Learning Temporally Causal Latent Processes from General Temporal Data
Weiran Yao†∗ Yuewen Sun‡∗ Alex Ho⋄ Changyin Sun‡ Kun Zhang† †Carnegie Mellon University, Pittsburgh PA, USA ‡Southeast University, Nanjing, China ⋄Rice University, Houston TX, USA ∗ Equal contribution. Code: https://github.com/weirayao/leap
Abstract
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
中文速览
从时序观测数据中恢复潜在因果变量（latent causal variables）的结构，是因果发现领域长期悬而未决的难题，核心障碍在于：当潜变量经过未知的非线性混合后，仅凭观测信号几乎无法唯一还原它们。这项工作分别针对非参数非平稳和参数化两种设定，从理论上证明了两个充分条件——噪声的非平稳性以及独立噪声约束——可保证时延因果潜过程（temporally causal latent processes）的可识别性。在此理论基础上，作者提出了 LEAP 框架，将变分自编码器（VAE）与因果过程先验网络结合，用流模型拟合残差噪声并强制执行独立噪声约束，从而在无监督条件下同时学习潜变量表示及其因果结构。在合成数据、视频和动作捕捉等多类数据集上的实验表明，LEAP 能可靠地还原不同依赖结构下的时延因果潜变量，且显著优于不利用历史信息或非平稳性信息的基线方法，是首批无需稀疏性或最小性假设即可完成此类恢复的工作之一。
原文 arXiv:2110.05428;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2110.05428v4