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Roland R. Draxler - One of the best experts on this subject based on the ideXlab platform.

  • Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature
    Geoscientific Model Development, 2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.

  • root mean square error rmse or mean absolute error mae arguments against avoiding rmse in the literature
    Geoscientific Model Development, 2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.

  • Root mean square error (RMSE) or mean absolute error (MAE)
    2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error and thus the MAE would be a better metric for that purpose. Their paper has been widely cited and may have influenced many researchers in choosing MAE when presenting their model evaluation statistics. However, we contend that the proposed avoidance of RMSE and the use of MAE is not the solution to the problem. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric.

Tianfeng Chai - One of the best experts on this subject based on the ideXlab platform.

  • Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature
    Geoscientific Model Development, 2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.

  • root mean square error rmse or mean absolute error mae arguments against avoiding rmse in the literature
    Geoscientific Model Development, 2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.

  • Root mean square error (RMSE) or mean absolute error (MAE)
    2014
    Co-Authors: Tianfeng Chai, Roland R. Draxler
    Abstract:

    Abstract. Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error and thus the MAE would be a better metric for that purpose. Their paper has been widely cited and may have influenced many researchers in choosing MAE when presenting their model evaluation statistics. However, we contend that the proposed avoidance of RMSE and the use of MAE is not the solution to the problem. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric.

Y Neuvo - One of the best experts on this subject based on the ideXlab platform.

  • Optimal parallel stack filtering under the mean absolute error criterion
    IEEE transactions on image processing : a publication of the IEEE Signal Processing Society, 1994
    Co-Authors: Bing Zeng, Y Neuvo
    Abstract:

    The authors extend the configuration of stack filtering to develop a new class of stack-type filters called parallel stack filters (PSFs). As a basis for the parallel stack filtering, the block threshold decomposition (BTD) is introduced, and its properties are investigated. The design of optimal PSHs under the mean absolute error (MAE) criterion is shown to be similar to the minimum MAE stack filtering theory. The only difference is that one needs now to design more than one stack filter that together construct an optimal PSF. As a result, while reviewing briefly the optimal stack filtering theory, they will put more efforts to demonstrate, via several examples, the improvement by switching from stack filtering to parallel stack filtering for the task of image noise removal. >

  • Adaptive generalized stack filtering under the mean-absolute-error criterion
    Nonlinear Image Processing III, 1992
    Co-Authors: L Yin, Jaakko Astola, Y Neuvo
    Abstract:

    A new adaptive algorithm is developed in this paper for determining optimal generalized stack (GS) filters under the mean absolute error criterion. This algorithm, based on the neural network representation of Boolean functions, is much more efficient than the traditional truth table based algorithms. This is because: (1) the number of variables to represent a GS filter is considerably reduced when a set of neurons is used to represent a GS filter, where the number of the variables is proportional to the filter window width, and (2) the procedure of enforcing the stacking constraints of GS filters is greatly simplified since a sufficient condition is derived under which the neurons satisfy the stacking property. Experimental results from image restoration are provided to demonstrate the performance of the new adaptive GS filters.

  • optimal weighted order statistic filters under the mean absolute error criterion
    International Conference on Acoustics Speech and Signal Processing, 1991
    Co-Authors: L Yin, Jaakko Astola, Y Neuvo
    Abstract:

    Based on the relationship between weighted order statistic (WOS) filters and threshold logic, an algorithm is developed for determining optimal WOS filters under the mean absolute error (MAE) criterion. This algorithm requires much less computation than the adaptive stack filtering algorithm. In addition, experimental results in image restoration demonstrate that the WOS filters obtained by the proposed algorithm can even give better results than the adaptive stack filters. >

  • ICASSP - Optimal weighted order statistic filters under the mean absolute error criterion
    [Proceedings] ICASSP 91: 1991 International Conference on Acoustics Speech and Signal Processing, 1991
    Co-Authors: L Yin, Jaakko Astola, Y Neuvo
    Abstract:

    Based on the relationship between weighted order statistic (WOS) filters and threshold logic, an algorithm is developed for determining optimal WOS filters under the mean absolute error (MAE) criterion. This algorithm requires much less computation than the adaptive stack filtering algorithm. In addition, experimental results in image restoration demonstrate that the WOS filters obtained by the proposed algorithm can even give better results than the adaptive stack filters. >

J.-h. Lin - One of the best experts on this subject based on the ideXlab platform.

  • ICASSP - Minimum mean absolute error nonlinear filtering
    ICASSP-88. International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: J.-h. Lin, E.j. Coyle
    Abstract:

    A class of sliding window operators called generalized stack filters is developed. This class of filters, which includes all rank order filters, stack filters, and digital morphological filters, is the set of all filters possessing the threshold decomposition architecture and a consistency property, called the stacking property. A linear program is provided which determines a generalized stack filter which minimizes the mean absolute error (MAE) between the output of the filter and a desired input signal, given noisy observations of that signal. These results show that choosing the generalized stack filter which minimizes the MAE is equivalent to massively parallel threshold-crossing decision making when these decisions are consistent with each other. >

  • Generalized stack filters and minimum mean absolute error estimation
    1988. IEEE International Symposium on Circuits and Systems, 1
    Co-Authors: J.-h. Lin, Edward J. Coyle
    Abstract:

    A class of sliding window operators called generalized stack filters is developed. This class of filters, which includes all rank order filters, stack filters, and digital morphological filters, is the set of all filters possessing the threshold decomposition architecture and a consistency property called the stacking property. A linear program is provided which determines a generalized stack filter which minimizes the mean absolute error (MAE) between the output of the filter and a desired input signal, given noisy observations of that signal. These results show that choosing the generalized stack filter that minimizes the MAE is equivalent to massively parallel threshold-crossing decision-making when these decisions are consistent with each other. >

Colin F. N. Cowan - One of the best experts on this subject based on the ideXlab platform.