Most modern probabilistic generative models, such as the variational autoencoder (VAE), have certain indeterminacies that are unresolvable even with an infinite amount of data. Different tasks tolerate different indeterminacies, however recent applications have indicated the need for strongly identifiable models, in which an observation corresponds to a unique latent code. Progress has been made towards reducing model indeterminacies while maintaining flexibility, and recent work excludes many--but not all--indeterminacies. In this work, we motivate model-identifiability in terms of task-identifiability, then construct a theoretical framework for analyzing the indeterminacies of latent variable models, which enables their precise characterization in terms of the generator function and prior distribution spaces. We reveal that strong identifiability is possible even with highly flexible nonlinear generators, and give two such examples. One is a straightforward modification of iVAE (arXiv:1907.04809 [stat.ML]); the other uses triangular monotonic maps, leading to novel connections between optimal transport and identifiability.

翻译：大多数现代概率生成模型（如变分自编码器VAE）即使拥有无限数据仍存在某些无法消除的不确定性。不同任务对不确定性的容忍度各异，但近期应用表明亟需强可辨识模型——即每个观测值需对应唯一隐编码。尽管在保持灵活性的同时减少模型不确定性的研究已取得进展，近期工作仍未能排除所有不确定性。本文首先从任务可辨识性角度阐述模型可辨识性的动机，随后构建分析潜变量模型不确定性的理论框架，从而能够从生成函数与先验分布空间的角度精确刻画这些不确定性。我们证明即使使用高度灵活的非线性生成器也能实现强可辨识性，并给出两个实例：其一为对iVAE（arXiv:1907.04809 [stat.ML]）的简单改进；其二采用三角单调映射，揭示了最优传输与可辨识性之间的新颖联系。