# Do we become wiser with time? On causal equivalence with tiered background knowledge

arXiv: https://arxiv.org/abs/2306.01638 · HTML: https://mlsanity.com/paper/2306.01638/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 5 of 5)

- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs](https://mlsanity.com/paper/2012.09679/) (2020)
- [Minimal enumeration of all possible total effects in a Markov equivalence class](https://mlsanity.com/paper/2010.08611/) (2020)
- [On the Representation of Pairwise Causal Background Knowledge and Its Applications in Causal Inference](https://mlsanity.com/paper/2207.05067/) (2022)

## Built on by (most cited first, 9 of 9)

- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Improving Finite Sample Performance of Causal Discovery by Exploiting Temporal Structure](https://mlsanity.com/paper/2406.19503/) (2024)
- [Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets](https://mlsanity.com/paper/2503.21526/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Orientability of Causal Relations in Time Series using Summary Causal Graphs and Faithful Distributions](https://mlsanity.com/paper/2508.21742/) (2025)
- [Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables](https://mlsanity.com/paper/2602.23611/) (2026)
- [A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs](https://mlsanity.com/paper/2605.06288/) (2026)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

Equivalence classes of DAGs (represented by CPDAGs) may be too large to provide useful causal information. Here, we address incorporating tiered background knowledge yielding restricted equivalence classes represented by 'tiered MPDAGs'. Tiered knowledge leads to considerable gains in informativeness and computational efficiency: We show that construction of tiered MPDAGs only requires application of Meek's 1st rule, and that tiered MPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This entails simplifications e.g. of determining valid adjustment sets for causal effect estimation. Further, we characterise when one tiered ordering is more informative than another, providing insights into useful aspects of background knowledge.