Bounding counterfactual distributions in discrete structural causal models

          @misc{ pirsa_PIRSA:23040118,
            doi = {10.48660/23040118},
            url = {https://pirsa.org/23040118},
            author = {Tian, Jin},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Bounding counterfactual distributions in discrete structural causal models},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {apr},
            note = {PIRSA:23040118 see, \url{https://pirsa.org}}
          }
          

Abstract

We investigate the problem of bounding counterfactual queries from an arbitrary collection of observational and experimental distributions and qualitative knowledge about the underlying data-generating model represented in the form of a causal diagram. We show that all counterfactual distributions in an arbitrary structural causal model (SCM) with finite discrete endogenous variables could be generated by a family of SCMs with the same causal diagram where unobserved (exogenous) variables are discrete with a finite domain. Utilizing this family of SCMs, we translate the problem of bounding counterfactuals into that of polynomial programming whose solution provides optimal bounds for the counterfactual query.