# Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets

arXiv: https://arxiv.org/abs/2503.21526 · HTML: https://mlsanity.com/paper/2503.21526/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 27 Mar 2025.

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

- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Learning Sparse Causal Models is not NP-hard](https://mlsanity.com/paper/1309.6824/) (2013)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [Do we become wiser with time? On causal equivalence with tiered background knowledge](https://mlsanity.com/paper/2306.01638/) (2023)
- [Towards Complete Causal Explanation with Expert Knowledge](https://mlsanity.com/paper/2407.07338/) (2024)
- [Improving Finite Sample Performance of Causal Discovery by Exploiting Temporal Structure](https://mlsanity.com/paper/2406.19503/) (2024)
- [Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data](https://mlsanity.com/paper/2108.13331/) (2021)

## Built on by (most cited first, 2 of 2)

- [Multi-Level Causal Embeddings](https://mlsanity.com/paper/2602.22287/) (2026)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

In this paper we consider the use of tiered background knowledge within constraint based causal discovery. Our focus is on settings relaxing causal sufficiency, i.e. allowing for latent variables which may arise because relevant information could not be measured at all, or not jointly, as in the case of multiple overlapping datasets. We first present novel insights into the properties of the 'tiered FCI' (tFCI) algorithm. Building on this, we introduce a new extension of the IOD (integrating overlapping datasets) algorithm incorporating tiered background knowledge, the 'tiered IOD' (tIOD) algorithm. We show that under full usage of the tiered background knowledge tFCI and tIOD are sound, while simple versions of the tIOD and tFCI are sound and complete. We further show that the tIOD algorithm can often be expected to be considerably more efficient and informative than the IOD algorithm even beyond the obvious restriction of the Markov equivalence classes. We provide a formal result on the conditions for this gain in efficiency and informativeness. Our results are accompanied by a series of examples illustrating the exact role and usefulness of tiered background knowledge.