# High Dimensional Causal Inference with Variational Backdoor Adjustment

arXiv: https://arxiv.org/abs/2310.06100 · HTML: https://mlsanity.com/paper/2310.06100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Intact-VAE: Estimating Treatment Effects under Unobserved Confounding](https://mlsanity.com/paper/2101.06662/) (2021)
- [A Neural Mean Embedding Approach for Back-door and Front-door Adjustment](https://mlsanity.com/paper/2210.06610/) (2022)
- [Semi-Symbolic Inference for Efficient Streaming Probabilistic Programming](https://mlsanity.com/paper/2209.07490/) (2022)
- [Interpolating between sampling and variational inference with infinite stochastic mixtures](https://mlsanity.com/paper/2110.09618/) (2021)

## Built on by (most cited first, 3 of 3)

- [CIGPose: Causal Intervention Graph Neural Network for Whole-Body Pose Estimation](https://mlsanity.com/paper/2603.09418/) (2026)
- [Are Good Generators Good Decision-Makers? Policy Learning for General Interventions via Retargeted Counterfactual Generation](https://mlsanity.com/paper/2606.07399/) (2026)
- [An End-to-End Pipeline for Causal ML with Continuous Treatments: An Application to Financial Decision Making](https://mlsanity.com/paper/2609.30396/) (2026)

## Abstract (arXiv)

Backdoor adjustment is a technique in causal inference for estimating interventional quantities from purely observational data. For example, in medical settings, backdoor adjustment can be used to control for confounding and estimate the effectiveness of a treatment. However, high dimensional treatments and confounders pose a series of potential pitfalls: tractability, identifiability, optimization. In this work, we take a generative modeling approach to backdoor adjustment for high dimensional treatments and confounders. We cast backdoor adjustment as an optimization problem in variational inference without reliance on proxy variables and hidden confounders. Empirically, our method is able to estimate interventional likelihood in a variety of high dimensional settings, including semi-synthetic X-ray medical data. To the best of our knowledge, this is the first application of backdoor adjustment in which all the relevant variables are high dimensional.