# Causal inference through multi-stage learning and doubly robust deep neural networks

arXiv: https://arxiv.org/abs/2407.08560 · HTML: https://mlsanity.com/paper/2407.08560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery](https://mlsanity.com/paper/1908.01842/) (2019)
- [The Difficulty of Training Sparse Neural Networks](https://mlsanity.com/paper/1906.10732/) (2019)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks](https://mlsanity.com/paper/2109.02832/) (2021)
- [A unifying approach for doubly-robust ℓ1 regularized estimation of causal contrasts](https://mlsanity.com/paper/1904.03737/) (2019)
- [Non-parametric causal effects based on longitudinal modified treatment policies](https://mlsanity.com/paper/2006.01366/) (2020)
- [Sequential Double Robustness in Right-Censored Longitudinal Models](https://mlsanity.com/paper/1705.02459/) (2017)
- [Sparsity Double Robust Inference of Average Treatment Effects](https://mlsanity.com/paper/1905.00744/) (2019)
- [On the multiply robust estimation of the mean of the g-functional](https://mlsanity.com/paper/1705.08582/) (2017)
- [Dynamic treatment effects: high-dimensional inference under model misspecification](https://mlsanity.com/paper/2111.06818/) (2021)

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

- [Adjustment for Confounding using Pre-Trained Representations](https://mlsanity.com/paper/2506.14329/) (2025)
- [New Approximation Results and Optimal Estimation for Fully Connected Deep Neural Networks](https://mlsanity.com/paper/2512.09853/) (2025)

## Abstract (arXiv)

Deep neural networks (DNNs) have demonstrated remarkable empirical performance in large-scale supervised learning problems, particularly in scenarios where both the sample size n and the dimension of covariates p are large. This study delves into the application of DNNs across a wide spectrum of intricate causal inference tasks, where direct estimation falls short and necessitates multi-stage learning. Examples include estimating the conditional average treatment effect and dynamic treatment effect. In this framework, DNNs are constructed sequentially, with subsequent stages building upon preceding ones. To mitigate the impact of estimation errors from early stages on subsequent ones, we integrate DNNs in a doubly robust manner. In contrast to previous research, our study offers theoretical assurances regarding the effectiveness of DNNs in settings where the dimensionality p expands with the sample size. These findings are significant independently and extend to degenerate single-stage learning problems.