通过ATLAS揭示异构环境中的不变和可转移潜在因素
Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS
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中文总结 AI 辅助
研究异构环境下多环境因素模型，提出ATLAS方法，利用不变性原理和辅助标签监督，分离不变与异构因素，用于潜在因素回归，在新环境中实现可转移预测，还建立了相关非渐近误差界。
中文摘要 AI 辅助
本文考虑一个多环境因素模型，其中高维协变量从异构环境中收集，且在部分环境中有辅助标签。协变量的联合分布可能因环境而异，潜在结构分解为具有共享载荷的不变因素和具有特定环境载荷的异构因素。该模型受迁移学习和潜在因素回归的启发。利用不变性原理，我们表明在最小结构条件下可解开不变和异构因素。基于此，我们提出ATLAS，它通过跨异构环境的潜在对齐，利用辅助标签和不变性指导进行转移。ATLAS是一个统一过程，利用不变性原理分离对齐的不变和未对齐的异构因素，并利用辅助标签监督从那些未对齐的异构因素中提取预测不变和可转移因素。ATLAS在下游潜在因素回归中产生接近最优的性能，当有辅助标签时通过完整潜在信号在新环境中实现可转移预测，否则简化为仅健壮的不变因素预测。我们为恢复不变和异构因素、识别所有响应不变因素以及估计Y中的不变信号建立了精确的非渐近误差界。
英文摘要
This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Such a model is motivated by transfer learning and latent factor regression, where one seeks stable low-dimensional representations for both interpretation and robust out-of-sample prediction of the response $Y$. Leveraging the invariance principle, we show that the invariant and heterogeneous factors are disentangled under a minimal structural condition. Based on this, we propose ATLAS, an Auxiliary-label and invariance-guided Transfer via Latent Alignment across heterogeneous environmentS. ATLAS is a unified procedure that leverages the invariance principle to separate aligned invariant and unaligned heterogeneous factors, and further exploits supervision from auxiliary labels to extract prediction-invariant and transferable factors from those unaligned heterogeneous factors. ATLAS yields near-oracle performance for downstream latent factor regression, enables transferable prediction in new environments through the full latent signal when auxiliary labels are available, and reduces to robust invariant-factor-only prediction otherwise. We establish sharp non-asymptotic error bounds for recovering invariant and heterogeneous factors, identifying all the response-invariant factors, and estimating the invariant signal in $Y$.
发表机构
- Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。
