🤖 AI Summary
This work addresses the identifiability of causal graphs under mixed discrete/continuous variables and causal effects influencing variance or tail behavior—e.g., heteroscedastic noise or heavy-tailed distributions. We propose the Conditional Parameterized Causal Model (CPCM), which relaxes the conventional additive noise assumption and accommodates flexible distribution families, including Gaussian, Poisson, and Pareto. Crucially, we establish the first rigorous identifiability theory for causal graphs under non-additive noise. Leveraging sufficient statistics, we develop a unified theoretical framework for identifiability proof and design an efficient causal structure learning algorithm. Empirical evaluation across diverse benchmark datasets demonstrates that our method significantly improves causal discovery accuracy in settings with mixed variable types and heteroscedastic noise, achieving state-of-the-art performance.
📝 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.
