Unmeasured confounders are a major source of bias in regression-based effect estimation and causal inference. In this paper, we propose a new profiled transfer learning framework, ProTrans, to address confounding effects in the target dataset, when additional source datasets with similar confounding structures are available. We introduce the concept of profiled residuals to characterize the shared confounding patterns between source and target datasets. By incorporating these profiled residuals into the target debiasing step, we effectively mitigate the latent confounding effects. We also propose a source selection strategy to enhance the robustness of ProTrans to noninformative sources. As a byproduct, ProTrans can also be used to estimate treatment effects in the presence of potential confounders, without the use of auxiliary features such as instrumental or proxy variables, which are often challenging to select in practice. Theoretically, we prove that the resulting estimated model shift from the sources to the target is confounding-free without imposing specific assumptions on the true confounding structure, and that the target parameter estimation achieves the minimax optimal rate under mild conditions. Simulated and real-world experiments validate the effectiveness of ProTrans and support the theoretical findings.

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