# On Efficient Adjustment for Micro Causal Effects in Summary Causal Graphs

arXiv: https://arxiv.org/abs/2512.18315 · HTML: https://mlsanity.com/paper/2512.18315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 20 Dec 2025.

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

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2102.10324/) (2021)
- [Identifiability of total effects from abstractions of time series causal graphs](https://mlsanity.com/paper/2310.14691/) (2023)
- [Efficient adjustment sets in causal graphical models with hidden variables](https://mlsanity.com/paper/2004.10521/) (2020)
- [Identifiability of Direct Effects from Summary Causal Graphs](https://mlsanity.com/paper/2306.16958/) (2023)
- [Identifying Macro Conditional Independencies and Macro Total Effects in Summary Causal Graphs with Latent Confounding](https://mlsanity.com/paper/2407.07934/) (2024)
- [Towards identifiability of micro total effects in summary causal graphs with latent confounding: extension of the front-door criterion](https://mlsanity.com/paper/2406.05805/) (2024)
- [Identifiability by common backdoor in summary causal graphs of time series](https://mlsanity.com/paper/2506.14862/) (2025)

## Abstract (arXiv)

Observational studies in fields such as epidemiology often rely on covariate adjustment to estimate causal effects. Classical graphical criteria, like the back-door criterion and the generalized adjustment criterion, are powerful tools for identifying valid adjustment sets in directed acyclic graphs (DAGs). However, these criteria are not directly applicable to summary causal graphs (SCGs), which are abstractions of DAGs commonly used in dynamic systems. In SCGs, each node typically represents an entire time series and may involve cycles, making classical criteria inapplicable for identifying causal effects. Recent work established complete conditions for determining whether the micro causal effect of a treatment or an exposure Xt-γ on an outcome Yt is identifiable via covariate adjustment in SCGs, under the assumption of no hidden confounding. However, these identifiability conditions have two main limitations. First, they are complex, relying on cumbersome definitions and requiring the enumeration of multiple paths in the SCG, which can be computationally expensive. Second, when these conditions are satisfied, they only provide two valid adjustment sets, limiting flexibility in practical applications. In this paper, we propose an equivalent but simpler formulation of those identifiability conditions and introduce a new criterion that identifies a broader class of valid adjustment sets in SCGs. Additionally, we characterize the quasi-optimal adjustment set among these, i.e., the one that minimizes the asymptotic variance of the causal effect estimator. Our contributions offer both theoretical advancement and practical tools for more flexible and efficient causal inference in abstracted causal graphs.