:i SrSSKrSSKJr SSKrSSKJr SSKJ r SSK J r J r J r JrJr SSKJrJrJrJr SS KJr SS KJrJrJrJrJr /S QrS=S jr\"S /S /S S/\"SS15S /S.SS9SSS.Sj5r\"S /S /S S/\"\SSSS9/\"SS15S /S.SS9SSSS.Sj5r \"S /S /S S/\"SS15S /S.SS9SSS.Sj5r!\"S /S /S S/\"SS15S /\"\"S155S/S.SS9SSSS .S!j5r"\"S /S /S S/\"SS15S /S.SS9SSS.S"j5r#\"S /S /S S/\"SS15S /\"\"S155S/S.SS9SSSS .S#j5r$\"S /S /S S/\"SS15S /S.SS9SSS.S$j5r%\"S /S /\"SS15S /S S/S%.SS9SSS&.S'j5r&S(r'\"S /S /S S/\"1S)k5S /S/S*.SS9SSSS+.S,j5r(\"S /S /S S/\"1S)k5S S/S/S*.SS9SSSS+.S-j5r)\"S /S /S..SS9S/5r*S0r+\"S /S /S S/\"\SSS1S9\"\SSS2S9/S3.SS9SSS4.S5j5r,\"S /S /S S/S6.SS9SS7.S8j5r-\"S /S /S S/S6.SS9SS7.S9j5r.\"S /S /S S/\"\SSS1S9\"\SSS2S9/S3.SS9SSS4.S:j5r/\"S /S /S S/\"\SSSS9/\"SS15S /S.SS9SSSS.S;j5r0\"S /S /S S/\"SS15S /S.SS9SSS.S<j5r1g)>zMetrics 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)HiddenInterval 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_scorec[XX$S9upE[X5 [USUS9n[USUS9nURS:XaUR US5nURS:XaUR US5nUR SUR S:wa5[ SRUR SUR S55eUR SnSn[U[5(a X';a[ SRXr55eOFUbC[USS 9nUS:Xa [ S 5eU[U5:wa[ S [U5U4-5eUS:XaS OS nXX4$)aCheck that y_true and y_pred belong to the same regression task. Parameters ---------- y_true : array-like y_pred : array-like 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. 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,zF 5 >F {{aFG, {{aFG, ||A&,,q/) J Q Q Qa    QIT+s##  5006+1  6  !+? >TU U #k* *Q{#Y/0 '!^\1IF 6 ..z array-liker.r/r;r< sample_weightr=T)prefer_skip_nested_validationrFr=c[XU5up@p[XU5 [R"[R"X- 5USS9n[ U[ 5(aUS:XaU$US:XaSn[R"XSS9$)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 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. 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) np.float64(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) np.float64(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]) np.float64(0.85...) rweightsaxisr.r/NrK)rCrnpaverageabsr8r9)r;r<rFr=rA output_errorss rBrrs{@+= +'FFFM:JJrvvfo6 TUVM+s## , & - -K ::m 99rDr,both)closed)r;r<rFalphar=?rFrTr=cn[XU5upPp[XU5 X- nUS:RUR5nX7-U-SU- SU- -U-- n[R "XSS9n [ U[5(aUS:XaU $[ U[5(aUS:XaSn[R "XS9$)anPinball 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,rJr.r/NrM)rCrastyper+rNrOr8r9) r;r<rFrTr=rAdiffsignlossrQs rBrrsN+= +'FFFM: ?D AI  djj )D <$ !e)D!9D!@ @DJJtCM+s## |(C+s## 7H(H ::m 99rDc[XU5up@p[XU5 [R"[R5R n[R "X- 5[R"[R "U5U5- n[R"XbSS9n[U[5(aUS:XaU$US:XaSn[R"XsS9$)a Mean absolute percentage error (MAPE) regression loss. Note here that the output is not a percentage in the range [0, 100] and a value of 100 does not mean 100% but 1e2. Furthermore, the output can be arbitrarily high when `y_true` is small (which is specific to the metric) or when `abs(y_true - y_pred)` is large (which is common for most regression metrics). 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) np.float64(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) np.float64(0.5515...) >>> mean_absolute_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7]) np.float64(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) np.float64(112589990684262.48) rrJr.r/NrM) rCrrNfinfofloat64epsrPmaximumrOr8r9)r;r<rFr=rAepsilonmaperQs rBrrAs\+= +'FFFM:hhrzz"&&G 66&/ "RZZv%H HDJJtCM+s## , & - -K ::m 99rD deprecatedboolean)r;r<rFr=squared)rFr=recDUS:wa,[R"S[5 U(d [XX#S9$[ XU5upPp[ XU5 [ R"X- S-SUS9n[U[5(aUS:XaU$US:XaS n[ R"XcS 9$) aMean squared error regression loss. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. squared : bool, default=True If True returns MSE value, if False returns RMSE value. .. deprecated:: 1.4 `squared` is deprecated in 1.4 and will be removed in 1.6. Use :func:`~sklearn.metrics.root_mean_squared_error` instead to calculate the root mean squared error. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import mean_squared_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> mean_squared_error(y_true, y_pred) np.float64(0.375) >>> y_true = [[0.5, 1],[-1, 1],[7, -6]] >>> y_pred = [[0, 2],[-1, 2],[8, -5]] >>> mean_squared_error(y_true, y_pred) np.float64(0.708...) >>> mean_squared_error(y_true, y_pred, multioutput='raw_values') array([0.41666667, 1. ]) >>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7]) np.float64(0.825...) rcz'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared error, use the function'root_mean_squared_error'.rHrr)rLrKr.r/NrM) warningswarn FutureWarningrrCrrNrOr8r9)r;r<rFr=rerArQs rBrrsV, -  *m += +'FFFM:JJA5A}UM+s## , & - -K ::m 99rDc [R"[XUSS95n[U[5(aUS:XaU$US:XaSn[R "XCS9$)aeRoot mean squared error regression loss. Read more in the :ref:`User Guide `. .. versionadded:: 1.4 Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats A non-negative floating point value (the best value is 0.0), or an array of floating point values, one for each individual target. Examples -------- >>> from sklearn.metrics import root_mean_squared_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> root_mean_squared_error(y_true, y_pred) np.float64(0.612...) >>> y_true = [[0.5, 1],[-1, 1],[7, -6]] >>> y_pred = [[0, 2],[-1, 2],[8, -5]] >>> root_mean_squared_error(y_true, y_pred) np.float64(0.822...) r.rHr/NrM)rNsqrtrr8r9rO)r;r<rFr=rQs rBrr s\tGG -\ M +s## , & - -K ::m 99rDczUS:wa,[R"S[5 U(d [XX#S9$[ XU5upPp[ XU5 US:R 5(dUS:R 5(a [S5e[[R"U5[R"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. squared : bool, default=True If True returns MSLE (mean squared log error) value. If False returns RMSLE (root mean squared log error) value. .. deprecated:: 1.4 `squared` is deprecated in 1.4 and will be removed in 1.6. Use :func:`~sklearn.metrics.root_mean_squared_log_error` instead to calculate the root mean squared logarithmic error. 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) np.float64(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) np.float64(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]) np.float64(0.060...) rcz'squared' is deprecated in version 1.4 and will be removed in 1.6. To calculate the root mean squared logarithmic error, use the function'root_mean_squared_log_error'.rHrzSMean Squared Logarithmic Error cannot be used when targets contain negative values.) rgrhrirrCranyr6rrNlog1p)r;r<rFr=rerAs rBrrTs\, 1  .m += +'FFFM: fqj--// /    #  rDc[XU5up@p[XU5 US:R5(dUS:R5(a [S5e[ [ R "U5[ R "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) np.float64(0.199...) rzXRoot Mean Squared Logarithmic Error cannot be used when targets contain negative values.rH)rCrrmr6rrNrn)r;r<rFr=r>s rBrrsp&8 %T"AvFM: fqj--// /  #  #  rD)r;r<r=rF)r=rFcF[XU5up@pUc,[R"[R"X- 5SS9nO+[ X15n[ [R"X- 5US9n[ U[5(aUS:XaU$US:XaSn[R"XRS9$)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) 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) NrrLrFr.r/rM) rCrNmedianrPrrr8r9rO)r;r<r=rFrArQs rBrr sB+= +'FF "&&"9B ,]C , FF6? #= +s## , & - -K ::m 99rDcURnUS: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 $) zCCommon part used by explained variance score and :math:`R^2` score.rr,)devicer+r.r/Nr0rM)r+onesr8r9rmrr float) numerator denominatorr?r= force_finiter)rur+nonzero_denominator output_scoresnonzero_numerator valid_score avg_weightsresults rB_assemble_r2_explained_variancerbs OOE%* Y45 %N FH )= %&  "[%= =& " CF +>*>>?+s## , & - -K / /%K66-..# ! m[ 9F F|qV} MrD>r.r/r0)r;r<rFr=r{)rFr=r{c T[XU5upPp[XU5 [R"X- USS9n[R"X- U- S-USS9n[R"XSS9n[R"X- S-USS9n [ UU UR SUU[ U5SSS9$)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 rrJrr,Nryrzr?r=r{r)ru)rCrrNrOrr5r ) r;r<rFr=r{rA y_diff_avgry y_true_avgrzs rBr r sh+= +'FFFM:FO]KJ : %!+]IFBJ**f1a7UVWK *,,q/!   #  rDc [XX#5upVn[XX%S9n[XX8US9up`p[XU5 [ U5S:a(Sn [ R "U [5 [S5$Ub[X(S9nUSS2S4n OSn URXU- S--S S 9n URX[US X%S 9- S--S S 9n [U U URS UUUUS 9$)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()r+r)rz9R^2 score is not well-defined with less than two samples.nanNr+g?rrq)rLrKr)r,r)r rrCrrrgrhrrxrsumrrr5) r;r<rFr=r{r)r>device_r+msgweightryrzs rBrr!sZ. NB7 *&- OE%7 R&"AvFM:FaI c12U| $]@ q$w'v&Q 66Q?I&&8FMQQVWWW K +,,q/!  rD)r;r<c[XS5up pUS:Xa [S5e[R"[R"X- 55$)a The max_error metric calculates the maximum residual error. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) Estimated target values. Returns ------- max_error : float A positive floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import max_error >>> y_true = [3, 2, 7, 1] >>> y_pred = [4, 2, 7, 1] >>> max_error(y_true, y_pred) np.int64(1) Nr2z&Multioutput not supported in max_error)rCr6rNmaxrP)r;r<rAr>s rBrrsED!364 HFF ))ABB 66"&&) **rDcUnUS:aS[R"[R"US5SU- 5SU- SU- -- U[R"USU- 5-SU- - - [R"USU- 5SU- - --nOUS:XaX- S-nOUS:XaS[XU- 5U- U--nOUS:Xa$S[R"X- 5X- -S- -nOnS[R"USU- 5SU- SU- -- U[R"USU- 5-SU- - - [R"USU- 5SU- - --n[R "XRS9$)z&Mean Tweedie deviance regression loss.rrr,rM)rNpowerr`rlogrO)r;r<rFrpdevs rB_mean_tweedie_deviancersq A1u HHRZZ*AE 2q1uQ6G HrxxA..!a%8 9hhvq1u%Q/ 0  a1$ 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) np.float64(1.4260...) Nrr2z2Multioutput 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) rCrNr^float32r6rrnewaxisrmr)r;r<rFrrAr>messages rBr!r!sVx!3RZZ$<!FF))MNNFM: $]3 %am4 7w>STG qy aK    W'BBC C  ! ea QJ    &A+!2!2!4!4W'UUV V"5 ! aK    6Q;"3"3"5"5W'HHI I#6 !m rDr;r<rFrrc[XUSS9$)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) np.float64(1.4260...) r,rr!rs rBr"r"zsP !}TU VVrDc[XUSS9$)a^Mean Gamma deviance regression loss. Gamma deviance is equivalent to the Tweedie deviance with the power parameter `power=2`. It is invariant to scaling of the target variable, and measures relative errors. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. Requires y_true > 0. y_pred : array-like of shape (n_samples,) Estimated target values. Requires y_pred > 0. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_gamma_deviance >>> y_true = [2, 0.5, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_gamma_deviance(y_true, y_pred) np.float64(1.0568...) rrrrs rBr#r#sR !}TU VVrDc[XS[R[R/S9up@pUS:Xa [ S5e[ U5S:a(Sn[ R"U[5 [S5$[R"U5[R"U5p[XX#S9n[R"XS 9n[XX#S9n S Xy- - $) ag :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) np.float64(0.285...) >>> d2_tweedie_score(y_true, y_pred, power=1) np.float64(0.487...) >>> d2_tweedie_score(y_true, y_pred, power=2) np.float64(0.630...) >>> d2_tweedie_score(y_true, y_true, power=2) np.float64(1.0) Nrr2z-Multioutput not supported in d2_tweedie_scorer9D^2 score is not well-defined with less than two samples.rrrMr,)rCrNr^rr6rrgrhrrxsqueezer!rOr) r;r<rFrrAr>rryy_avgrzs rBr$r$sr!3RZZ$<!FF))HIIFaI c12U|ZZ'F);F%mI JJv 5E(]K y& &&rDc[XU5upPp[XU5 [U5S:a(Sn[R"U[ 5 [ S5$[UUUUSS9nUc9[R"[R"XS-SS 9[U5S 45nO8[X 5n[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 9$)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.rVNdr)qrLr,)rF percentilervrM)rCrrrgrhrrxrrNtilerr:rrrwr5r8r9rO)r;r<rFrTr=rArry y_quantilerzr~r|rr}rs rBr%r%Bsx+= +'FFFM:FaI c12U|!# IWW MM&CKa 83v;:J -]C WW   [!   $# K"Q%*#9KGGFLLO,M!"i&<{?W&W!XM>AM':&::;+s## , & K! ::m 99rDc[XUSUS9$)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) 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) rUrV)r%rEs rBr&r&s~ m3K rD)numericN)2__doc__rgnumbersrnumpyrN scipy.specialr exceptionsrutils._array_apirrr r r utils._param_validationr r rr utils.statsrutils.validationrrrrr__ALL__rCrrrrrrrrrr rrrr!r"r#r$r%r&rDrBrs :/TS. *J/Z..&-"L2C#DE|T  #'&*7HC:C:L..&-4Af56"L2C#DE|T #' &*BSM: M:`..&-"L2C#DE|T  #'&*7HS:S:l..&-"L2C#DE|T:|n56 B #' !  ]: ]:@..&-"L2C#DE|T  #'&*7H>:>:B..&-"L2C#DE|T:|n56 B #' !  c cL..&-"L2C#DE|T  #'&*7H==@.."L2C#DE|T&-  #'$5DI:I:X/d..&- M N  #  #' "! } }@..&- M N   #  #' $! c cL..#' ++B2:..&- T47 3 T1d6 2 #' <@qQ Qh..&- #' <@ W WF..&- #' :>!W!WH..&- T47 3 T1d6 2 #' 7;!b' b'J..&-4Af56  &78 9  #' &*BSH: H:V..&-  &78 9  #' &*7HU UrD