Multiobjective

Multiobjective metrics evaluate model performance across multiple, often conflicting, objectives simultaneously (e.g., Accuracy vs. Diversity). These metrics aggregate individual scores to assess the overall trade-off or distance from an ideal state.

API Reference

For class signatures and source code, see the Multiobjective Metrics API Reference.

EucDistance

Euclidean Distance (EucDistance@K). Computes the Euclidean Distance between the model's performance and an Utopia Point (ideal performance). A lower value indicates the model is closer to the desired objectives.

\[ \text{EucDistance} = \sqrt{\sum_{i=1}^{n} \left( s_i - u_i \right)^2} \]

where \(s_i\) is the score of sub-metric \(i\) and \(u_i\) is the utopia (ideal) value for that metric.

For further details, please refer to this link and this paper.

evaluation:
    top_k: [10, 20, 50]
    complex_metrics:
        - name: EucDistance
          params:
              metric_names: [Precision, Recall, nDCG]
              utopia_points: [1.0, 1.0, 1.0]

Hypervolume

Hypervolume (Hypervolume@K). Measures the volume of the objective space dominated by the model's performance relative to a Nadir Point (worst-case reference). A higher volume indicates a better trade-off between metrics.

\[ \text{HV} = \prod_{i=1}^{n} \max\!\left(0,\; d_i\right), \quad d_i = \begin{cases} s_i - n_i & \text{if higher is better} \\ n_i - s_i & \text{otherwise} \end{cases} \]

where \(s_i\) is the score of sub-metric \(i\) and \(n_i\) is the nadir (worst-case) reference value.

For further details, please refer to this book and this paper.

evaluation:
    top_k: [10, 20, 50]
    complex_metrics:
        - name: Hypervolume
          params:
              metric_names: [Precision, Recall, nDCG]
              nadir_points: [0.0, 0.0, 0.0]
              higher_is_better: [True, True, True]