# Causal Bias Quantification for Continuous Treatments

arXiv: https://arxiv.org/abs/2106.09762 · HTML: https://mlsanity.com/paper/2106.09762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Machine learning for causal inference: on the use of cross-fit estimators](https://mlsanity.com/paper/2004.10337/) (2020)
- [Observational-Interventional Priors for Dose-Response Learning](https://mlsanity.com/paper/1605.01573/) (2016)
- [Model Criticism for Bayesian Causal Inference](https://mlsanity.com/paper/1610.09037/) (2016)

## Abstract (arXiv)

We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero if, and only if, the causal effect is identifiable via covariate adjustment. We show that under some restrictions on the structural equations, the causal bias can be estimated efficiently and allows for causal regularization of predictive probabilistic models. We demonstrate the effectiveness of our method for causal bias quantification in various settings where (not) controlling for certain covariates would introduce causal bias.