Mean Absolute Error
Contents |
close forecasts or predictions are to the eventual outcomes. The mean absolute error is given by M A E = 1 n ∑ i = 1 n | f i mean absolute error example − y i | = 1 n ∑ i = 1 n |
Mean Absolute Error Vs Mean Squared Error
e i | . {\displaystyle \mathrm {MAE} ={\frac {1}{n}}\sum _{i=1}^{n}\left|f_{i}-y_{i}\right|={\frac {1}{n}}\sum _{i=1}^{n}\left|e_{i}\right|.} As the name suggests, the mean absolute error mean absolute error calculator is an average of the absolute errors | e i | = | f i − y i | {\displaystyle |e_{i}|=|f_{i}-y_{i}|} , where f i {\displaystyle f_{i}} is the prediction and y i {\displaystyle
Mean Absolute Error Interpretation
y_{i}} the true value. Note that alternative formulations may include relative frequencies as weight factors. The mean absolute error used the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series using different scales.[1] The mean absolute error is a common measure of forecast error in time [2]series analysis, where the terms mean absolute error range "mean absolute deviation" is sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally. Related measures[edit] The mean absolute error is one of a number of ways of comparing forecasts with their eventual outcomes. Well-established alternatives are the mean absolute scaled error (MASE) and the mean squared error. These all summarize performance in ways that disregard the direction of over- or under- prediction; a measure that does place emphasis on this is the mean signed difference. Where a prediction model is to be fitted using a selected performance measure, in the sense that the least squares approach is related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2011) (Learn how and when to remove this template message) This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2011) (Learn how and when to remove this template messa
The equation is given in the library references. Expressed in words, the MAE is the average over the verification sample of the absolute
Mean Absolute Error Weka
values of the differences between forecast and the corresponding observation. The MAE
Mean Absolute Error In R
is a linear score which means that all the individual differences are weighted equally in the average. Root relative absolute error mean squared error (RMSE) The RMSE is a quadratic scoring rule which measures the average magnitude of the error. The equation for the RMSE is given in both of the https://en.wikipedia.org/wiki/Mean_absolute_error references. Expressing the formula in words, the difference between forecast and corresponding observed values are each squared and then averaged over the sample. Finally, the square root of the average is taken. Since the errors are squared before they are averaged, the RMSE gives a relatively high weight to large errors. This means the RMSE is most useful when large http://www.eumetcal.org/resources/ukmeteocal/verification/www/english/msg/ver_cont_var/uos3/uos3_ko1.htm errors are particularly undesirable. The MAE and the RMSE can be used together to diagnose the variation in the errors in a set of forecasts. The RMSE will always be larger or equal to the MAE; the greater difference between them, the greater the variance in the individual errors in the sample. If the RMSE=MAE, then all the errors are of the same magnitude Both the MAE and RMSE can range from 0 to ∞. They are negatively-oriented scores: Lower values are better. Loading Questions ... You read that a set of temperature forecasts shows a MAE of 1.5 degrees and a RMSE of 2.5 degrees. What does this mean? Choose the best answer: Feedback This is true, but not the best answer. If RMSE>MAE, then there is variation in the errors. Feedback This is true too, the RMSE-MAE difference isn't large enough to indicate the presence of very large errors. Feedback This is true, by the definition of the MAE, but not the best answer. Feedback This is the best answer. See the other choices for more feedback.
Up API Reference API Reference This documentation is for scikit-learn version 0.18 — Other versions If you use the software, http://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_absolute_error.html please consider citing scikit-learn. sklearn.metrics.mean_absolute_error sklearn.metrics.mean_absolute_error¶ sklearn.metrics.mean_absolute_error(y_true, y_pred, sample_weight=None, multioutput='uniform_average')[source]¶ Mean absolute error regression loss Read more in the 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, absolute error n_outputs) Estimated target values. sample_weight : array-like of shape = (n_samples), optional Sample weights. multioutput : string in [‘raw_values', ‘uniform_average'] or array-like of shape (n_outputs) Defines aggregating of multiple output values. Array-like value defines weights used to average errors. ‘raw_values' : Returns a full set of errors in mean absolute error 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]) ... 0.849... © 2010 - 2016, scikit-learn developers (BSD License). Show this page source Previous