This work extends the theory of identifiability in supervised learning by considering the consequences of having access to a distribution of tasks. In such cases, we show that identifiability is achievable even in the case of regression, extending prior work restricted to the single-task classification case. Furthermore, we show that the existence of a task distribution which defines a conditional prior over latent variables reduces the equivalence class for identifiability to permutations and scaling, a much stronger and more useful result. When we further assume a causal structure over these tasks, our approach enables simple maximum marginal likelihood optimization together with downstream applicability to causal representation learning. Empirically, we validate that our model outperforms more general unsupervised models in recovering canonical representations for synthetic and real-world data.

翻译：本文通过考虑任务分布可获得性，将监督学习中的可辨识性理论进行拓展。在此类情形下，我们证明即使是在回归任务中也能实现可辨识性，这突破了先前仅适用于单任务分类场景的研究局限。进一步研究表明，定义隐变量条件先验的任务分布存在性，可将可辨识性的等价类约简至置换与尺度变换——这一结论具有更强的实用价值。当假设这些任务存在因果结构时，我们的方法既能实现简单的最大边际似然优化，又能支持后续的因果表示学习应用。实验证明，在合成数据与真实数据上，本模型在恢复标准表示方面优于更具通用性的无监督模型。