# Variational Causal Inference

arXiv: https://arxiv.org/abs/2209.05935 · HTML: https://mlsanity.com/paper/2209.05935/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 13 Sep 2022.

## Builds on (most cited first, 3 of 3)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Deep Generative Stochastic Networks Trainable by Backprop](https://mlsanity.com/paper/1306.1091/) (2013)
- [Tutorial: Deriving The Efficient Influence Curve for Large Models](https://mlsanity.com/paper/1903.01706/) (2019)

## Built on by (most cited first, 4 of 4)

- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Predicting Cellular Responses with Variational Causal Inference and Refined Relational Information](https://mlsanity.com/paper/2210.00116/) (2022)
- [Season combinatorial intervention predictions with Salt & Peper](https://mlsanity.com/paper/2404.16907/) (2024)
- [In-silico biological discovery with large perturbation models](https://mlsanity.com/paper/2503.23535/) (2025)

## Abstract (arXiv)

Estimating an individual's potential outcomes under counterfactual treatments is a challenging task for traditional causal inference and supervised learning approaches when the outcome is high-dimensional (e.g. gene expressions, impulse responses, human faces) and covariates are relatively limited. In this case, to construct one's outcome under a counterfactual treatment, it is crucial to leverage individual information contained in its observed factual outcome on top of the covariates. We propose a deep variational Bayesian framework that rigorously integrates two main sources of information for outcome construction under a counterfactual treatment: one source is the individual features embedded in the high-dimensional factual outcome; the other source is the response distribution of similar subjects (subjects with the same covariates) that factually received this treatment of interest.