Meaningful Causal Aggregation and Paradoxical Confounding (2304.11625v3)
Abstract: In aggregated variables the impact of interventions is typically ill-defined because different micro-realizations of the same macro-intervention can result in different changes of downstream macro-variables. We show that this ill-definedness of causality on aggregated variables can turn unconfounded causal relations into confounded ones and vice versa, depending on the respective micro-realization. We argue that it is practically infeasible to only use aggregated causal systems when we are free from this ill-definedness. Instead, we need to accept that macro causal relations are typically defined only with reference to the micro states. On the positive side, we show that cause-effect relations can be aggregated when the macro interventions are such that the distribution of micro states is the same as in the observational distribution; we term this natural macro interventions. We also discuss generalizations of this observation.
- C. J. Adkins. Equilibrium Thermodynamics. Cambridge University Press, 3 edition, 1983.
- Causal effect identification in cluster dags. AAAI Press, 2023.
- Roger Balian. From microphysics to macrophysics, volume 1. Springer, 2007.
- Abstracting causal models. In AAAI, 2019.
- Approximate causal abstraction. UAI, 2019.
- Causal models with constraints. In Proceedings of the Second Conference on Causal Learning and Reasoning, 2023.
- Representation learning: a review and new perspectives. IEEE transactions on pattern analysis and machine intelligence, 35(8):1798—1828, August 2013.
- Beyond structural causal models: Causal constraints models. In UAI, 2019.
- Multi-level cause-effect systems. In AISTATS, 2016.
- A calculus for stochastic interventions:causal effect identification and surrogate experiments. In AAAI, volume 34, pages 10093–10100, Apr. 2020.
- Thermodynamic depth of causal states: Objective complexity via minimal representations. Phys. Rev. E, 59:275–283, Jan 1999.
- Dominik Janzing and Sergio Garrido Mejia. Phenomenological causality. 11 2022. 10.48550/arXiv.2211.09024.
- Causal abstraction with soft interventions. In Proceedings of the Second Conference on Causal Learning and Reasoning, 2023.
- Economic shocks and civil conflict: An instrumental variables approach. Journal of Political Economy, 112:725 – 753, 2004.
- Judea Pearl. Causality: Models, Reasoning and Inference. Cambridge University Press, USA, 2nd edition, 2009.
- Elements of Causal Inference: Foundations and Learning Algorithms. The MIT Press, 2017. ISBN 0262037319.
- Compositional abstraction error and a category of causal models. In UAI, 2021.
- Backshift: Learning causal cyclic graphs from unknown shift interventions. In NeurIPS, 2015.
- Causal consistency of structural equation models. In UAI, 2017.
- Identification and estimation of causal effects defined by shift interventions. In UAI, 2020.
- Towards causal representation learning. Proceedings of the IEEE, 109(5):1–23, 2021.
- Causal inference of ambiguous manipulations. 71:833–845, 2004.
- Quantifying consistency and information loss for causal abstraction learning. In IJCAI, 2023.