# Do-calculus enables estimation of causal effects in partially observed biomolecular pathways

arXiv: https://arxiv.org/abs/2102.06626 · HTML: https://mlsanity.com/paper/2102.06626/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 12 Feb 2021.

## Builds on (most cited first, 11 of 11)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives](https://mlsanity.com/paper/1902.10286/) (2019)
- [Testing Identifiability of Causal Effects](https://mlsanity.com/paper/1302.4948/) (2013)
- [Estimation of causal effects with small data in the presence of trapdoor variables](https://mlsanity.com/paper/2003.03187/) (2020)
- [Leveraging Structured Biological Knowledge for Counterfactual Inference: a Case Study of Viral Pathogenesis](https://mlsanity.com/paper/2101.05136/) (2021)
- [Replacing the do-calculus with Bayes rule](https://mlsanity.com/paper/1906.07125/) (2019)

## Abstract (arXiv)

Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. In this manuscript, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl's do-calculus, and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. The code and the data documenting all the case studies are available at urlhttps://github.com/srtaheri/LVMwithDoCalculus