# Multiregression: objectives and metrics

## Objectives and metrics

### MultiRMSE

$\sqrt{\displaystyle\frac{\sum\limits_{i=1}^{N}\sum\limits_{d=1}^{dim}(a_{i,d} - t_{i, d})^{2} w_{i}}{\sum\limits_{i=1}^{N} w_{i}}}$

$dim$ is the identifier of the dimension of the label.

Usage information

User-defined parameters

use_weights

Use object/group weights to calculate metrics if the specified value is true and set all weights to 1 regardless of the input data if the specified value is false.

Default: true

### MultiRMSEWithMissingValues

$\sqrt{\sum_{d=1}^{dim} \frac{\sum_{i=1}^N Num(a_{i,d}, t_{i,d}, w_i)}{\sum_{i=1}^N Den(t_{i,d}, w_i)}}$

$Num(a, t, w) = \begin{cases} w(a - t)^2, \space if \space t \neq NaN\\ 0 \end{cases}$

$Den(t, w) = \begin{cases} w, \space if \space t \neq NaN\\ 0 \end{cases}$

$dim$ is the identifier of the dimension of the label.

Usage information

User-defined parameters

use_weights

Use object/group weights to calculate metrics if the specified value is true and set all weights to 1 regardless of the input data if the specified value is false.

Default: true

## Used for optimization

Name Optimization GPU Support
MultiRMSE + -
MultiRMSEWithMissingValues + -