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，仍存在某些难以消除的不确定性。不同任务对不同不确定性的容忍度各异，但近期应用表明需要强可识别模型——即观测值对应唯一潜在编码的模型。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，近期工作排除了许多（但并非全部）不确定性。本文首先从任务可识别性角度论证模型可识别性的必要性，继而构建分析潜变量模型不确定性的理论框架，该框架能够依据生成函数与先验分布空间精确刻画不确定性。我们揭示出即使使用高度灵活的非线性生成器，强可识别性依然可能实现，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，建立了最优传输与可识别性之间的新颖联系。