标题： 基于梯度正则化的神经格兰杰因果关系 显示英文标题

标题： Gradient Regularization-based Neural Granger Causality

摘要： 随着深度学习技术的进步，各种基于神经网络的格兰杰因果关系模型已被提出。 尽管这些模型已表现出显著的改进，但仍存在一些局限性。 大多数现有方法采用逐个组件的架构，需要为每个时间序列构建一个单独的模型，这导致了巨大的计算成本。 此外，对神经网络第一层权重施加稀疏性诱导惩罚以提取因果关系，会削弱模型捕捉复杂交互的能力。 为了解决这些限制，我们提出了基于梯度正则化的神经格兰杰因果关系（GRNGC），它只需要一个时间序列预测模型，并对模型输入和输出之间的梯度应用$L_{1}$正则化以推断格兰杰因果关系。 此外，GRNGC不依赖于特定的时间序列预测模型，可以使用KAN、MLP和LSTM等多样化架构实现，提供了更高的灵活性。 在DREAM、Lorenz-96、fMRI BOLD和CausalTime上的数值模拟表明，GRNGC优于现有基线方法，并显著降低了计算开销。 同时，在真实世界的DNA、酵母、HeLa和膀胱尿路上皮癌数据集上的实验进一步验证了该模型在重构基因调控网络中的有效性。 显示英文摘要

摘要： With the advancement of deep learning technologies, various neural network-based Granger causality models have been proposed. Although these models have demonstrated notable improvements, several limitations remain. Most existing approaches adopt the component-wise architecture, necessitating the construction of a separate model for each time series, which results in substantial computational costs. In addition, imposing the sparsity-inducing penalty on the first-layer weights of the neural network to extract causal relationships weakens the model's ability to capture complex interactions. To address these limitations, we propose Gradient Regularization-based Neural Granger Causality (GRNGC), which requires only one time series prediction model and applies $L_{1}$ regularization to the gradient between model's input and output to infer Granger causality. Moreover, GRNGC is not tied to a specific time series forecasting model and can be implemented with diverse architectures such as KAN, MLP, and LSTM, offering enhanced flexibility. Numerical simulations on DREAM, Lorenz-96, fMRI BOLD, and CausalTime show that GRNGC outperforms existing baselines and significantly reduces computational overhead. Meanwhile, experiments on real-world DNA, Yeast, HeLa, and bladder urothelial carcinoma datasets further validate the model's effectiveness in reconstructing gene regulatory networks.