RocAuc Pairwise objective for gradient boosting

This is GPU implementation of rocauc pairwise objective for gradient boosting: $$L = \sum_{i, j} \left(\hat P_{ij}\log{P_{ij}} + (1 - \hat P_{ij})\log{(1 - P_{ij})}\right)\lvert \Delta_{AUC_{ij}}\vert$$ Where: $$P_{ij} = \frac{1}{1 + e^{-(x_i - x_j)}} $$ This package could be used to solve classification problems with relative small numbers of objects, where you need to improve rocauc score.
Also there is cpu multithread implementation of this objectives and losses.

Objectives that are implemented in this package

1. Sigmoid pairwise loss. (GPU or CPU implementations) $$L = \sum_{i, j}\left(\hat P_{ij}\log{P_{ij}} + (1 - \hat P_{ij})\log{(1 - P_{ij})}\right)$$
2. RocAuc Pairwise Loss with approximate auc computation. (GPU or CPU implementations) $$L = \sum_{i, j} \left(\hat P_{ij}\log{P_{ij}} + (1 - \hat P_{ij})\log{(1 - P_{ij})}\right)\lvert \Delta_{AUC^{approx}_{ij}}\vert$$
3. RocAuc Pairwise Loss Exact (GPU or CPU implementations) with exact auc computation. This could be more compute intensive, but this loss might be helpfull for first boosting rounds (if you are using gradient boosting) $$L = \sum_{i, j} \left(\hat P_{ij}\log{P_{ij}} + (1 - \hat P_{ij})\log{(1 - P_{ij})}\right)\lvert \Delta_{AUC^{exact}_{ij}}\vert$$
4. RocAuc Pairwise Loss Exact Smoothened (GPU or CPU implementations). This loss allows you to incorporate information about equal instances. Because $\Delta_{AUC_{ij}} = 0$ if $y_i = y_j$. So we just add small $\epsilon > 0$ in equation. $$L = \sum_{i, j} \left(\hat P_{ij}\log{P_{ij}} + (1 - \hat P_{ij})\log{(1 - P_{ij})}\right)(\epsilon + \lvert \Delta_{AUC^{exact}_{ij}}\vert)$$

Installation

You can use pip to install this package.

pip install roc_auc_pairwise

Project page on PyPI - roc_auc_pairwise

Basic usage examples.

• You can see example notebook: ./examples/gradient_boosting_example.ipynb
• Or you can try to run example notebook on Google Colab
• Or you can try to run example notebook on Kaggle

Performance

Losses, Gradients and Hessians are require $\mathcal{O}(n^2)$ to compute. So it is very compute intensive.
Here you can see package perfomance on Intel Core i5 10600KF and Nvidia RTX 3060.

References

[1] Sean J. Welleck, Efficient AUC Optimization for Information Ranking Applications, IBM USA (2016)
[2] Burges, C.J.: From ranknet to lambdarank to lambdamart: An overview. Learning (2010)
[3] Calders, T., Jaroszewicz, S.: Efficient auc optimization for classification. Knowledge Discovery in Databases. (2007)