The indices used in evaluating prediction results of this component are described below.

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  * - Formula
    - Description
  * - :math:`X_{\mbox{p}}`
    - Array of predicted value.
  * - :math:`X_{\mbox{a}}`
    - Array of actual value.
  * - :math:`\mbox{mean}(X)`
    - Mean of :math:`X`.
  * - :math:`\mbox{median}(X)`
    - Median value in :math:`X`.
  * - :math:`\mbox{max}(X)`
    - Maximum value in :math:`X`.
  * - :math:`[\cdot]_+`
    - A function which returns the argument directly if it is greater than :math:`0`, otherwise returns :math:`0`.

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.. list-table::
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  * - Evaluation Index
    - Type
    - Description
  * - root_mean_squared_error
    - float
    - | RMSE (Root Mean Square Error), which is the square root of the mean squared error as shown below:
      |
      | :math:`\sqrt{\mbox{mean}((X_{\mbox{p}} - X_{\mbox{a}})^2)}`
  * - root_median_squared_error
    - float
    - | RMdSE (Root Median Square Error), which is the square root of the median squared error as shown below:
      |
      | :math:`\sqrt{\mbox{median}((X_{\mbox{p}} - X_{\mbox{a}})^2)}`
  * - mean_abs_error
    - float
    - | Mean of absolute error as shown below:
      |
      | :math:`\mbox{mean}(|X_{\mbox{p}} - X_{\mbox{a}}|)`
  * - median_abs_error
    - float
    - | Median of absolute error as shown below:
      |
      | :math:`\mbox{median}(|X_{\mbox{p}} - X_{\mbox{a}}|)`
  * - max_abs_error
    - float
    - | Maximum value of absolute error.
      |
      | :math:`\mbox{max}(|X_{\mbox{p}} - X_{\mbox{a}}|)`
  * - relative_root_mean_squared_error
    - float
    - | The square root of the mean squared relative error as shown below:
      |
      | :math:`\sqrt{\mbox{mean}((\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}})^2)}`
  * - relative_root_median_squared_error
    - float
    - | The square root of the median squared relative error as shown below:
      |
      | :math:`\sqrt{\mbox{median}((\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}})^2)}`
  * - relative_mean_abs_error
    - float
    - | The mean abs relative error as shown below:
      |
      | :math:`\mbox{mean}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)`
  * - relative_median_abs_error
    - float
    - | The median abs relative error as shown below:
      |
      | :math:`\mbox{median}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)`
  * - relative_max_abs_error
    - float
    - | The maximum abs relative error as shown below:
      |
      | :math:`\mbox{max}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)`
  * - positive_side_root_mean_squared_error
    - float
    - ``root_mean_squared_error`` for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}`.
  * - positive_side_root_median_squared_error
    - float
    - ``root_median_squared_error`` for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}`.
  * - positive_side_mean_abs_error
    - float
    - ``mean_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}`.
  * - positive_side_median_abs_error
    - float
    - ``median_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}`.
  * - positive_side_max_abs_error
    - float
    - ``max_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}`.
  * - negative_side_root_mean_squared_error
    - float
    - ``root_mean_squared_error`` for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}`.
  * - negative_side_root_median_squared_error
    - float
    - ``root_median_squared_error`` for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}`.
  * - negative_side_mean_abs_error
    - float
    - ``mean_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}`.
  * - negative_side_median_abs_error
    - float
    - ``median_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}`.
  * - negative_side_max_abs_error
    - float
    - ``max_abs_error`` for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}`.
  * - max_upside_err_mean_obs
    - float
    - | Proportion of the maximum error for samples that satisfy the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}` against the mean of actual values as shown below:
      |
      | :math:`\frac{\mbox{max}({\large X}_{\mbox{p}} {\large - X}_{\mbox{a}})}{\mbox{mean}({\large X}_{\mbox{a}})}`
  * - mean_upside_err_mean_obs
    - float
    - | Proportion of the mean error whose value is only available if it satisfies the condition, :math:`X_{\mbox{p}} > X_{\mbox{a}}` (otherwise :math:`0`) against the mean of actual values as shown below:
      |
      | :math:`\frac{\mbox{mean}([{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}]_+)}{\mbox{mean}({\large X}_{\mbox{a}})}`
  * - max_downside_err_mean_obs
    - float
    - | Proportion of the maximum error for samples that satisfy the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}` against the mean of actual values as shown below:
      |
      | :math:`\frac{\mbox{max}({\large X}_{\mbox{a}} {\large - X}_{\mbox{p}})}{\mbox{mean}({\large X}_{\mbox{a}})}`
  * - mean_downside_err_mean_obs
    - float
    - | Proportion of the mean error whose value is only available if it satisfies the condition, :math:`X_{\mbox{a}} \geq X_{\mbox{p}}` (otherwise :math:`0`) against the mean of actual values as shown below:
      |
      | :math:`\frac{\mbox{mean}([{\large X}_{\mbox{a}} - {\large X}_{\mbox{p}}]_+)}{\mbox{mean}({\large X}_{\mbox{a}})}`
  * - negative_pred_num
    - int
    - The number of the samples that satisfy the condition, :math:`X_{\mbox{p}} < 0`.
  * - std_root_mean_squared_error
    - float
    - ``root_mean_squared_error`` for standardized predicted/actual values.
  * - std_root_median_squared_error
    - float
    - ``root_median_squared_error`` for standardized predicted/actual values.
  * - std_mean_abs_error
    - float
    - ``mean_abs_error`` for standardized predicted/actual values.
  * - std_median_abs_error
    - float
    - ``median_abs_error`` for standardized predicted/actual values.
  * - std_max_abs_error
    - float
    - ``max_abs_error`` for standardized predicted/actual values.
  * - std_relative_root_mean_squared_error
    - float
    - ``relative_root_mean_squared_error`` for standardized predicted/actual values.
  * - std_relative_root_median_squared_error
    - float
    - ``relative_root_median_squared_error`` for standardized predicted/actual values.
  * - std_relative_mean_abs_error
    - float
    - ``relative_mean_abs_error`` for standardized predicted/actual values.
  * - std_relative_median_abs_error
    - float
    - ``relative_median_abs_error`` for standardized predicted/actual values.
  * - std_relative_max_abs_error
    - float
    - ``relative_max_abs_error`` for standardized predicted/actual values.
  * - std_positive_side_root_mean_squared_error
    - float
    - ``positive_side_root_mean_squared_error`` for standardized predicted/actual values.
  * - std_positive_side_root_median_squared_error
    - float
    - ``positive_side_root_median_squared_error`` for standardized predicted/actual values.
  * - std_positive_side_mean_abs_error
    - float
    - ``positive_side_mean_abs_error`` for standardized predicted/actual values.
  * - std_positive_side_median_abs_error
    - float
    - ``positive_side_median_abs_error`` for standardized predicted/actual values.
  * - std_positive_side_max_abs_error
    - float
    - ``positive_side_max_abs_error`` for standardized predicted/actual values.
  * - std_negative_side_root_mean_squared_error
    - float
    - ``negative_side_root_mean_squared_error`` for standardized predicted/actual values.
  * - std_negative_side_root_median_squared_error
    - float
    - ``negative_side_root_median_squared_error`` for standardized predicted/actual values.
  * - std_negative_side_mean_abs_error
    - float
    - ``negative_side_mean_abs_error`` for standardized predicted/actual values.
  * - std_negative_side_median_abs_error
    - float
    - ``negative_side_median_abs_error`` for standardized predicted/actual values.
  * - std_negative_side_max_abs_error
    - float
    - ``negative_side_max_abs_error`` for standardized predicted/actual values.
  * - std_max_upside_err_mean_obs
    - float
    - ``max_upside_err_mean_obs`` for standardized predicted/actual values.
  * - std_mean_upside_err_mean_obs
    - float
    - ``mean_upside_err_mean_obs`` for standardized predicted/actual values.
  * - std_max_downside_err_mean_obs
    - float
    - ``max_downside_err_mean_obs`` for standardized predicted/actual values.
  * - std_mean_downside_err_mean_obs
    - float
    - ``mean_downside_err_mean_obs`` for standardized predicted/actual values.
  * - std_negative_pred_num
    - int
    - ``negative_pred_num`` for standardized predicted/actual values.
