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 linear identifiability in the single-task classification case. Furthermore, we show that the existence of a task distribution which defines a conditional prior over latent factors reduces the equivalence class for identifiability to permutations and scaling, a much stronger and more useful result than linear identifiability. 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 both synthetic and real-world molecular data.

翻译：本文通过考虑访问任务分布所带来的影响，扩展了监督学习中可辨识性理论。在此类情形下，我们证明即使在回归问题中也能实现可辨识性，从而将先前仅适用于单任务分类中线性可辨识性的工作进行了推广。此外，我们表明，定义隐因子条件先验的任务分布的存在，可将可辨识性的等价类缩小至排列与缩放，这比线性可辨识性更为强大且更具实用性。当我们进一步假设这些任务具有因果结构时，所提方法能够实现简单的最大边际似然优化，并适用于下游因果表示学习。实验验证表明，在恢复合成与真实分子数据的规范表示方面，我们的模型优于更通用的无监督模型。