# Coupling Generative Modeling and an Autoencoder with the Causal Bridge

arXiv: https://arxiv.org/abs/2509.25599 · HTML: https://mlsanity.com/paper/2509.25599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Proximal Causal Inference for Marginal Counterfactual Survival Curves](https://mlsanity.com/paper/2204.13144/) (2022)
- [Density Ratio-based Proxy Causal Learning Without Density Ratios](https://mlsanity.com/paper/2503.08371/) (2025)
- [Causal Effect Estimation using identifiable Variational AutoEncoder with Latent Confounders and Post-Treatment Variables](https://mlsanity.com/paper/2408.07219/) (2024)

## Abstract (arXiv)

We consider inferring the causal effect of a treatment (intervention) on an outcome of interest in situations where there is potentially an unobserved confounder influencing both the treatment and the outcome. This is achievable by assuming access to two separate sets of control (proxy) measurements associated with treatment and outcomes, which are used to estimate treatment effects through a function termed the em causal bridge (CB). We present a new theoretical perspective, associated assumptions for when estimating treatment effects with the CB is feasible, and a bound on the average error of the treatment effect when the CB assumptions are violated. From this new perspective, we then demonstrate how coupling the CB with an autoencoder architecture allows for the sharing of statistical strength between observed quantities (proxies, treatment, and outcomes), thus improving the quality of the CB estimates. Experiments on synthetic and real-world data demonstrate the effectiveness of the proposed approach in relation to the state-of-the-art methodology for proxy measurements.