Discovering Mixtures of Structural Causal Models from Time Series Data

TL;DR

This paper introduces a variational inference framework called MCD for discovering multiple causal models from heterogeneous time series data, extending causal discovery to more realistic, diverse scenarios.

Contribution

It proposes a novel method to identify and separate different causal models within mixed time series data, including linear and nonlinear cases, with theoretical guarantees.

Findings

Outperforms existing methods on synthetic datasets.

Effective in real-world datasets with heterogeneous causal structures.

Proven identifiability under mild assumptions.

Abstract

Discovering causal relationships from time series data is significant in fields such as finance, climate science, and neuroscience. However, contemporary techniques rely on the simplifying assumption that data originates from the same causal model, while in practice, data is heterogeneous and can stem from different causal models. In this work, we relax this assumption and perform causal discovery from time series data originating from a mixture of causal models. We propose a general variational inference-based framework called MCD to infer the underlying causal models as well as the mixing probability of each sample. Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood. We present two variants: MCD-Linear for linear relationships and independent noise, and MCD-Nonlinear for nonlinear causal relationships and history-dependent noise. We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks through extensive experimentation on synthetic and real-world datasets, particularly when the data emanates from diverse underlying causal graphs. Theoretically, we prove the identifiability of such a model under some mild assumptions.