# A Neural Mean Embedding Approach for Back-door and Front-door Adjustment

arXiv: https://arxiv.org/abs/2210.06610 · HTML: https://mlsanity.com/paper/2210.06610/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)

## Built on by (most cited first, 8 of 8)

- [Causal Evaluation of Language Models](https://mlsanity.com/paper/2405.00622/) (2024)
- [An Overview of Causal Inference using Kernel Embeddings](https://mlsanity.com/paper/2410.22754/) (2024)
- [High Dimensional Causal Inference with Variational Backdoor Adjustment](https://mlsanity.com/paper/2310.06100/) (2023)
- [Rating Multi-Modal Time-Series Forecasting Models (MM-TSFM) for Robustness Through a Causal Lens](https://mlsanity.com/paper/2406.12908/) (2024)
- [Automatic debiasing of neural networks via moment-constrained learning](https://mlsanity.com/paper/2409.19777/) (2024)
- [Debiased Front-Door Learners for Heterogeneous Effects](https://mlsanity.com/paper/2509.22531/) (2025)
- [An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation](https://mlsanity.com/paper/2510.25128/) (2025)
- [Creating a Causally Grounded Rating Method for Assessing the Robustness of AI Models for Time-Series Forecasting](https://mlsanity.com/paper/2502.12226/) (2025)

## Abstract (arXiv)

We consider the estimation of average and counterfactual treatment effects, under two settings: back-door adjustment and front-door adjustment. The goal in both cases is to recover the treatment effect without having an access to a hidden confounder. This objective is attained by first estimating the conditional mean of the desired outcome variable given relevant covariates (the "first stage" regression), and then taking the (conditional) expectation of this function as a "second stage" procedure. We propose to compute these conditional expectations directly using a regression function to the learned input features of the first stage, thus avoiding the need for sampling or density estimation. All functions and features (and in particular, the output features in the second stage) are neural networks learned adaptively from data, with the sole requirement that the final layer of the first stage should be linear. The proposed method is shown to converge to the true causal parameter, and outperforms the recent state-of-the-art methods on challenging causal benchmarks, including settings involving high-dimensional image data.