AP@k (average precision)#
This metric is also counted for each object individually. So for \(j\)-th object it’ll take following formula:
\[AP_j@k=\frac{1}{N_j} \sum_{t=1}^k precision_j@t*r_{tj}\]
Where \(N_j=\sum_{i}^k r_{ij}\) - number of relevant items for \(j\)-th object in \(k\) best according to the model. We take \(k\) best elements and try to compute \(precision@t\) for each \(t=\overline{1,k}\). We add to the numerator only those precisions that correspond to the relevant values - in irrelevant cases \(r_{tj}=0\) will remove the corresponding \(precision@t\).
import pandas as pd
from IPython.display import HTML, Latex, Markdown
R_frame = pd.read_parquet("example.parquet")
Consider specific#
\(t\) |
\(r_{i_t}\) |
\(precision@t\) |
\(precision@t \times r_{i_t}\) |
|---|---|---|---|
1 |
1 |
1.0 |
1.0 |
2 |
0 |
0.5 |
0.0 |
3 |
0 |
0.33 |
0.0 |
4 |
1 |
0.5 |
0.5 |
5 |
1 |
0.6 |
0.6 |
6 |
0 |
0.5 |
0.0 |
7 |
1 |
- |
- |
8 |
1 |
- |
- |
9 |
0 |
- |
- |
10 |
0 |
- |
- |