利用因果图结构，用改进的期望最大化算法提升域偏移下的目标变量预测准确率。
An Expectation-Maximization Algorithm for Domain Adaptation in Gaussian Causal Models
- 基于因果图构建统一的梯度化EM框架，用投影梯度替代高成本步骤。
- 在协变量偏移和局部机制变化下实现几何收敛，参数误差有理论保证。
- 只重估受域偏移影响的条件分布，适合高维数据，适用于生物网络等复杂场景。
我们研究在部署域发生系统性偏移时，如何对缺失的目标变量进行推断，前提是在源域中存在一个完全可观测的高斯因果有向无环图（Gaussian Causal DAG）。本文提出一种统一的基于期望最大化（EM）的框架，通过因果图结构融合源域与目标域数据，将观测变量的信息迁移至缺失的目标变量。方法上，我们在因果图参数空间中定义了群体级的EM算子，并引入一阶（梯度）更新机制，以单步投影梯度替代耗时的广义最小二乘M步。在标准局部强凹性与光滑性假设，以及类BWY的梯度稳定性（有限缺失信息）条件下，证明该一阶EM算子在真实目标参数附近是局部压缩的，从而在高斯结构方程模型（SEM）下实现几何收敛，并给出参数误差和诱导目标推断误差的有限样本保证，适用于协变量偏移和局部机制偏移。算法上，利用已知因果图冻结源域不变机制，仅重新估计受偏移直接影响的条件分布，使方法可扩展至高维模型。在包含7节点合成模型、64节点MAGIC-IRRI遗传网络及Sachs蛋白信号数据的实验中，所提的因果图感知的一阶EM算法在显著域偏移下，显著优于仅拟合源域的贝叶斯网络和Kiiveri风格的EM基线方法。
原文摘要 · Abstract (English)
We study the problem of imputing a designated target variable that is systematically missing in a shifted deployment domain, when a Gaussian causal DAG is available from a fully observed source domain. We propose a unified EM-based framework that combines source and target data through the DAG structure to transfer information from observed variables to the missing target. On the methodological side, we formulate a population EM operator in the DAG parameter space and introduce a first-order (gradient) EM update that replaces the costly generalized least-squares M-step with a single projected gradient step. Under standard local strong-concavity and smoothness assumptions and a BWY-style \cite{Balakrishnan2017EM} gradient-stability (bounded missing-information) condition, we show that this first-order EM operator is locally contractive around the true target parameters, yielding geometric convergence and finite-sample guarantees on parameter error and the induced target-imputation error in Gaussian SEMs under covariate shift and local mechanism shifts. Algorithmically, we exploit the known causal DAG to freeze source-invariant mechanisms and re-estimate only those conditional distributions directly affected by the shift, making the procedure scalable to higher-dimensional models. In experiments on a synthetic seven-node SEM, the 64-node MAGIC-IRRI genetic network, and the Sachs protein-signaling data, the proposed DAG-aware first-order EM algorithm improves target imputation accuracy over a fit-on-source Bayesian network and a Kiiveri-style EM baseline, with the largest gains under pronounced domain shift.
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