Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required for identifiability and by challenges in applying them to real-world settings. Most current approaches are applicable only to relatively restrictive model classes, such as linear or polynomial models, which limits their flexibility and robustness in practice. One promising approach to this problem seeks to address these issues by leveraging changes in causal influences among latent variables. In this vein we propose a more general and relaxed framework than typically applied, formulated by imposing constraints on the function classes applied. Within this framework, we establish partial identifiability results under weaker conditions, including scenarios where only a subset of causal influences change. We then extend our analysis to a broader class of latent post-nonlinear models. Building on these theoretical insights, we develop a flexible method for learning latent causal representations. We demonstrate the effectiveness of our approach on synthetic and semi-synthetic datasets, and further showcase its applicability in a case study on human motion analysis, a complex real-world domain that also highlights the potential to broaden the practical reach of identifiable CRL models.

翻译：因果表示学习（CRL）旨在揭示观测数据生成背后的因果模型，但现有方法的实际应用仍受限于可辨识性所需的强假设以及将其应用于现实场景所面临的挑战。当前大多数方法仅适用于相对受限的模型类别（如线性或多项式模型），这限制了其实践中的灵活性与鲁棒性。针对该问题，一种有前景的解决路径是通过利用潜变量间因果影响的变化来应对这些局限。基于此思路，我们提出了一个比通常应用更通用且宽松的框架，其通过约束所采用的函数类别来构建。在此框架内，我们在更弱的条件下建立了部分可辨识性结果，包括仅部分因果影响发生变化的情形。随后，我们将分析拓展至更广泛的潜后非线性模型类别。基于这些理论见解，我们开发了一种学习潜因果表示的灵活方法。我们在合成与半合成数据集上验证了所提方法的有效性，并进一步通过人体运动分析案例研究展示了其适用性——这一复杂的现实领域也凸显了可辨识CRL模型拓展实际应用范围的潜力。