发表机构
East China Normal University; Riken AIP; The Graduate University for Advanced Studies, SOKENDAI; The Institute of Statistical Mathematics; Hunan Normal University; The University of Tokyo; Hasso Plattner Institute（华东师范大学; 理化学研究所人工智能研究中心; 综合研究大学院大学; 统计数学研究所; 湖南师范大学; 东京大学; 哈索·普拉特纳研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出域自适应扩散框架（DA-Diff）及检验方法（DA-CIT），通过多源域迁移学习改进条件生成估计，实现条件独立性检验的渐近第一类错误控制，实验验证了生成质量与检验性能的提升。
AI 中文摘要
条件独立性（CI）是统计学和机器学习中的一个基本概念。近年来，条件生成建模的进展为基于生成模型的CI检验提供了灵活的工具，这些检验依赖于估计的条件分布来生成随机样本。然而，估计该分布时的误差会累积到现有的第一类错误界中，并且仅凭生成式估计量的一致性并不能保证渐近的第一类错误控制。为解决这一局限性，我们将条件生成建模表述为一个域自适应问题，并利用来自多个源域的辅助数据来改进目标CI检验域中的估计。我们提出了域自适应扩散（DA-Diff），这是一个基于目标域和源域上加权经验风险最小化的多源域自适应框架，用于条件扩散模型。我们建立了DA-Diff的收敛速率，并展示了可迁移的源数据如何通过增加有效样本量同时控制迁移偏差来改进目标域的估计。基于DA-Diff，我们进一步提出了域自适应条件独立性检验（DA-CIT），并证明其第一类错误满足$P(p \leq \alpha) \leq \alpha + o(1)$。实验表明，与迁移学习扩散基线相比，DA-Diff提高了条件生成质量，而DA-CIT提供了强大的第一类错误控制和有竞争力的功效。
英文摘要
Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies $P(p \leq α) \leq α+ o(1)$. Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.
