  Discovering reliable and informative relationships among brain regions from
functional magnetic resonance imaging (fMRI) signals is essential in phenotypic
predictions. Most of the current methods fail to accurately characterize those
interactions because they only focus on pairwise connections and overlook the
high-order relationships of brain regions. We propose that these high-order
relationships should be maximally informative and minimally redundant (MIMR).
However, identifying such high-order relationships is challenging and
under-explored due to the exponential search space and the absence of a
tractable objective. In response to this gap, we propose a novel method named
HYBRID which aims to extract MIMR high-order relationships from fMRI data.
HYBRID employs a CONSTRUCTOR to identify hyperedge structures, and a WEIGHTER
to compute a weight for each hyperedge, which avoids searching in exponential
space. HYBRID achieves the MIMR objective through an innovative information
bottleneck framework named multi-head drop-bottleneck with theoretical
guarantees. Our comprehensive experiments demonstrate the effectiveness of our
model. Our model outperforms the state-of-the-art predictive model by an
average of 11.2%, regarding the quality of hyperedges measured by CPM, a
standard protocol for studying brain connections.
