Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables

摘要

We provide a scheme for inferring causal relations from uncontrolledstatistical data based on tools from computational algebraic geometry, inparticular, the computation of Groebner bases. We focus on causal structurescontaining just two observed variables, each of which is binary. We considerthe consequences of imposing different restrictions on the number andcardinality of latent variables and of assuming different functionaldependences of the observed variables on the latent ones (in particular, thenoise need not be additive). We provide an inductive scheme for classifyingfunctional causal structures into distinct observational equivalence classes.For each observational equivalence class, we provide a procedure for derivingconstraints on the joint distribution that are necessary and sufficientconditions for it to arise from a model in that class. We also demonstrate howthis sort of approach provides a means of determining which causal parametersare identifiable and how to solve for these. Prospects for expanding the scopeof our scheme, in particular to the problem of quantum causal inference, arealso discussed.