Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that extends Variational AutoEncoders (VAEs) by enforcing our conditions through proper constraints in causal process prior. Experimental results on various datasets demonstrate that temporally causal latent processes are reliably identified from observed variables under different dependency structures and that our approach considerably outperforms baselines that do not properly leverage history or nonstationarity information. This demonstrates that using temporal information to learn latent processes from their invertible nonlinear mixtures in an unsupervised manner, for which we believe our work is one of the first, seems promising even without sparsity or minimality assumptions.

翻译：我们的目标是从测量的时间数据中恢复时间延迟的潜在因果变数,并从测量的时间数据中确定其关系。从观察中估计与因果相关的潜在变数特别具有挑战性,因为在最一般的情况下,潜在变数并非独特的可回收性。在这项工作中,我们既考虑非参数性、非静止的设置,也考虑潜在过程的参数设置,并提议两个可辨别的条件,据此可以从非线性混合物中查明时间因果潜在变数。我们提议LEAP,这是一个理论上基于基础的框架,通过在因果关系过程之前的适当限制来实施我们的条件,扩展变异性自动电算器(VAE),从而扩展变异性自动电算器(VAE)。各种数据集的实验结果表明,从不同依赖结构下观察到的变数中可以可靠地识别出时间因果潜在变数过程,而且我们的方法大大超出基线,不能适当地利用历史或非静性信息。这说明,利用时间信息从不可测的非线性混合物中学习潜在过程。我们用时间信息,我们认为我们的工作是第一种,即使没有空间或最小的假设,也似乎有希望。