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Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation · 0 citations (OpenAlex)

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Proposes CoDEAL, a covariate-adjusted deep causal matrix completion method that removes covariate effects with a DNN and imputes counterfactuals via a multi-output autoencoder for unit-specific ATT in staggered panel designs.

Problem

Estimating unit-specific heterogeneous average treatment effects on the treated in causal panel data with missing-not-at-random counterfactuals, nonlinear factor structures, and nonlinear covariate effects.

Approach

Combine a feed-forward DNN that removes nonlinear covariate effects with a multi-output autoencoder (shared encoder, unit-specific decoders) that recovers nonlinear latent factors and unit heterogeneity, then impute counterfactuals block-wise via a four-block reduction of staggered adoption designs.

Key results

• Under linear factor effects in four-block Config.1 with linear covariates, CoDEAL achieves MAE 0.646 vs 0.699 for MC-NNM (the second-best).
• In staggered Config.4 with ReLU MLP factors and linear covariates, CoDEAL achieves MAE 0.633 vs 0.656 for MC-NNM; MC-NNM is competitive or better in some linear-factor settings.
• On OxCGRT data, estimated counterfactual cumulative cases and deaths without mandatory vaccination are 29.81 million (+12.2%) and 0.52 million (+34.6%) vs observed 26.57 million and 0.39 million.

Surprising findings

• Linear covariate removal (LR) often outperforms the DNN removal when covariate effects are truly linear, and MC-NNM matches or beats CoDEAL in several linear-factor settings.

Limitations

• Only designed for binary treatment; multiple-treatment extension left to future work.
• Performs comparably to MC-NNM under linear settings rather than uniformly better.
• Theoretical rates depend on DNN parameter choices and assumptions (Hölder smoothness, pervasiveness) that are standard but restrictive.

Experimental setup

Datasets: simulated panel data (four-block and staggered designs) OxCGRT COVID-19 government response tracker

Benchmarks: simulated four-block and staggered adoption configurations OxCGRT COVID-19 case and death counts

Metrics: MAE MSE

Baselines: Single AE AEMC-NE MC-NNM Vert-Reg DiD LR-based covariate removal

Builds on: nonlinear factor models synthetic control matrix completion with nuclear norm minimization neuron-enhanced autoencoder matrix completion (AEMC-NE)

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