Average 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 − y i | = 1 standard deviation absolute error n ∑ i = 1 n | e i | . {\displaystyle \mathrm {MAE}
Average Absolute Deviation
={\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 is an average of the absolute errors | e
Average Relative Error
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 y_{i}} the true value. Note that alternative formulations may include relative frequencies
Average Percent Error
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 deviation" is sometimes used in confusion with the more standard definition of mean absolute deviation. The average standard deviation 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 message) See also[edit] Least absolute deviations Mean absolute percentage error Mean percentage error Symmetric mean absolute percentage error References[edit] ^ "2.5 Evaluating forecast accuracy | OTexts". www.otexts.org. Retrieved 2016-05-18. ^ Hyndman, R. and Koehler A. (2005). "Anoth
error (MAE) is https://en.wikipedia.org/wiki/Mean_absolute_error a quantity used to measure how close forecasts or predictions are to the eventual outcomes. The mean absolute error https://www.kaggle.com/wiki/MeanAbsoluteError is given by $$ \mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \left| y_i - \hat{y_i}\right| =\frac{1}{n}\sum_{i=1}^n \left| e_i \right|. $$ Where $$ AE = |e_i| = |y_i-\hat{y_i}| $$ $$ Actual = y_i $$ $$ Predicted = \hat{y_i} $$ ## Competitions using this metric: * https://www.kaggle.com/c/how-much-did-it-rain-ii Last Updated: 2016-03-05 14:48 by inversion © 2016 Kaggle Inc Our Team Careers Terms Privacy Contact/Support
August 24 Nate Watson named new President of CAN. Nate Watson on May 15, 2015 January 23, 2012 Using Mean Absolute Error for Forecast Accuracy Using mean absolute error, CAN helps our clients that are interested in determining the accuracy of industry forecasts. They want to know if they can trust these industry http://canworksmart.com/using-mean-absolute-error-forecast-accuracy/ forecasts, and get recommendations on how to apply them to improve their strategic planning process. This http://gisgeography.com/mean-absolute-error-mae-gis/ posts is about how CAN accesses the accuracy of industry forecasts, when we don't have access to the original model used to produce the forecast. First, without access to the original model, the only way we can evaluate an industry forecast's accuracy is by comparing the forecast to the actual economic activity. This is a backwards looking forecast, and unfortunately does not provide insight into the accuracy of absolute error the forecast in the future, which there is no way to test. Thus it is important to understand that we have to assume that a forecast will be as accurate as it has been in the past, and that future accuracy of a forecast can be guaranteed. As consumers of industry forecasts, we can test their accuracy over time by comparing the forecasted value to the actual value by calculating three different measures. The simplest measure of forecast accuracy is called Mean average absolute error Absolute Error (MAE). MAE is simply, as the name suggests, the mean of the absolute errors. The absolute error is the absolute value of the difference between the forecasted value and the actual value. MAE tells us how big of an error we can expect from the forecast on average. One problem with the MAE is that the relative size of the error is not always obvious. Sometimes it is hard to tell a big error from a small error. To deal with this problem, we can find the mean absolute error in percentage terms. Mean Absolute Percentage Error (MAPE) allows us to compare forecasts of different series in different scales. For example, we could compare the accuracy of a forecast of the DJIA with a forecast of the S&P 500, even though these indexes are at different levels. Since both of these methods are based on the mean error, they may understate the impact of big, but infrequent, errors. If we focus too much on the mean, we will be caught off guard by the infrequent big error. To adjust for large rare errors, we calculate the Root Mean Square Error (RMSE). By squaring the errors before we calculate their mean and then taking the square root of the mean, we arrive at a measure of the size of the error that gives more weight to the large but infrequent errors than the mean. We can also compare RMSE and MAE to determine w
Maps & Cartography [ September 12, 2016 ] How to Sketch a Voronoi Diagram with Thiessen Polygons Maps & Cartography [ September 10, 2016 ] Lossless Compression vs Lossy Compression Remote Sensing [ September 5, 2016 ] Huff Gravity Model: Who Will Visit Your Store? GIS Analysis Search for: HomeGIS AnalysisMean Absolute Error MAE in GIS Mean Absolute Error MAE in GIS FacebookTwitterSubscribe Last updated: Saturday, July 30, 2016What is Mean Absolute Error? Mean Absolute Error (MAE) measures how far predicted values are away from observed values. It’s a bit different than Root Mean Square Error (RMSE). MAE sums the absolute value of the residual Divides by the number of observations. MAE Formula: Calculating MAE in Excel 1. In A1, type “observed value”. In B2, type “predicted value”. In C3, type “difference”. 2. If you have 10 observations, place observed values in A2 to A11. Place predicted values in B2 to B11. 3. In column C2 to C11, subtract observed value and predicted value. C2 will use this formula: =A2-B2. Copy and paste formula to the last row. 4. Now, calculate MAE. In cell D2, type: =SUMPRODUCT(ABS(C2:C11))/COUNT(C2:C11) Cell D2 is the Mean Absolute Error value. How is MAE used in GIS? MAE is used to validate any type of GIS modelling. MAE quantifies the difference between forecasted and observed values. For example, the SMOS (Soil Moisture Ocean Salinity) passive satellite uses a mathematical model to measure soil moisture in 15 km grid cells. The satellite-derived soil moisture values are the forecasted values. A network of stations on the ground measuring the true soil moisture values is the observed value Forecasted value: Satellite-derived soil moisture value () Observed value: Ground station network soil moisture measurement () Geostatistics Related Articles GIS Analysis Python Minimum or Maximum Values in ArcGIS GIS Analysis Use Principal Component Analysis to Eliminate Redundant Data GIS Analysis How to Build Spatial Regression Models in ArcGIS Be the first to comment Leave a Reply C