---
metadata:
  - name: generator
    content: Diplodoc Platform v5.52.0
alternate:
  - https://catboost.ai/docs/en/references/filtereddcg.md
  - href: en/references/filtereddcg.md
    type: text/markdown
    title: Markdown version
  - href: ../llms.txt
    type: text/markdown
    title: llms.txt
---
> **Documentation Index:** Fetch the complete configuration index at https://catboost.ai/docs/en/llms.txt

# FilteredDCG

<!-- source: en/_includes/work_src/reusage-common-phrases/ranking-quality-assessment.md -->
This function is usually used to assess the quality of ranking.
<!-- endsource: en/_includes/work_src/reusage-common-phrases/ranking-quality-assessment.md -->

- [Calculation principles](#calculation)
- [User-defined parameters](#user-defined-parameters)

## Calculation principles {#calculation}

<!-- source: en/_includes/work_src/reusage-common-phrases/function-calculation.md -->
The calculation of this function consists of the following steps:
<!-- endsource: en/_includes/work_src/reusage-common-phrases/function-calculation.md -->


1. Filter out all objects with negative predicted relevancies ($a_i$).

1. The FilteredDCG metric is calculated for each group ($group \in groups$) with filtered objects.

   The calculation principle depends on the specified value of the `type` and `denominator` parameters:

   | type/denominator|LogPosition| Position|
   |-----------------|-----------------------------------------------------|-------------------------------------------------|
   | **Base** | $FilteredDCG(group) = \sum\limits_{i}\displaystyle\frac{t_{g(i,group)}}{log_{2}(i+1)}$| $FilteredDCG(group) = \sum\limits_{i}\displaystyle\frac{t_{g(i,group)}}{i}$|
   | **Exp**  | $FilteredDCG(group) = \sum\limits_{i}\displaystyle\frac{2^{t_{g(i,group)}} - 1}{log_{2}(i+1)}$| $FilteredDCG(group) = \sum\limits_{i}\displaystyle\frac{2^{t_{g(i,group)}} - 1}{i}$|

   $t_{g(i, group)}$ is the label value for the i-th object in the group after filtering objects with negative predicted relevancies.

1. The aggregated value of the metric for all groups is calculated as follows:
    $FilteredDCG = \frac{\sum\limits_{group \in groups}  FilteredDCG(group)}{|groups|}$


## User-defined parameters {#user-defined-parameters}

### type

#### Description

Metric calculation principles.

Possible values:
- Base
- Exp

_Default_: Base


### denominator

#### Description

Metric denominator type.

Possible values:
- LogPosition
- Position

_Default_: Position