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

Formula

Description

\(X_{\mbox{p}}\)

Array of predicted value.

\(X_{\mbox{a}}\)

Array of actual value.

\(\mbox{mean}(X)\)

Mean of \(X\).

\(\mbox{median}(X)\)

Median value in \(X\).

\(\mbox{max}(X)\)

Maximum value in \(X\).

\([\cdot]_+\)

A function which returns the argument directly if it is greater than \(0\), otherwise returns \(0\).


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:

\(\sqrt{\mbox{mean}((X_{\mbox{p}} - X_{\mbox{a}})^2)}\)

root_median_squared_error

float

RMdSE (Root Median Square Error), which is the square root of the median squared error as shown below:

\(\sqrt{\mbox{median}((X_{\mbox{p}} - X_{\mbox{a}})^2)}\)

mean_abs_error

float

Mean of absolute error as shown below:

\(\mbox{mean}(|X_{\mbox{p}} - X_{\mbox{a}}|)\)

median_abs_error

float

Median of absolute error as shown below:

\(\mbox{median}(|X_{\mbox{p}} - X_{\mbox{a}}|)\)

max_abs_error

float

Maximum value of absolute error.

\(\mbox{max}(|X_{\mbox{p}} - X_{\mbox{a}}|)\)

relative_root_mean_squared_error

float

The square root of the mean squared relative error as shown below:

\(\sqrt{\mbox{mean}((\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}})^2)}\)

relative_root_median_squared_error

float

The square root of the median squared relative error as shown below:

\(\sqrt{\mbox{median}((\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}})^2)}\)

relative_mean_abs_error

float

The mean abs relative error as shown below:

\(\mbox{mean}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)\)

relative_median_abs_error

float

The median abs relative error as shown below:

\(\mbox{median}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)\)

relative_max_abs_error

float

The maximum abs relative error as shown below:

\(\mbox{max}(|\frac{{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}}{ {\large X}_{\mbox{a}}}|)\)

positive_side_root_mean_squared_error

float

root_mean_squared_error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\).

positive_side_root_median_squared_error

float

root_median_squared_error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\).

positive_side_mean_abs_error

float

mean_abs_error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\).

positive_side_median_abs_error

float

median_abs_error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\).

positive_side_max_abs_error

float

max_abs_error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\).

negative_side_root_mean_squared_error

float

root_mean_squared_error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\).

negative_side_root_median_squared_error

float

root_median_squared_error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\).

negative_side_mean_abs_error

float

mean_abs_error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\).

negative_side_median_abs_error

float

median_abs_error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\).

negative_side_max_abs_error

float

max_abs_error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\).

max_upside_err_mean_obs

float

Proportion of the maximum error for samples that satisfy the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\) against the mean of actual values as shown below:

\(\frac{\mbox{max}({\large X}_{\mbox{p}} {\large - X}_{\mbox{a}})}{\mbox{mean}({\large X}_{\mbox{a}})}\)

mean_upside_err_mean_obs

float

Proportion of the mean error whose value is only available if it satisfies the condition, \(X_{\mbox{p}} > X_{\mbox{a}}\) (otherwise \(0\)) against the mean of actual values as shown below:

\(\frac{\mbox{mean}([{\large X}_{\mbox{p}} {\large - X}_{\mbox{a}}]_+)}{\mbox{mean}({\large X}_{\mbox{a}})}\)

max_downside_err_mean_obs

float

Proportion of the maximum error for samples that satisfy the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\) against the mean of actual values as shown below:

\(\frac{\mbox{max}({\large X}_{\mbox{a}} {\large - X}_{\mbox{p}})}{\mbox{mean}({\large X}_{\mbox{a}})}\)

mean_downside_err_mean_obs

float

Proportion of the mean error whose value is only available if it satisfies the condition, \(X_{\mbox{a}} \geq X_{\mbox{p}}\) (otherwise \(0\)) against the mean of actual values as shown below:

\(\frac{\mbox{mean}([{\large X}_{\mbox{a}} - {\large X}_{\mbox{p}}]_+)}{\mbox{mean}({\large X}_{\mbox{a}})}\)

negative_pred_num

int

The number of the samples that satisfy the condition, \(X_{\mbox{p}} < 0\).

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.