power = 0 : Normal distribution, output corresponds to r2_score. y_true and y_pred can be any real numbers. - power = 1 : Poisson distribution. Requires: y_true >= 0 and y_pred > 0. - 1 < p < 2 : Compound Poisson distribution. Requires: y_true >= 0 and y_pred > 0. - power = 2 : Gamma distribution. Requires: y_true > 0 and y_pred > 0. - power = 3 : Inverse Gaussian distribution. Requires: y_true > 0 and y_pred > 0. - otherwise : Positive stable distribution. Requires: y_true > 0 and y_pred > 0. Returns ------- z : float The D^2 score. Notes ----- This is not a symmetric function. Like R^2, D^2 score may be negative (it need not actually be the square of a quantity D). This metric is not well-defined for single samples and will return a NaN value if n_samples is less than two. References ---------- .. [1] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J. Wainwright. "Statistical Learning with Sparsity: The Lasso and Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/ Examples -------- >>> from sklearn.metrics import d2_tweedie_score >>> y_true = [0.5, 1, 2.5, 7] >>> y_pred = [1, 1, 5, 3.5] >>> d2_tweedie_score(y_true, y_pred) 0.285... >>> d2_tweedie_score(y_true, y_pred, power=1) 0.487... >>> d2_tweedie_score(y_true, y_pred, power=2) 0.630... >>> d2_tweedie_score(y_true, y_true, power=2) 1.0 Nrr0z-Multioutput not supported in d2_tweedie_scorer9D^2 score is not well-defined with less than two samples.r|r*rgr)rHr') rrDr4rr}r~rrLsqueezerrr) r8r9r:rr'r<r?rrny_avgror@r@rAr" s&Y    r"cCs0t||||\}}}}}t|dkrd}t|ttdSt||||dd}|dur>ttj ||ddd t |d f}ntt |||dd t |d f}t||||dd} |dk} | dk} | | @} t |j d } d || | | | | <d | | | @<t|tr|dkr| Sd}n|}ttj| |d S)u :math:`D^2` regression score function, fraction of pinball loss explained. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A model that always uses the empirical alpha-quantile of `y_true` as constant prediction, disregarding the input features, gets a :math:`D^2` score of 0.0. Read more in the :ref:`User Guide `. .. versionadded:: 1.1 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. alpha : float, default=0.5 Slope of the pinball deviance. It determines the quantile level alpha for which the pinball deviance and also D2 are optimal. The default `alpha=0.5` is equivalent to `d2_absolute_error_score`. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average scores. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Scores of all outputs are averaged with uniform weight. Returns ------- score : float or ndarray of floats The :math:`D^2` score with a pinball deviance or ndarray of scores if `multioutput='raw_values'`. Notes ----- Like :math:`R^2`, :math:`D^2` score may be negative (it need not actually be the square of a quantity D). This metric is not well-defined for a single point and will return a NaN value if n_samples is less than two. References ---------- .. [1] Eq. (7) of `Koenker, Roger; Machado, José A. F. (1999). "Goodness of Fit and Related Inference Processes for Quantile Regression" `_ .. [2] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J. Wainwright. "Statistical Learning with Sparsity: The Lasso and Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/ Examples -------- >>> from sklearn.metrics import d2_pinball_score >>> y_true = [1, 2, 3] >>> y_pred = [1, 3, 3] >>> d2_pinball_score(y_true, y_pred) 0.5 >>> d2_pinball_score(y_true, y_pred, alpha=0.9) 0.772... >>> d2_pinball_score(y_true, y_pred, alpha=0.1) -1.045... >>> d2_pinball_score(y_true, y_true, alpha=0.1) 1.0 rrr|r,rRNdr)qrIr*)r:percentile_rankrlrJ)rBrr}r~rrLrritile percentilelenrrmr3r6r7rk)r8r9r:rPr;r<rrn y_quantilerorsrqrtrrrur@r@rAr#sV\     r#cCst|||d|dS)a :math:`D^2` regression score function, fraction of absolute error explained. Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A model that always uses the empirical median of `y_true` as constant prediction, disregarding the input features, gets a :math:`D^2` score of 0.0. Read more in the :ref:`User Guide `. .. versionadded:: 1.1 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average scores. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Scores of all outputs are averaged with uniform weight. Returns ------- score : float or ndarray of floats The :math:`D^2` score with an absolute error deviance or ndarray of scores if 'multioutput' is 'raw_values'. Notes ----- Like :math:`R^2`, :math:`D^2` score may be negative (it need not actually be the square of a quantity D). This metric is not well-defined for single samples and will return a NaN value if n_samples is less than two. References ---------- .. [1] Eq. (3.11) of Hastie, Trevor J., Robert Tibshirani and Martin J. Wainwright. "Statistical Learning with Sparsity: The Lasso and Generalizations." (2015). https://hastie.su.domains/StatLearnSparsity/ Examples -------- >>> from sklearn.metrics import d2_absolute_error_score >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> d2_absolute_error_score(y_true, y_pred) 0.764... >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> d2_absolute_error_score(y_true, y_pred, multioutput='uniform_average') 0.691... >>> d2_absolute_error_score(y_true, y_pred, multioutput='raw_values') array([0.8125 , 0.57142857]) >>> y_true = [1, 2, 3] >>> y_pred = [1, 2, 3] >>> d2_absolute_error_score(y_true, y_pred) 1.0 >>> y_true = [1, 2, 3] >>> y_pred = [2, 2, 2] >>> d2_absolute_error_score(y_true, y_pred) 0.0 >>> y_true = [1, 2, 3] >>> y_pred = [3, 2, 1] >>> d2_absolute_error_score(y_true, y_pred) -1.0 rQrR)r#rEr@r@rAr$)s_ r$)r%N)N)2__doc__r}numbersrnumpyri exceptionsrutils._array_apirrrrr r rutils._param_validationr r r utils.statsrutils.validationrrrrr__ALL__rBrDrrrrrrrrrwrrrrrr r!r"r#r$r@r@r@rAs     b ; T Y a P K O E K2    & $!  T#$  g