Disentangled Double Machine Learning for Accurate Causal Effect Estimation

Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.

Unobserved confounding prevents standard covariate adjustment from identifying causal response functions in observational studies. Proxy causal learning addresses this problem through bridge equations involving treatment- and outcome-inducing proxies, avoiding direct recovery of the latent confounder. Existing doubly robust proxy estimators combine outcome and treatment bridges, but typically rely on fixed kernels, sieves, or low-dimensional semiparametric models; existing neural proxy methods are more flexible, but are largely single-bridge estimators. We develop a neural doubly robust framework for proxy causal learning with continuous and structured treatments. Our method introduces a neural mean-embedding estimator for the treatment bridge, combines it with a neural outcome bridge, and estimates the doubly robust correction through a final regression stage. The framework covers population, heterogeneous, and conditional dose-response functions, yielding full response-curve estimators rather than binary-treatment effects. The algorithms use two stages for each bridge and history-aware updates of the final linear layers to stabilize stochastic multi-stage training. We prove consistency of the algorithms showing that the doubly robust error is controlled by the final averaging and regression errors together with the smaller of the outcome- and treatment-side weak-norm bridge errors. Across synthetic and image-valued benchmarks, the proposed estimators outperform existing baselines and single-bridge neural estimators, showing the benefit of combining learned outcome and treatment bridges in a doubly robust construction. Our implementation is available at https://github.com/BariscanBozkurt/DRPCL-Neural-Mean-Embedding.

Deep Metric Learning (DML) often struggles with zero-shot generalization because standard objectives inherently capture what co-occurs rather than what causes similarity. Consequently, DML models are vulnerable to shortcut learning driven by two structurally distinct confounders: background spurious correlations (which create backdoor paths via scene context) and foreground nuisance perturbations (which inject non-semantic variations like pose or illumination). Although existing methods have proposed targeted solutions for each pathway individually, none can simultaneously address both due to their fundamentally distinct causal roles. To bridge this gap, we propose the Counterfactual Causal Embedding (CouCE), a unified causal framework that explicitly models and neutralizes both confounders. Specifically, we introduce Orthogonal Dictionary-Based Backdoor Adjustment (ODBA), which isolates spurious background patterns into a variance-gated dictionary and stably disentangles them from the learned embeddings via soft orthogonal regularization. Simultaneously, we propose Multi-Scale Randomized Causal Intervention (MSRCI) to enforce causal invariance against foreground nuisances through multi-scale Fourier amplitude randomization and a symmetric KL invariance constraint. Notably, CouCE seamlessly integrates with any proxy-based loss, incurring modest training overhead without requiring architectural modifications during inference. Extensive experiments on CUB-200-2011, Cars-196, and Stanford Online Products demonstrate that CouCE consistently achieves state-of-the-art performance, providing a principled and robust solution for debiased DML.