-i SrSSKrSSKJr SSKrSSKJr SSKJ r J r J r J r J r SSKJr SSKJrJrJr SS KJr SS KJrJrJrJrJr /S QrS;S jrSF 5 >F ,]%P  {{aFG, {{aFG, ||A&,,q/) J Q Q Qa    QIT+s##  5006+1  6  !+? >TU U ++A. .%%a() {"F '!^\1IF 6+ ==c >[XX$S9n[XX#XTS9up`pnX`XU4$)a~Ensures y_true, y_pred, and sample_weight correspond to 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()rrB)r9r:r;r<r( dtype_namer@s rA&_check_reg_targets_with_floating_dtyperFs8d/v}TJ9K *:6FF; 6+ ==rCz array-liker-r.r9r:r;r<T)prefer_skip_nested_validationr;r<c[XX#5upE[XX#US9upPpn[URX- 5USUS9n[ U[ 5(aUS:XaU$US:XaSn[XcS9n[ U5$)aMean absolute error regression loss. The mean absolute error is a non-negative floating point value, where 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. 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.NrK)rrFrabsr7r8float)r9r:r;r<r(r= output_errorsrs rArrsB &- EEB / M2 2Avk  vQ2M+s## , & - -K#=F $ %%rCr+both)closed)r9r:r;alphar<?r;rSr<cZ[XX$5upV[XX$US9up`pnX- nURUS:UR5nX8-U-SU- SU- -U-- n [ XSS9n [ U[ 5(aUS:XaU $[ U[ 5(aUS:XaSn[[ XS95$) 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) 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+rKrLr-r.NrM)rrFastyper*rr7r8rO) r9r:r;rSr<r(r=diffsignlossrPs rArr5sN &- EEB / M2 2Avk ?D 99TQY +D <$ !e)D!9D!@ @DTqAM+s## |(C+s## 7H(H  -= >>rCc[XX#5upEn[XX#US9upPpnURURUR5R UR US9nURU5nURX- 5URX5- n [XSS9n [U[5(aUS:XaU $US:XaSn[XS9n [U 5$) aH 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*devicerrWr-r.NrM) r rFasarrayfinfofloat64epsr*rNmaximumrr7r8rO) r9r:r;r<r(r=device_epsilon y_true_absmaperPrs rArrsZ. NB7 / M2 2Avk jj"**-11gjVGJ 66&/ "RZZ %D DDTqAM+s## , & - -K&.m%Q" / 00rCc[XX#5upE[XX#US9upPpn[X- S-SUS9n[U[5(aUS:XaU$US:XaSn[XcS9n[ U5$) aMean 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)rLrKr-r.NrM)rrFrr7r8rO)r9r:r;r<r(r=rPrs rArrs@ &- EEB. M2 2Avk fo!3!]SM+s## , & - -K"-E # $$rCc [XX#5upEUR[XUSS95n[U[5(aUS:XaU$US:XaSn[ XcS9n[ U5$)aMRoot 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-rIr.NrM)rsqrtrr7r8rrO)r9r:r;r<r(r=rPrs rArr[stv &- EEBGG -\ M +s## , & - -K'}J ( ))rCc[X5upE[XX#US9upPpnURUS:*5(dURUS:*5(a [S5e[ UR U5UR U5UUS9$)aMean squared logarithmic error regression loss. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors when the input is of multioutput format. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import mean_squared_log_error >>> y_true = [3, 5, 2.5, 7] >>> y_pred = [2.5, 5, 4, 8] >>> mean_squared_log_error(y_true, y_pred) 0.039... >>> y_true = [[0.5, 1], [1, 2], [7, 6]] >>> y_pred = [[0.5, 2], [1, 2.5], [8, 8]] >>> mean_squared_log_error(y_true, y_pred) 0.044... >>> mean_squared_log_error(y_true, y_pred, multioutput='raw_values') array([0.00462428, 0.08377444]) >>> mean_squared_log_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.060... r'r,zcMean Squared Logarithmic Error cannot be used when targets contain values less than or equal to -1.rI)rrFanyr5rlog1pr9r:r;r<r(r=s rArrsD & )EB / M2 2Avk  vvflrvvfl33 ?    #  rCc[X5upE[XX#US9upPpnURUS:*5(dURUS:*5(a [S5e[ UR U5UR U5UUS9$)aRoot 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.rI)rrFrkr5rrlrms rArrsp & )EB / M2 2Avk  vvflrvvfl33 ?  #  #  rC)r9r:r<r;)r<r;cD[XX25up@pnUc,[R"[R"X- 5SS9nO [ [R"X- 5US9n[ U[ 5(aUS:XaU$US:XaSn[[R"XRS95$)aMedian 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 NrrLr;r-r.rM) rBnpmedianrNrr7r8rOaverage)r9r:r<r;r=rPs rArrUsB5G 51Avk "&&"9B , FF6? #= +s## , & - -K M? @@rCcURnUS:gnU(dSX- - n O0US:gn URU/XgS9n X-n SX X- - X'SXU)-'[U[5(a2US:XaU $US:XaSn O#US:XaUn UR U5(dSn OUn [ U W S 9n [ U 5S:Xa [U 5$U $) zCCommon part used by explained variance score and :math:`R^2` score.rr+)r]r*r-r.Nr/rM)r*onesr7r8rkrr rO) numerator denominatorr>r< force_finiter(r]r*nonzero_denominator output_scoresnonzero_numerator valid_score avg_weightsresults rA_assemble_r2_explained_variancers OOE%* Y45 %N FH )= %&  "[%= =& " CF +>*>>?+s## , & - -K / /%K66-..# ! m[ 9F F|qV} MrC>r-r.r/boolean)r9r:r;r<rz)r;r<rzc [XX#5upVn[XX#US9up`pn[X- USS9n[X- U- S-USS9n [XSS9n [X - S-USS9n [U U URSUUUUS9$)aT 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'rrWrr+rxryr>r<rzr(r])r rFrrr4) r9r:r;r<rzr(r=r] y_diff_avgrx y_true_avgrys rArrsh-V]XMB6 / M2 2Avk &/=qIJ : %!+]I&a@JF/A5}STUK *,,q/!  rCc [XX#5upVn[XX#US9up`pn[U5S:a(Sn[R"U[ 5 [ S5$Ub[U5nUSS2S4n OSn URXU- S--SS9n URX[USX%S 9- S--SS9n [U U URS UUUUS 9$) a: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?rrp)rLrKr(r+r) r rFrwarningswarnrrOrsumrrr4) r9r:r;r<rzr(r=rcmsgweightrxrys rArrjsZ. NB7 / M2 2Avk FaI c12U| $]3 q$w'v&Q 66Q?I&&8FMQQVWWW K +,,q/!  rC)r9r:c[X5up#[XSSUS9up@n nUS:Xa [S5e[UR UR X- 555$)a The max_error metric calculates the maximum residual error. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) Estimated target values. Returns ------- max_error : float A positive floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import max_error >>> y_true = [3, 2, 7, 1] >>> y_pred = [4, 2, 7, 1] >>> max_error(y_true, y_pred) 1.0 N)r;r<r(r1z&Multioutput not supported in max_error)rrBr5rOmaxrN)r9r:r(r=r@s rArrscD & )EB#5d$ FFAq))ABB v/0 11rCc[X5upEnUnUS:asSURURUS:US5SU- 5SU- SU- -- XRUSU- 5-SU- - - URUSU- 5SU- - --nOUS:XaX- S-nOUS:XaS[XU- 5U- U--nOUS:XaSUR X- 5X- -S- -nO^SURUSU- 5SU- SU- -- XRUSU- 5-SU- - - URUSU- 5SU- - --n[ [ XS95$)z&Mean Tweedie deviance regression loss.rrrvr+rM)r powwherexlogylogrOr) r9r:r;powerr(r=rcpdevs rA_mean_tweedie_deviancerHs-f=NB7 A1u FF!VS1A A!a%  " vvfa!e,,A6  7 ffVQU#q1u-  .  a1$ a5&1F:VCD a266&/*V_`. 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(r1z2Multioutput 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)rrFr5rrrnewaxisrkr)r9r:r;rr(r=r@messages rAr r isOx & )EB/U 4B0,FF1))MNN $]3 %am4 7w>STG qy 66&A+  W'BBC C  ! ea 66&1*  ! !4!4W'UUV V"5 ! 66&A+  "&&1"5"5W'HHI I#6 !m rCr9r:r;rqc[XUSS9$)aMean 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 VVrCc[XUSS9$)aRMean Gamma deviance regression loss. Gamma deviance is equivalent to the Tweedie deviance with the power parameter `power=2`. It is invariant to scaling of the target variable, and measures relative errors. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. Requires y_true > 0. y_pred : array-like of shape (n_samples,) Estimated target values. Requires y_pred > 0. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_gamma_deviance >>> y_true = [2, 0.5, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_gamma_deviance(y_true, y_pred) 1.0568... rrrrs rAr"r"sR !}TU VVrCcT[X5upE[XUSUS9up`pnUS:Xa [S5e[U5S:a(Sn[R "U[ 5 [S5$URUSS 9URUSS 9p[XX#S 9n[XUS 9n [X X#S 9n SX- - $) 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 Nrr1z-Multioutput not supported in d2_tweedie_scorer9D^2 score is not well-defined with less than two samples.rr+rpr)rKr() rrFr5rrrrrOsqueezer rr) r9r:r;rr(r=r@rrxy_avgrys rAr#r# sr & )EB/U 4B0,FF1))HIIFaI c12U|ZZQZ/F1KF%mI Vr :E(]K y& &&rCc[XX$5upPpn[U5S:a(Sn[R"U[5 [ S5$[ UUUUSS9nUc9[R"[R"XS-SS 9[U5S 45nO-[R"[XUS-S 9[U5S 45n[ UUUUSS9n US:gn U S:gn X-n [R"URS 5n S X|X- - X'S XU )-'[U[5(a US:XaU $SnOUn[ [R "XS 95$)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 rrrr-rUNdr)qrLr+)r;percentile_rankrvrM)rBrrrrrOrrrtile percentilelenrrwr4r7r8rt)r9r:r;rSr<r=rrx y_quantileryr}r{r~r|rs rAr$r$sxx5G 51AvkFaI c12U|!# IWW MM&CKa 83v;:J WW US[ [!   $# K"Q%*#9KGGFLLO,M!"i&<{?W&W!XM>AM':&::;+s## , & K! M? @@rCc[XUSUS9$)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 rTrU)r$rGs rAr%r%)s~ m3K rC)numericN)N)2__doc__rnumbersrnumpyrr exceptionsrutils._array_apirrrr r r rutils._param_validationr r r utils.statsrutils.validationrrrrr__ALL__rBrFrrrrrrrrrrrrrr r!r"r#r$r%rCrArs/LK. ,EI^>D488>v..&-"L2C#DE|T  #'&*7HQ&Q&h..&-4Af56"L2C#DE|T #' &*BSV? 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