  Building comprehensive brain connectomes has proved of fundamental importance
in resting-state fMRI (rs-fMRI) analysis. Based on the foundation of brain
network, spatial-temporal-based graph convolutional networks have dramatically
improved the performance of deep learning methods in rs-fMRI time series
classification. However, existing works either pre-define the brain network as
the correlation matrix derived from the raw time series or jointly learn the
connectome and model parameters without any topology constraint. These methods
could suffer from degraded classification performance caused by the deviation
from the intrinsic brain connectivity and lack biological interpretability of
demonstrating the causal structure (i.e., effective connectivity) among brain
regions. Moreover, most existing methods for effective connectivity learning
are unaware of the downstream classification task and cannot sufficiently
exploit useful rs-fMRI label information. To address these issues in an
end-to-end manner, we model the brain network as a directed acyclic graph (DAG)
to discover direct causal connections between brain regions and propose
Spatial-Temporal DAG Convolutional Network (ST-DAGCN) to jointly infer
effective connectivity and classify rs-fMRI time series by learning brain
representations based on nonlinear structural equation model. The optimization
problem is formulated into a continuous program and solved with score-based
learning method via gradient descent. We evaluate ST-DAGCN on two public
rs-fMRI databases. Experiments show that ST-DAGCN outperforms existing models
by evident margins in rs-fMRI classification and simultaneously learns
meaningful edges of effective connectivity that help understand brain activity
patterns and pathological mechanisms in brain disease.
