One critical challenge of time-series modeling is how to learn and quickly
correct the model under unknown distribution shifts. In this work, we propose a
principled framework, called LiLY, to first recover time-delayed latent causal
variables and identify their relations from measured temporal data under
different distribution shifts. The correction step is then formulated as
learning the low-dimensional change factors with a few samples from the new
environment, leveraging the identified causal structure. Specifically, the
framework factorizes unknown distribution shifts into transition distribution
changes caused by fixed dynamics and time-varying latent causal relations, and
by global changes in observation. We establish the identifiability theories of
nonparametric latent causal dynamics from their nonlinear mixtures under fixed
dynamics and under changes. Through experiments, we show that time-delayed
latent causal influences are reliably identified from observed variables under
different distribution changes. By exploiting this modular representation of
changes, we can efficiently learn to correct the model under unknown
distribution shifts with only a few samples.

本文提出了一个名为 LiLY 的框架，用于解决时间序列建模中如何在未知分布转换下学习和快速更正模型的问题，该框架首先从不同的分布转移中恢复时间延迟的潜在因果变量并确定它们之间的关系，然后通过利用识别出的因果结构，将更正步骤进行公式化，将未知的分布转移分解为由固定动态和时变的潜在因果关系所引起的过渡分布更改和观察结果的全局更改，并且通过实验证明了潜在因果影响可靠地从不同的分布变化中识别出来，通过利用这种模块化的变化表示，我们只需使用少量样本就可以高效地学习在未知分布转换下更正模型。