Hybrids of Constraint-based and Noise-based Algorithms for Causal
  Discovery from Time Series
Charles K. Assaad Daria Bystrova Julyan Arbel Emilie Devijver Eric Gaussier Wilfried Thuiller
Constraint-based and noise-based methods have been proposed to discover
summary causal graphs from observational time series under strong assumptions
which can be violated or impossible to verify in real applications. Recently, a
hybrid method (Assaad et al, 2021) that combines these two approaches, proved
to be robust to assumption violation. However, this method assumes that the
summary causal graph is acyclic, but cycles are common in many applications.
For example, in ecological communities, there may be cyclic relationships
between predator and prey populations, creating feedback loops. Therefore, this
paper presents two new frameworks for hybrids of constraint-based and
noise-based methods that can discover summary causal graphs that may or may not
contain cycles. For each framework, we provide two hybrid algorithms which are
experimentally tested on simulated data, realistic ecological data, and real
data from various applications. Experiments show that our hybrid approaches are
robust and yield good results over most datasets.