Results on Counterfactual Invariance

• URL: http://arxiv.org/abs/2307.08519v1
• Date: Mon, 17 Jul 2023 14:27:32 GMT
• Title: Results on Counterfactual Invariance
• Authors: Jake Fawkes, Robin J. Evans
• Abstract summary: We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. For discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.
• Score: 3.616948583169635
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major question surrounding counterfactual invariance, how does it relate to conditional independence? We show that whilst counterfactual invariance implies conditional independence, conditional independence does not give any implications about the degree or likelihood of satisfying counterfactual invariance. Furthermore, we show that for discrete causal models counterfactually invariant functions are often constrained to be functions of particular variables, or even constant.

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