Ordinal-Poisson Causal Discovery — Allerton Conference on Communication, Control and Computing

Shaska J, Mitra U, Wang Y, Johnson CK. Ordinal-Poisson causal discovery. In: 2025 61st Allerton Conference on Communication, Control, and Computing Proceedings. Allerton Conference on Communication, Control, and Computing; 2025.

Abstract: This paper deals with causal discovery in the setting where random variables in the causal graph can be either ordinal or Poisson. In particular, we show that it is possible to recover the causal network (modeled by a directed acyclic graph) from purely observational data. Such results are important in the field of causal discovery since, in general, it is impossible to recover causal relationships from purely observational data, and the identifiability of causal network structures relies on assumptions regarding the data-generating process. Causal discovery in the setting where all variables in the graph are ordinal and the setting where all variables are Poisson has been separately considered. However, the setting in this paper where the two are allowed to co-exist in the graph has, to the best of our knowledge, not been considered. In addition to proving the identifiability of ordinal-Poisson causal discovery, we show, through numerical simulations, that the Bayesian information criterion (BIC) tends to reliably recover the true causal graph as the number of observations increases.