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.
翻译:时间序列建模的关键挑战之一是如何学习并快速纠正分布变化不明的模型。在这项工作中,我们提出了一个原则框架,称为Lily,以首先从不同分布变化的测量时间延迟的潜在因果变数中恢复时间被延迟的潜在因果变数,并从不同分布变化中测量的时间数据中确定它们之间的关系。随后,修正步骤的制定是学习低维变化因子,从新环境中提取少量样本,利用已确定的因果结构。具体地说,该框架将未知的分布变化纳入由固定动态和时间变化的潜在因果关系以及全球观察变化引起的过渡分布变化中。我们在固定动态和变化中从非线性混合物中建立非参数性潜在因果动态和变化的可识别理论。我们通过实验表明,从不同分布变化所观察到的变量中可靠地识别了时间延迟的潜在因果影响。通过利用这种模块形式的变化,我们可以有效地学习如何校正在未知分布变化下的模型,只有少量样本。