# A Deep Learning Library for X-Risk Optimization

## Why LibAUC?

LibAUC is a novel deep learning library to offer an easier way to directly optimize commonly used performance measures and losses with user-friendly APIs. LibAUC has broad applications in AI for tackling both classic and emerging challenges, such as **Classification of Imbalanced Data (CID)**, **Learning to Rank (LTR)**, and **Contrastive Learning of Representation (CLR)**.

LibAUC provides a unified framework to abstract the optimization of a family of risk functions called **X-Risk**, including surrogate losses for AUROC, AUPRC/AP, and partial AUROC that are suitable for CID, surrogate losses for NDCG, top-K NDCG, and listwise losses that are used in LTR, and global contrastive losses for CLR. Here’s an overview:

For more details, please check our LibAUC paper.

## What is X-Risk?

LibAUC is powered by **Deep X-Risk Optimization (DXO)**, where **X-Risk** formally refers to a family of compositional measures in which the loss function of each data point is defined in a way that contrasts the data point with a large number of others. Mathematically, **X-Risk** optimization can be cast into the following abstract optimization problem:

where \(g: \mathbb{R}^d \mapsto \mathcal{R}\) is a mapping, \(f_i: \mathcal{R} \mapsto \mathbb{R}\) is a simple deterministic function, \(\mathcal{S}=\left\{\mathbf{z}_1, \ldots, \mathbf{z}_m\right\}\) denotes a target set of data points, and \(\mathcal{S}_i\) denotes a reference set of data points dependent or independent of \(\mathbf{z}_i\). For mathmetrical derviations, please check the DXO paper.

## Reference

If any questions, please reach out to Zhuoning Yuan and Tianbao Yang. If you find our works helpful, please consider citing the following papers:

```
@inproceedings{yuan2023libauc,
title={LibAUC: A Deep Learning Library for X-risk Optimization.},
author={Zhuoning Yuan and Dixian Zhu and Zi-Hao Qiu and Gang Li and Xuanhui Wang and Tianbao Yang},
booktitle={29th SIGKDD Conference on Knowledge Discovery and Data Mining},
year={2023}}
```

```
@article{yang2022algorithmic,
title={Algorithmic Foundation of Deep X-risk Optimization},
author={Yang, Tianbao},
journal={arXiv preprint arXiv:2206.00439},
year={2022}}
```