2020/10/10 by Feng Xie, Ruichu Cai, Xie, Feng +9
Computer Science · Decision Sciences · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Multi-Criteria Decision Making #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2010.04917
openalex publication_date 2020/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the observed ones may not be the underlying causal variables (e.g., image pixels), but are generated by latent causal variables or confounders that are causally related. To this end, in this paper, we consider Linear, Non-Gaussian Latent variable Models (LiNGLaMs), in which latent confounders are also causally related, and propose a Generalized Independent Noise (GIN) condition to estimate such latent variable graphs. Specifically, for two observed random vectors Y and Z, GIN holds if and only if ω\intercalY and Z are statistically independent, where ω is a parameter vector characterized from the cross-covariance between Y and Z. From the graphical view, roughly speaking, GIN implies that causally earlier latent common causes of variables in Y d-separate Y from Z. Interestingly, we find that the independent noise condition, i.e., if there is no confounder, causes are independent from the error of regressing the effect on the causes, can be seen as a special case of GIN. Moreover, we show that GIN helps locate latent variables and identify their causal structure, including causal directions. We further develop a recursive learning algorithm to achieve these goals. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.