Identifiability of causal graphs under nonadditive conditionally parametric causal models

Abstract: Causal discovery from observational data typically requires strong assumptions about the data-generating process. Previous research has established the identifiability of causal graphs under various models, including linear non-Gaussian, post-nonlinear, and location-scale models. However, these models may have limited applicability in real-world situations that involve a mixture of discrete and continuous variables or where the cause affects the variance or tail behavior of the effect. In this study, we introduce a new class of models, called Conditionally Parametric Causal Models (CPCM), which assume that the distribution of the effect, given the cause, belongs to well-known families such as Gaussian, Poisson, Gamma, or heavy-tailed Pareto distributions. These models are adaptable to a wide range of practical situations where the cause can influence the variance or tail behavior of the effect. We demonstrate the identifiability of CPCM by leveraging the concept of sufficient statistics. Furthermore, we propose an algorithm for estimating the causal structure from random samples drawn from CPCM. We evaluate the empirical properties of our methodology on various datasets, demonstrating state-of-the-art performance across multiple benchmarks.