An Expectation-Maximization Algorithm for Domain Adaptation in Gaussian Causal Models

• URL: http://arxiv.org/abs/2601.03459v1
• Date: Tue, 06 Jan 2026 23:07:52 GMT
• Title: An Expectation-Maximization Algorithm for Domain Adaptation in Gaussian Causal Models
• Authors: Mohammad Ali Javidian,
• Abstract summary: We study the problem of imputing a designated target variable that is systematically missing in a shifted deployment domain.<n>We propose a unified EM-based framework that combines source and target data through the DAG structure.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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