  Discovering causal relationships between different variables from time series
data has been a long-standing challenge for many domains such as climate
science, finance, and healthcare. Given the complexity of real-world
relationships and the nature of observations in discrete time, causal discovery
methods need to consider non-linear relations between variables, instantaneous
effects and history-dependent noise (the change of noise distribution due to
past actions). However, previous works do not offer a solution addressing all
these problems together. In this paper, we propose a novel causal relationship
learning framework for time-series data, called Rhino, which combines vector
auto-regression, deep learning and variational inference to model non-linear
relationships with instantaneous effects while allowing the noise distribution
to be modulated by historical observations. Theoretically, we prove the
structural identifiability of Rhino. Our empirical results from extensive
synthetic experiments and two real-world benchmarks demonstrate better
discovery performance compared to relevant baselines, with ablation studies
revealing its robustness under model misspecification.
