  Causal discovery, beyond the inference of a network as a collection of
connected dots, offers a crucial functionality in scientific discovery using
artificial intelligence. The questions that arise in multiple domains, such as
physics, physiology, the strategic decision in uncertain environments with
multiple agents, climatology, among many others, have roots in causality and
reasoning. It became apparent that many real-world temporal observations are
nonlinearly related to each other. While the number of observations can be as
high as millions of points, the number of temporal samples can be minimal due
to ethical or practical reasons, leading to the curse-of-dimensionality in
large-scale systems. This paper proposes a novel method using kernel principal
component analysis and pre-images to obtain nonlinear dependencies of
multivariate time-series data. We show that our method outperforms
state-of-the-art causal discovery methods when the observations are restricted
by time and are nonlinearly related. Extensive simulations on both real-world
and synthetic datasets with various topologies are provided to evaluate our
proposed methods.
