Invariant quantile regression for heterogeneous environments
异质环境下的不变量分位数回归AI 解读 ↓
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异质环境下的不变量分位数回归
- 研究问题
- 当不同环境中的条件响应分布发生变化时，能否利用分位数层面的不变性筛选稳定的潜在因果变量，并实现跨环境估计？
- 方法与思路
- 作者提出不变量分位数回归及核平滑估计器，利用环境间异质性与分位数不变结构，研究因果发现性质和非渐近估计误差。
- 材料陈述的贡献
- 摘要称，该框架能比条件均值不变性排除更多伪相关变量，并给出因果发现性质及 ℓ₂ 误差界；真实数据应用报告了生物学相关关系。
- 阅读关注点
- 应核对环境变化与结构因果模型的条件、分位数不变性如何指向因果变量，以及内生变量集合比较和非渐近误差界的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未说明具体识别假设和误差界形式，生物学解释也不能仅据摘要视为已验证。
原文摘要
In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer learning, causal inference, and fair machine learning, and is motivated by scenarios in which the conditional probability of the response given covariates varies, while certain key variables remain invariant. This perspective differs notably from previous works that restrict attention to the conditional mean, which is often insufficient to capture the full causal relationships between covariates and the response in heterogeneous environments. In contrast, quantile-based invariance naturally accommodates heterogeneity, and aligns more closely with structural causal models, in which variables invariant across environments at one or multiple quantile levels directly indicate potential and stable causal variables. Moreover, we show that IQR may yield a larger set of endogenous variables compared to the conditional mean framework, which in turn promotes more effective exclusion of spurious (non-causal) variables. To achieve this, we introduce a Kernel-Smoothed Invariant Quantile Regression (KS-IQR) estimator, which leverages the underlying invariance structure and heterogeneity among environments, ensuring stable estimation across multiple environments. We establish the causal discovery properties of our method, demonstrate its ability to overcome the ``curse of endogeneity'', and derive an $\ell_2$ error bound for our estimator, all in a non-asymptotic framework. We apply our method to real data for causal discovery and obtain biologically meaningful relationships, recovering known signaling pathways and revealing additional quantile-specific effects.