# Substitute adjustment via recovery of latent variables

arXiv: https://arxiv.org/abs/2403.00202 · HTML: https://mlsanity.com/paper/2403.00202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 1 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Identifying effects of multiple treatments in the presence of unmeasured confounding](https://mlsanity.com/paper/2011.04504/) (2020)
- [The Projected Covariance Measure for assumption-lean variable significance testing](https://mlsanity.com/paper/2211.02039/) (2022)
- [Spectral Deconfounding via Perturbed Sparse Linear Models](https://mlsanity.com/paper/1811.05352/) (2018)
- [Towards Clarifying the Theory of the Deconfounder](https://mlsanity.com/paper/2003.04948/) (2020)
- [Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding](https://mlsanity.com/paper/2004.03758/) (2020)
- [Assumption-lean inference for generalised linear model parameters](https://mlsanity.com/paper/2006.08402/) (2020)
- [Counterexamples to "The Blessings of Multiple Causes" by Wang and Blei](https://mlsanity.com/paper/2001.06555/) (2020)
- [Confounder Adjustment in Multiple Hypothesis Testing](https://mlsanity.com/paper/1508.04178/) (2015)
- [Na"ive regression requires weaker assumptions than factor models to adjust for multiple cause confounding](https://mlsanity.com/paper/2007.12702/) (2020)
- [Assumption Lean Regression](https://mlsanity.com/paper/1806.09014/) (2018)

## Built on by (most cited first, 1 of 1)

- [Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes](https://mlsanity.com/paper/2410.04996/) (2024)

## Abstract (arXiv)

The deconfounder was proposed as a method for estimating causal parameters in a context with multiple causes and unobserved confounding. It is based on recovery of a latent variable from the observed causes. We disentangle the causal interpretation from the statistical estimation problem and show that the deconfounder in general estimates adjusted regression target parameters. It does so by outcome regression adjusted for the recovered latent variable termed the substitute. We refer to the general algorithm, stripped of causal assumptions, as substitute adjustment. We give theoretical results to support that substitute adjustment estimates adjusted regression parameters when the regressors are conditionally independent given the latent variable. We also introduce a variant of our substitute adjustment algorithm that estimates an assumption-lean target parameter with minimal model assumptions. We then give finite sample bounds and asymptotic results supporting substitute adjustment estimation in the case where the latent variable takes values in a finite set. A simulation study illustrates finite sample properties of substitute adjustment. Our results support that when the latent variable model of the regressors hold, substitute adjustment is a viable method for adjusted regression.