---
title: "Controlling for Omitted Variable Bias in Deep Neural Networks"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2608.25930v1"
permalink: "https://feed.astralor.com/items/itm_2057e4e36eb5144377b3414c"
published: "2026-08-26T15:42:12.000Z"
score: 76
channel: "ai"
tags: ["Generalized Additive Models","Shortcut Learning","Deep Neural Networks","Neuroimaging","Omitted Variable Bias"]
---

# Controlling for Omitted Variable Bias in Deep Neural Networks

## AI commentary

> This paper deserves attention because it brings classical control variable thinking into deep learning interpretability and fairness. For anyone using deep models in medical imaging or social computing, it offers a more robust bias-correction tool than simple decorrelation.

## At a glance

This paper highlights that deep learning models encode image-inferable covariates such as demographic variables into their predictions when these covariates correlate with the outcome, a form of omitted variable bias known as shortcut learning. Existing fairness or confound-control methods only restrict the correlation between such covariates and model predictions, which fails to correct the bias. The authors propose a control variable approach based on generalized additive modeling of model inputs and covariate effects. Their estimation procedure refits the final layer of a pre-trained network with cross-fitting and ridge penalization, orthogonalizes covariate effects, and marginalizes predictions over the covariate distribution. This yields unbiased, interpretable predictions. The method is verified on simulated images and real neuroimaging data with experimentally induced confounding, recovering performance near a model trained on unconfounded data.

## Key points

- Existing confound-control and fairness methods fail to correct omitted variable bias as they only restrict association rather than model causal structure.
- The paper proposes a control variable approach using generalized additive modeling, refitting the final layer of a pre-trained network with cross-fitting and ridge penalization.
- Orthogonalizing covariate effects and marginalizing over the covariate distribution yields unbiased, interpretable predictions with flexibility for scientific or fairness objectives.
- Validation on simulated images and real neuroimaging data shows the method recovers true effects and outperforms existing approaches.

## Full text

Control variables are widely used in statistical modelling to account for omitted variable bias of known confounders. However, they have largely been underexplored in deep learning. This is surprising, given that deep learning models encode image-inferable covariates, such as demographic variables, into their predictions when these covariates are correlated with the outcome---a form of omitted variable bias referred to as 'shortcut learning'. While many existing confound-control or fairness methods try to restrict the correlation of such covariates with model predictions, we show that this fails to correct for omitted variable bias. We therefore propose a control variable approach for deep learning models, based on generalised additive modelling of the effects of model inputs and covariates. As flexible additive models can suffer from concurvity, we introduce an estimation procedure that refits the final layer of a pre-trained network to include covariate effects, using cross-fitting with ridge penalisation. We show how these effects can be orthogonalised with respect to covariates to exclude their mediated effects and that model predictions can be marginalised over the covariate distribution to control for their effect. This yields unbiased, interpretable predictions and offers flexibility to model the desired effects depending on the scientific or fairness objective. We verify our approach using simulated images, and demonstrate consistent estimation of true effects. Existing methods either require more data or fail to recover the true effects. We apply our method to real neuroimaging data with experimentally induced confounding, where it recovers prediction performance to near the level of a model trained on unconfounded data. Code is available at https://github.com/mpff/cocodeel.

---

Verify against the original before citing; curated by Astral Feed: https://feed.astralor.com/items/itm_2057e4e36eb5144377b3414c