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# Structure Learning for Groups of Variables in Nonlinear Time-Series Data with Location-Scale Noise

*Proceedings of the 2023 Causal Analysis Workshop Series*, PMLR 223:20-39, 2023.

#### Abstract

Learning causal structures from observational data
has recently attracted considerable
attention.Although many studies have focused on
uncovering the connections between scalar random
variables,estimation algorithms for groups of
variables—particularly for multiple groups of
variables—remain scarce.This paper proposes a
novel differentiable algebraic constraint that can
be used along with existing continuous
optimization-based structure-learning algorithms to
learn the causal relationships among groups of
variables.Considering the complex functional
relationships among variables in real-world
scenarios, we propose a structure-learning algorithm
for nonlinear time-series data with location-scale
noise.Experimental results for synthetic and
real-world data indicate that the proposed group
acyclicity constraint significantly increases the
estimation accuracy for the causal relationship
among the groups of variables and verify the
effectiveness of the proposed structure-learning
algorithm.