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In this paper, we develop a generic methodology to encode hierarchicalcausality structure among observed variables into a neural network in order toimprove its predictive performance. The proposed methodology, calledcausality-informed neural network (CINN), leverages three coherent steps tosystematically map the structural causal knowledge into the layer-to-layerdesign of neural network while strictly preserving the orientation of everycausal relationship. In the first step, CINN discovers causal relationshipsfrom observational data via directed acyclic graph (DAG) learning, where causaldiscovery is recast as a continuous optimization problem to avoid thecombinatorial nature. In the second step, the discovered hierarchical causalitystructure among observed variables is systematically encoded into neuralnetwork through a dedicated architecture and customized loss function. Bycategorizing variables in the causal DAG as root, intermediate, and leaf nodes,the hierarchical causal DAG is translated into CINN with a one-to-onecorrespondence between nodes in the causal DAG and units in the CINN whilemaintaining the relative order among these nodes. Regarding the loss function,both intermediate and leaf nodes in the DAG graph are treated as target outputsduring CINN training so as to drive co-learning of causal relationships amongdifferent types of nodes. As multiple loss components emerge in CINN, weleverage the projection of conflicting gradients to mitigate gradientinterference among the multiple learning tasks. Computational experimentsacross a broad spectrum of UCI data sets demonstrate substantial advantages ofCINN in predictive performance over other state-of-the-art methods. Inaddition, an ablation study underscores the value of integrating structural andquantitative causal knowledge in enhancing the neural network's predictiveperformance incrementally.

Enhancing the Performance of Neural Networks Through Causal Discovery and Integration of Domain Knowledge