In this paper, we study stochastic optimization of areas under
precision-recall curves (AUPRC), which is widely used for combating imbalanced
classification tasks. Although a few methods have been proposed for maximizing
AUPRC, stochastic optimization of AUPRC with convergence guarantee remains an
undeveloped territory. A state-of-the-art complexity is $O(1/\epsilon^5)$ for
finding an $\epsilon$-stationary solution. In this paper, we further improve
the stochastic optimization of AURPC by (i) developing novel stochastic
momentum methods with a better iteration complexity of $O(1/\epsilon^4)$ for
finding an $\epsilon$-stationary solution; and (ii) designing a novel family of
stochastic adaptive methods with the same iteration complexity, which enjoy
faster convergence in practice. To this end, we propose two innovative
techniques that are critical for improving the convergence: (i) the biased
estimators for tracking individual ranking scores are updated in a randomized
coordinate-wise manner; and (ii) a momentum update is used on top of the
stochastic gradient estimator for tracking the gradient of the objective. The
novel analysis of Adam-style updates is also one main contribution. Extensive
experiments on various data sets demonstrate the effectiveness of the proposed
algorithms. Of independent interest, the proposed stochastic momentum and
adaptive algorithms are also applicable to a class of two-level stochastic
dependent compositional optimization problems.

本文研究随机优化下精度 - 召回曲线（AUPRC）的最优化问题，通过开发随机动量方法和随机自适应方法，分别提升算法的收敛速度和迭代次数复杂度；通过实验验证效果。

动量加速随机 AUPRC 最大化的收敛

Momentum Accelerates the Convergence of Stochastic AUPRC Maximization

Properties of molecules are indicative of their functions and thus are useful
in many applications. With the advances of deep learning methods, computational
approaches for predicting molecular properties are gaining increasing momentum.
However, there lacks customized and advanced methods and comprehensive tools
for this task currently. Here we develop a suite of comprehensive machine
learning methods and tools spanning different computational models, molecular
representations, and loss functions for molecular property prediction and drug
discovery. Specifically, we represent molecules as both graphs and sequences.
Built on these representations, we develop novel deep models for learning from
molecular graphs and sequences. In order to learn effectively from highly
imbalanced datasets, we develop advanced loss functions that optimize areas
under precision-recall curves. Altogether, our work not only serves as a
comprehensive tool, but also contributes towards developing novel and advanced
graph and sequence learning methodologies. Results on both online and offline
antibiotics discovery and molecular property prediction tasks show that our
methods achieve consistent improvements over prior methods. In particular, our
methods achieve #1 ranking in terms of both ROC-AUC and PRC-AUC on the AI Cures
Open Challenge for drug discovery related to COVID-19. Our software is released
as part of the MoleculeX library under AdvProp.

我们开发了一套深度学习方法和综合工具，针对分子属性预测和药物发现，跨越不同的计算模型、分子表示和损失函数。我们将分子表示为图和序列，并围绕这些表示所构建的深度模型进行学习。为了有效地从高度不平衡的数据集中学习，开发了优化精度 - 召回曲线下面积的先进损失函数。在在线和离线抗生素发现和分子属性预测任务中的结果表明，我们的方法相对于之前的方法实现了持续的改进，并在与 COVID-19 相关的 AI Cures Open Challenge 中以 ROC-AUC 和 PRC-AUC 方面均排名第一。

分子属性预测和药物发现的高级图形和序列神经网络

Advanced Graph and Sequence Neural Networks for Molecular Property  Prediction and Drug Discovery

In this article we revisit the definition of Precision-Recall (PR) curves for
generative models proposed by Sajjadi et al. (arXiv:1806.00035). Rather than
providing a scalar for generative quality, PR curves distinguish mode-collapse
(poor recall) and bad quality (poor precision). We first generalize their
formulation to arbitrary measures, hence removing any restriction to finite
support. We also expose a bridge between PR curves and type I and type II error
rates of likelihood ratio classifiers on the task of discriminating between
samples of the two distributions. Building upon this new perspective, we
propose a novel algorithm to approximate precision-recall curves, that shares
some interesting methodological properties with the hypothesis testing
technique from Lopez-Paz et al (arXiv:1610.06545). We demonstrate the interest
of the proposed formulation over the original approach on controlled
multi-modal datasets.

重新定义 Sajjadi 等人提出的生成模型的 Precision-Recall curves，推广到任意度量，建立 PR curves 和似然比分类器的 type I 和 type II error rates 之间的联系，并提出新算法近似 PR curves，证明该算法在受控多模态数据集上优于原始方法。

对生成模型评估中的精确度和召回率定义的重新审视

Revisiting Precision and Recall Definition for Generative Model  Evaluation

Precision-recall (PR) curves and the areas under them are widely used to
summarize machine learning results, especially for data sets exhibiting class
skew. They are often used analogously to ROC curves and the area under ROC
curves. It is known that PR curves vary as class skew changes. What was not
recognized before this paper is that there is a region of PR space that is
completely unachievable, and the size of this region depends only on the skew.
This paper precisely characterizes the size of that region and discusses its
implications for empirical evaluation methodology in machine learning.

该论文精确刻画了不可达到的 PR 空间区域的大小，并讨论了它对机器学习中的经验评估方法的影响。