Causality-Informed Neural Networks for Regularized Learning in Regression Problems

Neural networks that overlook the underlying causal relationships among observed variables pose significant risks in high-stakes decision-making contexts due to concerns about the robustness and stability of model performance. To tackle this issue, we present a general approach for embedding hierarchical causal structure among observed variables into a neural network to inform its learning. The proposed methodology, termed causality-informed neural network (CINN), exploits hierarchical causal structure learned from observational data as a structurally informed prior to guide the layer-to-layer architectural design of the neural network while maintaining the orientation of causal relationships in the discovered causal graph. The proposed method involves three steps. First, CINN mines causal relationships from observational data via directed acyclic graph (DAG) learning, where causal discovery is recast as a continuous optimization problem to circumvent the combinatorial nature of DAG learning. Second, we encode the discovered hierarchical causal graph among observed variables into a neural network via a dedicated architecture and loss function. By classifying observed variables in the DAG as root, intermediate, and leaf nodes, we translate the hierarchical causal DAG into CINN by creating a one-to-one correspondence between DAG nodes and certain CINN neurons. For the loss function, both intermediate and leaf nodes in the DAG are treated as target outputs during CINN training, facilitating the co-learning of causal relationships among the observed variables. Finally, as multiple loss components emerge in CINN, we leverage the projection of conflicting gradients (PCGrads) to mitigate the gradient interference among the multiple learning tasks. Computational studies indicate that CINN outperforms several state-of-the-art methods across a broad range of datasets. In addition, an ablation study that incrementally incorporates structural and quantitative causal knowledge into the neural network is conducted to highlight the pivotal role of causal knowledge in enhancing neural network’s prediction performance.