[作者-陈君、王浩｜审核-王欣芮]近日，人工智能领域顶级国际会议AAAI-2025（The 39th Annual AAAI Conference on Artificial Intelligence，CCF-A类）公布论文接收结果，录用了信息学院陈洪教授课题组在机器学习理论领域的两项研究成果。

论文一：Error Analysis Affected by Heavy-Tailed Gradients for Non-Convex Pairwise Stochastic Gradient Descent

论文概述：作为机器学习领域一种重要的学习形式，成对学习存在于许多学习范式中，比如度量学习、排序学习、AUC最大化、梯度学习以及最小误差熵准则下的学习。从学习理论的角度来看，大多数文献研究的是单点学习算法的学习保证，很少工作研究成对学习算法的泛化和优化性能保证。本文基于稳定性分析工具发展了非凸成对SGD算法在多种场景下的学习保证。具体来说，考虑到成对学习的数据形式，我们设计了新的一致模型稳定性分析工具，避免了理论分析中成对数据之间依赖性的影响。在损失函数为非凸函数的场景下，我们建立了令人满意的成对SGD算法的泛化理论保证，随后引入更加实际的条件（梯度噪声服从次威布尔分布）替换Lipschitz连续性假设，得到了与前者类似的理论保证。其次，通过引入波利亚克-洛贾谢维奇条件，我们发展了更紧的超额风险上界。最后，将上述理论分析推广到小批量SGD算法，建立了首个基于稳定性分析的泛化理论保证，经验观测验证了我们理论的合理性。

信息学院2022级博士研究生陈君为论文第一作者，陈洪教授为通讯作者，李伟夫副教授等参与了论文的研究工作。该研究获得了国家自然科学基金面上项目、青年基金等的资助。

【英文摘要】In recent years, there have been a growing number of works studying the generalization properties of stochastic gradient descent (SGD) from the perspective of algorithmic stability. However, few of them devote to simultaneously studying the generalization and optimization for the non-convex setting, especially pairwise SGD with heavy-tailed gradient noise. This paper considers the impact of the heavy-tailed gradient noise obeying sub-Weibull distribution on the stability-based learning guarantees for non-convex pairwise SGD by investigating its generalization and optimization jointly. Specifically, based on two novel pairwise uniform model stability tools, we firstly bound the generalization error of pairwise SGD in the general non-convex setting after bridging the quantitative relationships between stability and generalization error. Then, we further consider the practical heavy-tailed sub-Weibull gradient noise condition to establish a refined generalization bound without the bounded gradient condition. Finally, sharper error bounds for generalization and optimization are built by introducing the gradient dominance condition. Comparing these results reveals that sub-Weibull gradient noise brings some positive dependencies on the heavy-tailed strength for generalization and optimization. Furthermore, we extend our analysis to the corresponding pairwise minibatch SGD and derive the first stability-based near-optimal generalization and optimization bounds which are consistent with many empirical observations.

论文二：Knockoffs Inference for Partially Linear Models with Automatic Structure Discovery

论文概述：部分线性模型（PLM）在统计机器学习领域引起了广泛的关注。由于对模型可解释性的高要求，PLM的变量选择能力得到了广泛的研究。然而，现有的研究很少涉及与PLM相关的变量选择的错误发现率（FDR）可控性。为了解决这个问题，我们提出了KI-LAND方法，在控制FDR的同时，对线性和非线性变量进行选择，可用于自动结构发现。对所提出的KI-LAND，建立了FDR可控性和POWER的理论保证，并提供了实验评价以验证其有效性。

信息学院2023级硕士研究生王浩为论文第一作者，宋必芹老师为通讯作者，陈洪教授和邓昊老师参与了论文研究工作。该研究获得了国家自然科学基金面上项目、湖北省自然科学基金等的资助。

【英文摘要】Partially linear models (PLMs) have attracted much attention in the field of statistical machine learning. Specially, the ability of variable selection of PLMs has been studied extensively due to the high requirement of model interpretability. However, few of the existing works concerns the false discovery rate (FDR) controllability of variable selection associated with PLMs. To address this issue, we formulate a new Knockoffs Inference scheme for Linear And Nonlinear Discoverer (called KI-LAND), where FDR is controlled with respect to both linear and nonlinear variables for automatic structure discovery. For the proposed KI-LAND, theoretical guarantees are established for both FDR controllability and power, and experimental evaluations are provided to validate its effectiveness.