While the cause and mechanism variability conditions provide a significant advancement in understanding identifiability in non-i.i.d. data, they also have limitations that warrant further exploration.
Assumption of Independence: The current conditions often assume independence between the causal mechanisms and the latent variables. In real-world scenarios, this independence may not hold, leading to challenges in accurately identifying causal structures. Future research could explore relaxing this assumption by allowing for dependencies between mechanisms, potentially through the introduction of latent confounders or shared parameters.
Specificity of Conditions: The conditions are tailored to specific types of data distributions and may not generalize well to all scenarios. For instance, the reliance on exchangeability may limit applicability in cases where data exhibits more complex structures, such as hierarchical or temporal dependencies. Generalizing these conditions to accommodate a broader range of data types, including those with temporal dynamics or hierarchical structures, could enhance their applicability.
Quantitative Measures: The current framework lacks quantitative measures to assess the degree of variability in causal mechanisms or sources. Developing metrics that quantify the extent of variability could provide clearer guidelines for when the conditions are satisfied, thus facilitating practical implementations.
Integration with Other Frameworks: The cause and mechanism variability conditions could be integrated with other frameworks, such as those focusing on robustness or fairness in machine learning. This could lead to a more comprehensive understanding of how to achieve identifiability in diverse settings, potentially allowing for the relaxation of existing conditions.