COD: 面向域适应回归的条件不变表示学习
COD: Learning Conditional Invariant Representation for Domain Adaptation Regression
- School of Mathematics, Sun Yat-Sen University（中山大学数学学院）
- School of Mathematics, Jiaying University（嘉应学院数学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对分类场景的条件分布对齐方法不适用于连续输出的域适应回归问题，本文提出条件算子差异COD刻画连续条件的分布差异，构建基于COD的条件不变表示学习模型，理论与实验均验证了其有效性与优越性。
AI中文摘要：
为将具有连续输出的源域标签知识泛化到无标记目标域，域适应回归（Domain Adaptation Regression, DAR）被提出用于解决复杂的实际学习问题。然而，由于回归任务的连续性特性，现有已被证明在分类场景中有效的、基于离散先验的条件分布对齐理论与方法不再适用。本文聚焦DAR中的可行性问题，建立了回归模型的充分性理论，表明泛化误差可被跨域条件差异充分约束。进一步地，为刻画带连续条件变量的条件差异，本文提出了一种新的条件算子差异（Conditional Operator Discrepancy, COD），该方法通过核嵌入理论满足条件分布上的度量性质。最后，为最小化该差异，本文提出了一种基于COD的条件不变表示学习模型，并推导了其重构形式，表明对矩统计量进行合理修改可进一步提升适应模型的判别性。在标准DAR数据集上的大量实验验证了理论结果的有效性，且该方法优于当前最优（SOTA）的DAR方法。
英文摘要：
Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.
