Identifiable Latent Polynomial Causal Models Through the Lens of Change

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments (Liu et al., 2022). However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency. Causal representation learning, aiming to discover high-level latent causal variables and causal structures among them from unstructured observed data, provides a prospective way to compensate for drawbacks in traditional machine learning paradigms, e.g., the most fundamental limitations that data, driving and promoting the machine learning methods, needs to be independent and identically distributed (i.i.d.) (Sch olkopf, 2015). From the perspective of causal representations, the changes in data distribution, arising from various real-world data collection pipelines (Karahan et al., 2016; Frumkin, 2016; Pearl et al., 2016; Chandrasekaran et al., 2021), can be attributed to the changes of causal influences among causal variables (Sch olkopf et al., 2021). These changes are observable across a multitude of fields. For instance, these could appear in the analysis of imaging data of cells, where the contexts involve batches of cells exposed to various small-molecule compounds.