0Ph @dZddlZddlmZddlZddlmZddlm Z ddl m Z m Z m Z mZmZddlmZmZmZdd lmZdd lmZmZmZmZmZgd ZdzMetrics 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)xlogy)UndefinedMetricWarning)_average_find_matching_floating_dtype get_namespaceget_namespace_and_devicesize)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_scorenumericc0t||||\}}t||t|d|}t|d|}|jdkr||d}|jdkr||d}|jd|jdkr9t d|jd|jd|jd}d}t|tr(||vr#t d||nZ|Xt|d }|dkrt d ||jd kr!t d |jd d|d|dkrdnd}||||fS)aYCheck that y_true and y_pred 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. 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. 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_2ddtype)r,z > >F 5 > > >F {aFG,, {aFG,, |A&,q/)) J Q Q Qa      QIT+s## 5 5 5006+[11  6  !+??? >>TUU U ++A. . .F%a(FF8AFFF '!^^\\1IF 66; ..ct||||}t|||||\}}}}||||}|||||fS)a Ensures that y_true, y_pred, and sample_weight correspond to the same regression task. Extends `_check_reg_targets` by automatically selecting a suitable floating-point data type for inputs using `_find_matching_floating_dtype`. Use this private method only when converting inputs to array API-compatibles. 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,) multioutput : array-like or string in ['raw_values', 'uniform_average', 'variance_weighted'] or None None is accepted due to backward compatibility of r2_score(). 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,), default=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. r()r+r)Nr+)rrBasarray)r:r; sample_weightr<r) dtype_namer@s rA&_check_reg_targets_with_floating_dtyperIsrf/vv}QSTTTJ*< :"+++'FFFK   = CC 66=+ ==rCz array-liker.r/r:r;rGr<T)prefer_skip_nested_validationrGr<c^t||||\}}t|||||\}}}}}t|||t|||z |d|}t |t r|dkr|S|dkrd}t||}t|S)aMean absolute 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 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/NrN)r rIrrabsr8r9float)r:r;rGr<r)r= output_errorsrs rArrs@ &&- E EEB / FM;2   2Avv}k FFM::: vQ2M+s## , & & - - -K#=+FFF $ % %%rCr,both)closed)r:r;rGalphar<?rGrVr<ct|||\}}}}t|||||z }|dk|j}||z|zd|z d|z z|zz }t j||d} t |tr|dkr| St |tr|dkrd}t j| |S)a"Pinball 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) np.float64(0.03...) >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.1) np.float64(0.3...) >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.9) np.float64(0.3...) >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.9) np.float64(0.03...) >>> mean_pinball_loss(y_true, y_true, alpha=0.1) np.float64(0.0) >>> mean_pinball_loss(y_true, y_true, alpha=0.9) np.float64(0.0) rr,rNrOr.r/NrP)rBrastyper+npaverager8r9) r:r;rGrVr<r@diffsignlossrSs rArr0sN+= ++'FFFKFFM::: F?D AI  dj ) )D 4<$ !e)D!9D!@ @DJt]CCCM+s## |(C(C+s## 7H(H(H :m[ 9 9 99rCc*t||||\}}t|||||\}}}}}t||||||jj|j}||}|||z | ||z }t||d} t|tr|dkr| S|dkrd}t| |} 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(rErrZr.r/NrP)r rIrrFfinfofloat64epsr+rQmaximumrr8r9rR) r:r;rGr<r)r=epsilon y_true_absmaperSrs rArrs'Z &&- E EEB. FM;2   2Avv}k FFM:::jj"*--1jFFGJ 66&6/ " "RZZ G%D%D DDT=qAAAM+s## , & & - - -K&.m[%Q%Q%Q" / 0 00rCc<t||||\}}t|||||\}}}}}t|||t||z dzd|}t |t r|dkr|S|dkrd}t||}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)rOrNr.r/NrP)r rIrrr8r9rR)r:r;rGr<r)r=rSrs rArrs@ &&- E EEB. FM;2   2Avv}k FFM:::fvo!3!]SSSM+s## , & & - - -K"-EEE # $ $$rCct||||\}}|t|||d}t|tr|dkr|S|dkrd}t ||}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.rLr/NrP)r sqrtrr8r9rrR)r:r;rGr<r)r=rSrs rArrMsv &&- E EEBGG F-\   M +s## , & & - - -K'}kJJJ ( ) ))rCcPt||\}}t|||||\}}}}}||dks||dkrtdt ||||||S)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.rL)r rIanyr6rlog1pr:r;rGr<r)r=s rArrsD && ) )EBD {rAvvq! vvfl rvvfl33  ?     #    rCcPt||\}}t|||||\}}}}}||dks||dkrtdt ||||||S)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.rL)r rIrmr6rrnros rArrsp && ) )EBD {rAvvq! vvfl rvvfl33  ?   #  #    rC)r:r;r<rG)r<rGclt|||\}}}}|,tjtj||z d}n6t ||}t tj||z |}t |tr|dkr|S|dkrd}tj||S)aaMedian 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) np.float64(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) np.float64(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]) np.float64(0.85) NrrOrGr.r/rP) rBr\medianrQrrr8r9r])r:r;r<rGr@rSs rArrCsB+= ++'FFFK "&&"9"9BBB ,]FCC , F6F? # #=   +s## , & & - - -K :m[ 9 9 99rCc|j}|dk}|s d||z z } nD|dk} ||g||} || z} d|| || z z | | <d| | |z<t|tr1|dkr| S|dkrd} n"|dkr|} ||sd} n|} t | | } t | dkrt| S| S) zCCommon part used by explained variance score and :math:`R^2` score.rr,)devicer+r.r/Nr0rP)r+onesr8r9rmrr rR) numerator denominatorr>r< force_finiter)rvr+nonzero_denominator output_scoresnonzero_numerator valid_score avg_weightsresults rA_assemble_r2_explained_variancers6 OE%* FY45 %N F%HH ),== %& k "[%= =& k" CF '+>*>>?+s##" , & & - - -KK / / /%K66-.. ## ! m[ 9 9 9F F||qV}} MrC>r.r/r0boolean)r:r;rGr<r{)rGr<r{c t|||\}}}}t|||tj||z |d}tj||z |z dz|d}tj||d}tj||z dz|d} t || |jd||t |ddS)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 rrZrr,Nryrzr>r<r{r)rv)rBrr\r]rr5r ) r:r;rGr<r{r@ y_diff_avgry y_true_avgrzs rArrsh+= ++'FFFKFFM:::FVO]KKKJ &: %!+]IFMBBBJ*fz1a7UVWWWK *,q/!   #    rCc $t||||\}}}t|||||\}}}}}t|||t|dkr+d}t j|t tdS|t|}|dddf} nd} | | ||z dzzd} | | |t|d|| z dzzd} t| | |j 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?rrr)rOrNr)r,r) r rIrrwarningswarnrrRrsumrrr5) r:r;rGr<r{r)r=device_msgweightryrzs rArrWs^Z. {NB7 / FM;2   2Avv}k FFM:::FaI c1222U|| $]33 qqq$w'v&Q 66Q??I&&&8FMbQQQQVWWW K +,q/!    rC)r:r;ct||\}}t||d|\}}}}|dkrtd||||z S)al 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) np.int64(1) Nr(r2z&Multioutput not supported in max_error)r rBr6maxrQ)r:r;r)r=r@s rArr stD && ) )EB 2664B O O OFFFA )))ABBB 66"&&&)) * **rCc ,t||\}}|}|d|j}|dkrd|||dk|||d|z d|z d|z zz ||||d|z zd|z z z |||d|z d|z z zz}n|dkr ||z dz}n|dkrdt |||z |z |zz}n|dkr%d|||z ||z zdz z}nd|||d|z d|z d|z zz ||||d|z zd|z z z |||d|z d|z z zz}tt||S)z&Mean Tweedie deviance regression loss.rrErr,rP) r rFr+powwhererlogrRr) r:r;rGpowerr)r=pzerodevs rA_mean_tweedie_deviancer5s/ && ) )EB A ::av|: , ,D1uu FF288FQJ55rzz!a%7H7H I IA!a%  "rvvfbjjQ&7&7888AEB CffVRZZA..//1q59 :  a1$ a5&11F:VCD a266&6/**Vf_`. 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)r2z2Multioutput 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) r rIr6rrr\newaxisrmr)r:r;rGrr)r=r@messages rAr r Tsx && ) )EB/U 4B000,FFFM1)))MNNNFFM::: $]33 %aaam4 TTTTG qyy 66&A+   DW'BBCC C D ! ea 66&1*   W! !4!4 WW'UUVV V W ! 66&A+   J"&&1"5"5 JW'HHII I J !m5   rCr:r;rGrsc(t|||dS)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,rr rs rAr!r!sP !}TU V V VVrCc(t|||dS)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... rrrrs rAr"r"sR !}TU V V VVrCct||\}}t|||d|\}}}}}|dkrtdt|dkr+d}t j|t tdS||d ||d }}t|||| }t||| } t|| || } d|| z z 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 or ndarray of floats 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 Nrr2z-Multioutput not supported in d2_tweedie_scorer9D^2 score is not well-defined with less than two samples.rr,rrr)rNr)) r rIr6rrrrrRsqueezer rr) r:r;rGrr)r=r@rryy_avgrzs rAr#r# s!r && ) )EB/U 4B000,FFFM1)))HIIIFaI c1222U||ZZQZ//F1K1KFF%m5I V]r : : :E(]%K y;& &&rCc8t|||\}}}}t|||t|dkr+d}tj|t t dSt||||d}|=tj tj ||dzd t|d f}nGt||}tj t|||dz t|d f}t||||d} |dk} | dk} | | z} tj|jd } d || | | z z | | <d | | | z<t!|t"r |dkr| Sd}n|}tj| | 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) np.float64(0.5) >>> d2_pinball_score(y_true, y_pred, alpha=0.9) np.float64(0.772...) >>> d2_pinball_score(y_true, y_pred, alpha=0.1) np.float64(-1.045...) >>> d2_pinball_score(y_true, y_true, alpha=0.1) np.float64(1.0) rrrr.rXNdr)qrOr,)rG percentilerwrP)rBrrrrrrRrr\tilerlenrrrxr5r8r9r])r:r;rGrVr<r@rry y_quantilerzr~r|rr}rs rAr$r$sx+= ++'FFFKFFM:::FaI c1222U||!# IW M&ECKa 8 8 83v;;:J  -]FCC W m    [[!    $# K"Q%*#&99KGFLO,,M!"i &<{;?W&W!XM+>AM#':&::;+s##" , & & KK! :m[ 9 9 99rCc*t|||d|S)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) np.float64(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') np.float64(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) np.float64(1.0) >>> y_true = [1, 2, 3] >>> y_pred = [2, 2, 2] >>> d2_absolute_error_score(y_true, y_pred) np.float64(0.0) >>> y_true = [1, 2, 3] >>> y_pred = [3, 2, 1] >>> d2_absolute_error_score(y_true, y_pred) np.float64(-1.0) rWrX)r$rJs rAr%r%s'~ m3K   rC)r&N)N)2__doc__rnumbersrnumpyr\ scipy.specialr exceptionsrutils._array_apirrr r r utils._param_validationr r r utils.statsrutils.validationrrrrr__ALL__rBrIrrrrrrrrrrrrrr r!r"r#r$r%rCrArs( //////LKKKKKKKKK......   *T/T/T/T/p48>>>>>>>>B..&-" L2C#DEE|T  #'&*7HR&R&R&R&R&j..&-(4Af5556" L2C#DEE|T #'   &*BSM:M:M:M:  M:`..&-" L2C#DEE|T  #'&*7H]1]1]1]1]1@..&-" L2C#DEE|T  #'! 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