B 0d @sVdZddlZddlZddlmZddlmZddlm Z m Z m Z m Z m Z mZddlmZdd d d d d ddddddg Zd0ddZddddd ZddddddZeddddddd Zddd d!d"d Zddd d!d#d Zddd$d%d Zdddd&dZdddd'dZd(dZddd)d*dZdd+d,dZdd+d-dZddd)d.d/ZdS)1zMetrics 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)TweedieDistribution)UndefinedMetricWarning) check_arraycheck_consistent_length _num_samples column_or_1d_check_sample_weight_deprecate_positional_args)_weighted_percentile max_errormean_absolute_errormean_squared_errormean_squared_log_errormedian_absolute_errormean_absolute_percentage_errormean_pinball_lossr2_scoreexplained_variance_scoremean_tweedie_deviancemean_poisson_deviancemean_gamma_deviancenumericcCst||t|d|d}t|d|d}|jdkr:|d}|jdkrN|d}|jd|jdkr~td|jd|jd|jd}d}t|tr||krtd||nF|dk rt|dd }|dkrtd n |t |krtd t ||f|dkrd nd }||||fS)aFCheck 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(). 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. dtype : str or list, default="numeric" the dtype argument passed to check_array. F) ensure_2ddtype)rz`. 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) 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)weightsaxisrrN)r/)r-rnpaverageabsr$r%)r'r(r.r)r* output_errorsr+r+r,r s8  g?)r.alphar)c Cst|||\}}}}t|||||}|dk|j}|||d|d||}tj||dd} t|tr|dkr~| S|dkrd}n td|tj| |dS) aPinball loss for quantile regression. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. alpha: float, slope of the pinball loss, default=0.5, this loss is equivalent to :ref:`mean_absolute_error` when `alpha=0.5`, `alpha=0.95` is minimized by estimators of the 95th percentile. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. Returns ------- loss : float or ndarray of floats If multioutput is 'raw_values', then mean absolute error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. The pinball loss output is a non-negative floating point. The best value is 0.0. Examples -------- >>> from sklearn.metrics import mean_pinball_loss >>> y_true = [1, 2, 3] >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.1) 0.03... >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.1) 0.3... >>> mean_pinball_loss(y_true, [0, 2, 3], alpha=0.9) 0.3... >>> mean_pinball_loss(y_true, [1, 2, 4], alpha=0.9) 0.03... >>> mean_pinball_loss(y_true, y_true, alpha=0.1) 0.0 >>> mean_pinball_loss(y_true, y_true, alpha=0.9) 0.0 rr)r/r0rrNzVmultioutput is expected to be 'raw_values' or 'uniform_average' but we got %r instead.)r/) r-rZastyperr1r2r$r%r") r'r(r.r5r)r*diffsignZlossr4r+r+r,rs =   z1.1)versioncCst|||\}}}}t|||ttjj}t||tt||}tj||dd}t |t r|dkrt|S|dkrd}tj||dS)ah 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) 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/r0rrN)r/) r-rr1Zfinfofloat64Zepsr3maximumr2r$r%)r'r(r.r)r*epsilonZmaper4r+r+r,r#sF   T)r.r)squaredcCsvt|||\}}}}t|||tj||dd|d}|sFt|}t|trh|dkr\|S|dkrhd}tj||dS)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. 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) 0.375 >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> mean_squared_error(y_true, y_pred, squared=False) 0.612... >>> 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, squared=False) 0.822... >>> 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... rr)r0r/rrN)r/)r-rr1r2sqrtr$r%)r'r(r.r)r<r*r4r+r+r,rzs<   cCs^t|||\}}}}t||||dks8|dkr@tdtt|t||||dS)aMean squared logarithmic error regression loss. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs) Estimated target values. sample_weight : array-like of shape (n_samples,), default=None Sample weights. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors when the input is of multioutput format. 'uniform_average' : Errors of all outputs are averaged with uniform weight. squared : bool, default=True If True returns MSLE (mean squared log error) value. If False returns RMSLE (root mean squared log error) value. 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... >>> mean_squared_log_error(y_true, y_pred, squared=False) 0.199... >>> 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... rzSMean Squared Logarithmic Error cannot be used when targets contain negative values.)r.r)r<)r-ranyr"rr1log1p)r'r(r.r)r<r*r+r+r,rs: )r)r.cCst|||\}}}}|dkr6tjt||dd}n t||}tt|||d}t|trx|dkrl|S|dkrxd}tj||dS)a?Median absolute error regression loss. Median absolute error output is non-negative floating point. The best value is 0.0. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape = (n_samples) or (n_samples, n_outputs) Ground truth (correct) target values. y_pred : array-like of shape = (n_samples) or (n_samples, n_outputs) Estimated target values. multioutput : {'raw_values', 'uniform_average'} or array-like of shape (n_outputs,), default='uniform_average' Defines aggregating of multiple output values. Array-like value defines weights used to average errors. 'raw_values' : Returns a full set of errors in case of multioutput input. 'uniform_average' : Errors of all outputs are averaged with uniform weight. sample_weight : array-like of shape (n_samples,), default=None Sample weights. .. versionadded:: 0.24 Returns ------- loss : float or ndarray of floats If multioutput is 'raw_values', then mean absolute error is returned for each output separately. If multioutput is 'uniform_average' or an ndarray of weights, then the weighted average of all output errors is returned. Examples -------- >>> from sklearn.metrics import median_absolute_error >>> y_true = [3, -0.5, 2, 7] >>> y_pred = [2.5, 0.0, 2, 8] >>> median_absolute_error(y_true, y_pred) 0.5 >>> y_true = [[0.5, 1], [-1, 1], [7, -6]] >>> y_pred = [[0, 2], [-1, 2], [8, -5]] >>> median_absolute_error(y_true, y_pred) 0.75 >>> median_absolute_error(y_true, y_pred, multioutput='raw_values') array([0.5, 1. ]) >>> median_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7]) 0.85 Nr)r0)r.rr)r/) r-r1Zmedianr3r r r$r%r2)r'r(r)r.r*r4r+r+r,rs8  cCs t|||\}}}}t|||tj|||dd}tj|||d|dd}tj||dd}tj||d|dd}|dk} |dk} | | @} t|jd} d|| || | | <d| | | @<t|tr|dkr| S|dkrd} q|d kr|} n|} tj| | d S) aExplained variance regression score function. Best possible score is 1.0, lower values are worse. 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. Returns ------- score : float or ndarray of floats The explained variance or ndarray if 'multioutput' is 'raw_values'. 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... r)r/r0rrgrrNr)r/)r-rr1r2onesr!r$r%)r'r(r.r)r*Z y_diff_avg numeratorZ y_true_avg denominatornonzero_numeratornonzero_denominator valid_score output_scores avg_weightsr+r+r,rcs.8  cCslt|||\}}}}t|||t|dkrDd}t|ttdS|dk rht|}|ddtj f}nd}|||dj dtj d}||tj |d|ddj dtj d}|dk} |dk} | | @} t |jd g} d || || | | <d | | | @<t|trZ|d kr| S|d kr*d} n.|d kr^|} t| s^t| sTdSd Sn|} tj | | dS)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). A constant model that always predicts the expected value of y, disregarding the input features, would get a :math:`R^2` score of 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', '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'. 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 rz9R^2 score is not well-defined with less than two samples.nanNg?r)r0r)r0r/rgrrr)r/)r-rrwarningswarnrfloatrr1newaxissumr9r2r@r!r$r%r>)r'r(r.r)r*msgweightrArBrDrCrErFrGr+r+r,rsBW          cCs8t||d\}}}}|dkr$tdtt||S)ab 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 Nzcontinuous-multioutputz&Multioutput not supported in max_error)r-r"r1maxr3)r'r(r*_r+r+r,r Fs)r.powercCst||dtjtjgd\}}}}|dkr0tdt||||dk r^t|}|ddtjf}t|d}|j ||dd}tj ||dS) a[Mean Tweedie deviance regression loss. 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. 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... N)rzcontinuous-multioutputz2Multioutput not supported in mean_tweedie_deviance)rRT) check_input)r/) r-r1r9float32r"rrrLr unit_deviancer2)r'r(r.rRr*rQdistdevr+r+r,rgs0  )r.cCst|||ddS)adMean Poisson deviance regression loss. Poisson deviance is equivalent to the Tweedie deviance with the power parameter `power=1`. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array-like of shape (n_samples,) Ground truth (correct) target values. Requires y_true >= 0. y_pred : array-like of shape (n_samples,) Estimated target values. Requires y_pred > 0. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- loss : float A non-negative floating point value (the best value is 0.0). Examples -------- >>> from sklearn.metrics import mean_poisson_deviance >>> y_true = [2, 0, 1, 4] >>> y_pred = [0.5, 0.5, 2., 2.] >>> mean_poisson_deviance(y_true, y_pred) 1.4260... r)r.rR)r)r'r(r.r+r+r,rs cCst|||ddS)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... r)r.rR)r)r'r(r.r+r+r,rs!c Cst||dtjtjgd\}}}}|dkr0tdt|||t|dkr`d}t|t t dS|dk rt |}|ddtj f}t |d}|j||d d }tj||d } tj||d } |j|| d d }tj||d } d | | S) a D^2 regression score function, percentage 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,), optional 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://trevorhastie.github.io 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 N)rzcontinuous-multioutputz-Multioutput not supported in d2_tweedie_scorerz9D^2 score is not well-defined with less than two samples.rH)rRT)rS)r/r)r-r1r9rTr"rrrIrJrrKrrLrrUr2) r'r(r.rRr*rQrNrVrWrAZy_avgrBr+r+r,d2_tweedie_scores&L    rX)r) __doc__rInumpyr1Z_loss.glm_distributionr exceptionsrZutils.validationrrrrr r Z utils.statsr Z__ALL__r-r rrrrrrrr rrrrXr+r+r+r,sD     LGTVONLZ !A#$