# Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models

arXiv: https://arxiv.org/abs/2505.20536 · HTML: https://mlsanity.com/paper/2505.20536/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 17 of 17)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks](https://mlsanity.com/paper/2108.00131/) (2021)
- [Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption](https://mlsanity.com/paper/1808.05293/) (2018)
- [Causal Imputation via Synthetic Interventions](https://mlsanity.com/paper/2011.03127/) (2020)
- [CP Factor Model for Dynamic Tensors](https://mlsanity.com/paper/2110.15517/) (2021)
- [Inverse Moment Methods for Sufficient Forecasting using High-Dimensional Predictors](https://mlsanity.com/paper/1705.00395/) (2017)
- [Tensor Factor Model Estimation by Iterative Projection](https://mlsanity.com/paper/2006.02611/) (2020)
- [Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models](https://mlsanity.com/paper/2308.02364/) (2023)
- [Tensor Principal Component Analysis in High Dimensional CP Models](https://mlsanity.com/paper/2108.04428/) (2021)
- [Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach](https://mlsanity.com/paper/2401.13665/) (2024)
- [Factor Augmented Tensor-on-Tensor Neural Networks](https://mlsanity.com/paper/2405.19610/) (2024)
- [Estimation and Inference for CP Tensor Factor Models](https://mlsanity.com/paper/2406.17278/) (2024)
- [Dynamic Matrix Factor Models for High Dimensional Time Series](https://mlsanity.com/paper/2407.05624/) (2024)
- [Generalized Causal Tree for Uplift Modeling](https://mlsanity.com/paper/2202.02416/) (2022)
- [Identification of Average Treatment Effects in Nonparametric Panel Models](https://mlsanity.com/paper/2503.19873/) (2025)

## Built on by (most cited first, 2 of 2)

- [Factor Augmented High-Dimensional SGD](https://mlsanity.com/paper/2605.19291/) (2026)
- [Discovering Entity-Conditioned Lag Heterogeneity: A Lag-Gated Neural Audit Framework for Panel Time Series](https://mlsanity.com/paper/2605.21542/) (2026)

## Abstract (arXiv)

This paper studies the task of estimating heterogeneous treatment effects in causal panel data models, in the presence of covariate effects. We propose a novel Covariate-Adjusted Deep Causal Learning (CoDEAL) for panel data models, that employs flexible model structures and powerful neural network architectures to cohesively deal with the underlying heterogeneity and nonlinearity of both panel units and covariate effects. The proposed CoDEAL integrates nonlinear covariate effect components (parameterized by a feed-forward neural network) with nonlinear factor structures (modeled by a multi-output autoencoder) to form a heterogeneous causal panel model. The nonlinear covariate component offers a flexible framework for capturing the complex influences of covariates on outcomes. The nonlinear factor analysis enables CoDEAL to effectively capture both cross-sectional and temporal dependencies inherent in the data panel. This latent structural information is subsequently integrated into a customized matrix completion algorithm, thereby facilitating more accurate imputation of missing counterfactual outcomes. Moreover, the use of a multi-output autoencoder explicitly accounts for heterogeneity across units and enhances the model interpretability of the latent factors. We establish theoretical guarantees on the convergence of the estimated counterfactuals, and demonstrate the compelling performance of the proposed method using extensive simulation studies and a real data application.