# Non parametric estimation of causal populations in a counterfactual scenario

arXiv: https://arxiv.org/abs/2112.04288 · HTML: https://mlsanity.com/paper/2112.04288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Deep Counterfactual Networks with Propensity-Dropout](https://mlsanity.com/paper/1706.05966/) (2017)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [Uplift Modeling from Separate Labels](https://mlsanity.com/paper/1803.05112/) (2018)
- [Estimating Individual Treatment Effects through Causal Populations Identification](https://mlsanity.com/paper/2004.05013/) (2020)

## Abstract (arXiv)

In causality, estimating the effect of a treatment without confounding inference remains a major issue because requires to assess the outcome in both case with and without treatment. Not being able to observe simultaneously both of them, the estimation of potential outcome remains a challenging task. We propose an innovative approach where the problem is reformulated as a missing data model. The aim is to estimate the hidden distribution of causal populations, defined as a function of treatment and outcome. A Causal Auto-Encoder (CAE), enhanced by a prior dependent on treatment and outcome information, assimilates the latent space to the probability distribution of the target populations. The features are reconstructed after being reduced to a latent space and constrained by a mask introduced in the intermediate layer of the network, containing treatment and outcome information.